CN117272776B - Uncertainty CPS modeling and verification method based on decision process - Google Patents

Uncertainty CPS modeling and verification method based on decision process Download PDF

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CN117272776B
CN117272776B CN202310813436.1A CN202310813436A CN117272776B CN 117272776 B CN117272776 B CN 117272776B CN 202310813436 A CN202310813436 A CN 202310813436A CN 117272776 B CN117272776 B CN 117272776B
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CN117272776A (en
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陈娜
耿生玲
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Qinghai Normal University
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    • G06—COMPUTING; CALCULATING OR COUNTING
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Abstract

The application provides an uncertainty CPS modeling and verification method based on a decision process, and belongs to the technical field of information physical fusion. The method comprises the steps of constructing a CPS system model based on a generalized likelihood decision process, and defining CPS grammar and semantics of generalized likelihood linear sequential logic of the model; introducing a clock invariant, and performing expansion modeling on the CPS system model based on a differential equation of time and an uncertainty mixed time automaton to obtain an uncertainty CPS expansion model; based on a likelihood measure theory, grammar and semantics, dynamically verifying the activity and safety attribute of the expansion model, and optimizing the execution path of the expansion model according to a dynamic verification result; and carrying out modeling simulation on the expansion model by using a preset modeling tool, analyzing the CPS dynamic execution process, and refining the dynamic behavior output by the expansion model according to the analysis result. The present application verifies the activity and security attributes of CPS systems, enabling the interior of each state of the system to be described by time-based state refinement.

Description

Uncertainty CPS modeling and verification method based on decision process
Technical Field
The application belongs to the technical field of information physical fusion, and particularly relates to an uncertainty CPS modeling and verification method based on a decision process.
Background
Uncertainty theory is the theoretical basis for building an uncertainty calculation model. Classical computational models mainly refer to classical automata, including finite automata and turing machines. Automaton theory is one of basic theories of computer science, and the application of the automaton theory is mainly embodied in the fields of programming language, network technology, natural language processing, artificial intelligence and the like. The weighted automaton is an uncertain calculation model with wider application, and the theory and application research of the weighted automaton are rich. Uncertainty information can be measured in terms of probabilistic, possible, fuzzy, coarse, etc. measures in uncertainty theory. However, with the development of society, a computing method for dealing with a lot of uncertainties is presented at present, and is operated by a turing machine, especially in recent years, the emerging internet of things is characterized by uncertain computation and uncertain reasoning. This has motivated some researchers to try to use uncertainty calculation models in the field of Cyber-Physical Systems (CPS) research, and also hope to play a role in reliable calculation and real-time intelligent control of information Physical fusion Systems. While uncertainty data management and intelligent computing are the primary problems faced by CPS computing systems.
The modeling technology of the current uncertain CPS can cause uncertainty of system behavior when encountering multiple probability distribution of complex system occurrence, namely, the uncertainty data cannot be processed correctly by the system, and the reliability of a system model is lower. Meanwhile, after modeling is completed, the activity and the safety of CPS are difficult to verify in the prior art, and a dynamic verification analysis means for the uncertainty CPS attribute is lacked.
Disclosure of Invention
Therefore, the method for modeling and verifying the CPS based on the uncertainty of the decision process is beneficial to solving the problems that the uncertainty of a system is generated during CPS modeling, the uncertainty data is difficult to process and the activity and the safety of CPS are difficult to verify in the prior art.
In order to achieve the above purpose, the present application adopts the following technical scheme:
the application provides an uncertainty CPS modeling and verification method based on a decision process, which comprises the following steps:
constructing a CPS system model based on a generalized likelihood decision process, and defining CPS grammar and semantics of generalized likelihood linear sequential logic of the CPS system model;
introducing a clock invariant, and performing expansion modeling on the CPS system model based on a differential equation of time and an uncertainty mixed time automaton to obtain an uncertainty CPS expansion model;
Based on CPS grammar and semantics of a likelihood measure theory and generalized likelihood linear sequential logic, dynamically verifying the activity and safety attribute of the uncertainty CPS expansion model, and optimizing the execution path of the uncertainty CPS expansion model according to a dynamic verification result;
modeling and simulating the uncertainty CPS extension model by using a preset modeling tool, analyzing the CPS dynamic execution process of the uncertainty CPS extension model, and refining the dynamic behavior output by the uncertainty CPS extension model according to the analysis result of the CPS dynamic execution process.
Further, the generalized likelihood decision process builds a CPS system model, and defines CPS grammar and semantics of generalized likelihood linear sequential logic of the CPS system model, specifically including:
a CPS system model is built by taking a generalized likelihood decision process as a system model; the generalized likelihood decision process is specifically a six-tuple m= (S, act, P, I, AP, L), where S is a set of countable non-empty states; act is a set of actions; p is a likelihood transfer function, P: s x Act x T → [0,1], there is one action a e Act for each state S e S, T e T, so that P (S, a, T) > 0; i is a likelihood initial distribution function; AP is a set of atomic propositions; l is a likelihood tag function;
Based on state s, determining a set Paths(s) of infinite path segments starting with state s and a set Paths of finite path segments starting with state s, respectively, in a generalized likelihood decision process fin (s)；
Presetting a strategy of the six-tuple M, and defining the strategy as a function zeta;
based on the atomic proposition set AP, CPS grammar of generalized likelihood linear sequential logic of CPS system model is defined, CPS grammar is shown as follows:
where r is the interval value of the likelihood, r ε [0,1 ]]，a∈AP；
According to the CPS grammar, language semantics and path semantics of generalized likelihood linear sequential logic are respectively defined.
Further, the clock invariants are introduced, and the CPS system model is subjected to expansion modeling based on a differential equation of time and an uncertainty hybrid time automaton to obtain an uncertainty CPS expansion model, which specifically comprises the following steps:
modeling the dynamic behavior of an uncertainty CPS system based on a differential equation of time, and describing the dynamic property of the system;
introducing clock invariants and possibility into the hybrid automaton to obtain an uncertainty hybrid time automaton, and constructing an uncertainty hybrid time automaton system model based on the uncertainty hybrid time automaton;
the uncertainty hybrid time automaton is specifically a nine-tuple H P The following formula is shown:
H P ＝(I,O,T,Init,M con ,{A x |x∈I},{A y |y∈O},A,CI)
wherein I is a set of possible values for the input port; o is the set of all possible values of the output port; t is a state variable set, defining the state set as Q T The method comprises the steps of carrying out a first treatment on the surface of the Init is a likelihood initialization distribution operation defining a set of likelihood initial states [ Init]≤Q T ；M con Is a set of control modes; a is the set of internal actions; CI isA clock invariant;
and combining an uncertainty CPS system dynamic behavior modeling result and an uncertainty hybrid time automaton system model to obtain an uncertainty CPS extension model.
Further, the dynamic verification of the activity and the security attribute of the uncertainty CPS extension model based on the CPS grammar and the semantics of the likelihood measure theory and the generalized likelihood linear sequential logic, and the optimization of the execution path of the uncertainty CPS extension model according to the dynamic verification result specifically comprises the following steps:
describing the activity of the uncertainty CPS expansion model between state labels in the expression execution process by utilizing CPS grammar and semantics of generalized likelihood linear sequential logic; the activities include final reachability, total reachability, repeated reachability, and persistent reachability;
based on the likelihood measure, calculating the likelihood that the execution path with the policy in the uncertainty CPS extension model satisfies the final reachability, always reachability, duplicate reachability, and persistent reachability of the CPS grammar and semantic depiction description of the generalized likelihood linear sequential logic, the process specifically comprising:
The generalized likelihood measure that the calculation model satisfies the final reachability is expressed as:
the computational model satisfies a generalized likelihood measure of always reachability expressed as:
the computing system satisfies a generalized likelihood measure of repeat reachability expressed as:
the generalized likelihood measure that a computing system meets the persistent reachability is expressed as:
wherein Po ζ A generalized likelihood measure representing an uncertainty system model Q; s is a set of countable non-empty states, S representing a state of the uncertainty CPS system; pi represents the dynamic execution trace of the uncertainty CPS system; i and j represent two positions in the execution path with the policy, respectively; s is(s) i Sum s j Respectively representing an ith state and a jth state in an execution path with a policy in an uncertainty CPS system; ζ -Path represents the execution Path with policy; b represents final reachability; and ∈b represents always reachability; b represents repeat reachability; and ∈b represents persistent reachability;
fuzzy canonical security attribute P defining an uncertainty CPS extension model safe Calculating fuzzy canonical security attribute P based on likelihood measure theory safe Is used for judging the fuzzy regular safety attribute P safe If any infinite string sigma contains a bad prefix, the regular security attribute P is obscured safe Is unsafe, and optimizes the unsatisfactory behaviors of the uncertain CPS extension model; if the prefix does not contain bad, the regular security attribute P is obscured safe Is safe.
Further, the preset modeling tool is specifically a Ptolemy II simulation modeling tool.
Further, the refinement of the dynamic behavior of the output of the uncertainty CPS extension model is specifically as follows: the dynamic behavior of the uncertainty CPS extension model output is taken as a function of the dynamic behavior of the next input.
The application adopts the technical scheme, possesses following beneficial effect at least:
by the method for modeling and verifying the uncertainty CPS based on the decision process, the CPS system model is built based on the generalized likelihood decision process, and CPS grammar and semantics of generalized likelihood linear sequential logic of the CPS system model are defined; introducing a clock invariant, and performing expansion modeling on the CPS system model based on a differential equation of time and an uncertainty mixed time automaton to obtain an uncertainty CPS expansion model; based on CPS grammar and semantics of a likelihood measure theory and generalized likelihood linear sequential logic, dynamically verifying the activity and safety attribute of the uncertainty CPS expansion model, and optimizing the execution path of the uncertainty CPS expansion model according to a dynamic verification result; modeling and simulating the uncertainty CPS extension model by using a preset modeling tool, analyzing the CPS dynamic execution process of the uncertainty CPS extension model, and refining the dynamic behavior output by the uncertainty CPS extension model according to the analysis result of the CPS dynamic execution process. The method introduces and describes the uncertainty CPS behavior, makes a decision on the uncertainty selection through a strategy, defines CPS grammar and semantics of generalized likelihood linear sequential logic with a decision process, verifies the activity and safety attribute of the system through a likelihood measure theory, and finally models and simulates the CPS system, so that continuous time models can be effectively informationized and discretized, and discrete event models can be physically and continuously processed. At this point, the present application describes the dynamic continuity of the system by time-based differential equations and the modeling of the uncertainty hybrid system by time-based state machines, enabling each state interior to be described by time-based state refinement.
It is to be understood that both the foregoing general description and the following detailed description are exemplary and explanatory only and are not restrictive of the application.
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In order to more clearly illustrate the embodiments of the present application or the technical solutions in the prior art, the drawings used in the description of the embodiments or the prior art will be briefly described below.
FIG. 1 is a flow chart of a method for modeling and verifying uncertainty CPS based on a decision process according to the present embodiment of the invention;
fig. 2 is a diagram of the structure of an existing CPS system provided in the present embodiment;
FIG. 3 is a schematic view of a GPDP with 3 states provided in this embodiment;
FIG. 4 is a schematic view of a GPDP with policies provided in this embodiment;
FIG. 5 is a diagram showing an example of a model of a thermostatic control system according to the present embodiment;
FIG. 6 is a schematic diagram of an uncertainty CPS thermostat model modeling process provided by the present embodiment;
FIG. 7 is a schematic diagram of the execution results of the uncertainty CPS thermostat model temperature over time provided in this embodiment;
fig. 8 is a schematic diagram of the execution result of the time-varying rate of the uncertainty CPS thermostat model provided in the present embodiment.
Detailed Description
For the purpose of making the objects, technical solutions and advantages of the present application more apparent, the technical solutions of the present application will be described in detail below.
The information physical fusion system is composed of mutually communicated computing devices, realizes man-machine interaction through physical processes and computing processes, and is an intelligent technology integrating computing, communication and control (3C) in functions, as shown in fig. 2. The students at home and abroad develop some related researches and make some research progress in theory and technology, and mainly analyze and propose some feasible solutions in CPS calculation, network and control system. Uncertainty data management and intelligent computing are the primary problems faced by CPS computing systems. In the current CPS related problem research, how to correctly and comprehensively know and understand the physical world, realize the autonomous coordination of the system, improve the real-time performance and reliability of the system, and need to correctly process uncertainty data, fuse multi-mode information, and inquire, analyze and mine data and state information. The theory and technology of modeling and attribute verification of the uncertainty CPS are research hotspots of domestic and foreign scholars, and still face the aspects of modeling, management, optimization decision control and the like at present.
In order to model information systems with uncertainty, a number of quantitative model checking techniques have been proposed, but some important problems remain unsolved. This is manifested by uncertainty in the behavior of the system when multiple likelihood distributions of the complex system occurrences are encountered. However, sometimes such a possible distribution is not available, the purpose of modeling is to meet the characteristics of the system through an interface of the uncertainty action with the environment.
Thus, uncertainty in behavior is necessary, and considering information of uncertainty, the present invention introduces the generalized likelihood decision process (GPDP) concept, which proposes a scheduler to select an operation to be performed. It allows both possible and uncertain selection. The purpose of GPDP is to enable transitions between states to meet a variety of possible distributions. Provides a good theoretical basis for uncertainty verification of a complex system.
In the system modeling and simulation tools, common CPS software modeling methods mainly comprise a Simulink/Stateflow and UML model-driven software development methods, and the modeling methods have certain sealing performance and still face challenges in aspects of uncertainty modeling, management, optimization decision control and the like at present. Ptolemy II is an open source and simulated modeling tool for experiments on system designs, particularly those involving various model combinations. It was developed by researchers at UC Berkeley with system design, modeling and simulation of hierarchical, heterogeneous systems. The whole development stage of Ptolemy II is supported by a design environment, so that the conversion from a conceptual model to a real system design can shorten the design link, improve the reusability of components and keep the authenticity of the system consistent with a simulation result. Therefore, the present application proposes a decision process-based uncertainty CPS modeling and verification method to solve the above-mentioned problems of the prior art. The detailed implementation of the invention is described in the following examples.
Referring to fig. 1, fig. 1 is a flowchart of an uncertainty CPS modeling and verification method based on a decision process according to the present embodiment of the invention. As shown in fig. 1, the method includes:
s1: constructing a CPS system model based on a generalized likelihood decision process, and defining CPS grammar and semantics of generalized likelihood linear sequential logic of the CPS system model;
s2: introducing a clock invariant, and performing expansion modeling on the CPS system model based on a differential equation of time and an uncertainty mixed time automaton to obtain an uncertainty CPS expansion model;
s3: based on CPS grammar and semantics of a likelihood measure theory and generalized likelihood linear sequential logic, dynamically verifying the activity and safety attribute of the uncertainty CPS expansion model, and optimizing the execution path of the uncertainty CPS expansion model according to a dynamic verification result;
s4: modeling and simulating the uncertainty CPS extension model by using a preset modeling tool, analyzing the CPS dynamic execution process of the uncertainty CPS extension model, and refining the dynamic behavior output by the uncertainty CPS extension model according to the analysis result of the CPS dynamic execution process.
The generalized likelihood decision process (i.e., GPDP) differs from the markov decision process in that: (1) The transition weight of the Markov decision process reflects the frequency of occurrence of the event, and the transition weight of the generalized likelihood decision process feeds back the likelihood of reaching the target state; (2) In the Markov decision process, the sum of transition weights starting from the same state is 1, and the generalized likelihood decision process has no constraint condition; (3) The label function in the markov decision process is explicit, while the label function in the generalized likelihood decision process is ambiguous. Thus, the present application regards the generalized likelihood decision process as a model of an uncertainty system.
Further, in this embodiment, a CPS system model is constructed based on a generalized likelihood decision process, and CPS syntax and semantics of generalized likelihood linear sequential logic of the CPS system model are defined, specifically including:
and constructing a CPS system model by taking a generalized likelihood decision process as a system model. Wherein the generalized likelihood decision process is specifically a six-tuple m= (S, act, P, I, AP, L), wherein,
s is a set of countable non-empty states;
act is a set of actions;
p is a likelihood transfer function, P: s x Act x T → [0,1], there is one action a e Act for each state S e S, T e T, so that P (S, a, T) >0;
(1) I is a likelihood initial distribution function, I S.fwdarw.0, 1 is a likelihood initial distribution function, s.epsilon.S exists, so that I (S) >0;
AP is a set of atomic propositions;
l is a likelihood tag function, L is S.times.AP.. Fwdarw.0, 1 is a likelihood tag function, and L (S, a) represents the true value that atomic proposition a holds on state S.
An action alpha is enabled, if and only if t∈S P(s,α,t)>At 0, let Act(s) = { α∈act| v. t∈S P(s,α,t)>0}. For arbitrary states s.epsilon.S, requirementsWherein P (s, alpha, t)>Each state t of 0 is referred to as α successor of s.
Furthermore, the likelihood transfer function P: S.times.Act.times.S.fwdarw.0, 1]It may also be represented by a fuzzy matrix. For convenience, this fuzzy matrix is also written as P, i.e., P α (s,t)＝(P(s,α,t)) s,t∈S 。P α The fuzzy likelihood α -transfer matrix, also known as M.
In a specific practical process, as shown in fig. 3, the embodiment provides a GPDP m= (S, act, P, I, AP, L) with 3 states, where a circle represents a state, a symbol outside the circle represents a state name, a symbol inside the circle represents a true value of an atomic proposition on the state, a labeled arc represents a transition, and a circle with an input arrow represents an initial state.
Referring to fig. 3, the state space s= { S of GPDP M 0 ,s 1 ,s 2 }；
The set act= { α, β };
the set of atomic propositions ap= { a, B };
initial state distribution I(s) 0 )＝1,I(s 1 )＝I(s 2 )＝0；
Tag function L(s) 0 ,A)＝0.6,L(s 0 ,B)＝0.3,L(s 1 ,A)＝0.8,L(s 2 ,B)＝0.4；
For Act(s) 0 ) = { α, β }, and P(s) 0 ,α,s 1 )＝0.7,P(s 0 ,β,s 2 )＝0.4；
For Act(s) 1 ) = { α, β }, and P(s) 1 ,α,s 1 )＝1,P(s 1 ,β,s 0 )＝0.6，P(s 1 ,β,s 2 )＝0.3；
For Act(s) 2 ) = { α, β }, and P(s) 2 ,β,s 2 )＝0.8,P(s 2 ,α,s 0 )＝0.5，P(s 2 ,α,s 1 )＝0.7；
For state s 0 ,Post(s 0 ,α)＝{s 1 },Post(s 0 ,β)＝{s 2 },Pref(s 0 )＝{(s 1 ,β),(s 2 ,α)}。
Use state order s 0 <s 1 <s 2 <s 3 The matrix P and vector I are given:
further, based on the state s, a set Paths(s) of infinite path segments starting with the state s and a set Paths of finite path segments starting with the state s in the generalized likelihood decision process are determined, respectively fin (s). Specifically, in GPDP M, an infinite path segment is an infinite sequence s 0 α 1 s 1 α 2 s 2 α 3 …∈(S×Act) ω The method is characterized by comprising the following steps:
for all i.gtoreq.0, so that P(s) i ,α i+1 ,s i+1 )>0. Any pi finite prefix ending in a state is a finite path segment. Paths(s) represents a set of infinite path segments starting with state s; pathsfin(s) denotes open in state sA set of initial finite path segments. Is provided withAndreasoning about the GPDP path set possibilities depends on the decision of uncertainty. This decision scheme is performed by a policy program (scheduler). Once a is selected, it does not impose any constraint on the choice of possibilities.
Specifically, the policy of the six-tuple M is preset, and the policy is defined as a function ζ, such that m= (S, act, P, I, AP, L) is a GPDP, and the policy of a GPDP M is defined as a function ζ: S + Act such that for each state sequence s 0 s 1 …s n ∈s + All have zeta(s) 0 s 1 …s n )∈Act(s n ) (here, s + Representing the set of all non-empty finite strings on the state space s). For all i>0, if alpha i ＝ζ(s 0 …s i-1 ) Then call the path (segment)The Path (fragment) with the policy is denoted as ζ -Path.
In addition, it is also possible to set M to be a GPDP with a state space S. For each state sequence s 0 s 1 …s n ∈s + And t 0 t 1 …t m ∈s + And s is 0 ＝t m All have zeta(s) 0 s 1 …s n )＝ζ(t 0 t 1 …t m ) Then the policy ζ on M is called a memoryless policy.
In this case ζ can be seen as a function: s→act. In other words, if policy program ζ always simply selects an alternate state (i.e., action) and ignores all other states, then the policy is memoryless.
Referring to FIG. 4, policy ζ α Always select a motion in state sAs alpha, policy ζ β The action beta in state s is always selected.
The only path with alpha action in M, i.e. ζ α-path :PathIs a path with an action beta, denoted as zeta β-path . Thus, when s n When=t, ζ (s 0 …s n s) =α, i.e., ζ(s) =α. Otherwise, when s n When=u, ζ (s 0 …s n s) =β. Note that the policy makes the decision based on the state of the last access. In states u and t, the only enabling action γ is selected. GPDP +.>Is an infinite string:
in GPDP M, a functionζ-Paths(M)→[0,1]The definition is as follows:
for any pi=s 0 α 1 s 1 α 2 …∈ζ-Paths(M)。So thatThus the execution sequence is +.>Is marked as
Further, for any ofThe present embodiment defines:then->2 ζ-Poths(M) →[0,1]For Ω=2 ζ-Paths A generalized likelihood measure on the model.
Specifically, the embodiment defines the CPS grammar of the generalized likelihood linear sequential logic of the CPS system model based on the atomic proposition set AP, and the CPS grammar is shown in the following formula:
where r is the interval value of the likelihood, r ε [0,1 ] ]，a∈AP；
The uncertainty CPS system model is set as Q, pi is an execution track of the model Q,describing a formula for attributes, thenExecution trace representing Q satisfies attribute +.>Possibility that its semantic meaning on Q is Paths (Q), i.e. +.>Paths(Q)→[0，1]. Pi represents an infinite path, pi e Paths (Q), i.e., pi=s 0 s 1 s 2 …. By pi j Indicating that from step jSuffix of the start trace, i.e. pi j ＝s j s j+1 The value of step j of the … variable y in pi is expressed as v= (pi, j, y).
Under GPDP conditions, the semantics of the GPoLTL formula relate to policies, uncertainty information, and fuzzy logic on the set of atomic propositions APs. The semantics of GPoLTL, i.e. speech semantics and path semantics, are given below in terms of CPS syntax.
Language semantics of uncertainty CPS: order theIs a GPoLTL formula. />In the alphabet Σ= [0,1 ]] AP The language semantics on this are a fuzzy omega-language, i.e./a language>∑ ω →[0,1]The iteration is defined as follows:
||r||(σ)＝r；
||a||(σ)＝A 0 (a)；
for σ=a 0 A 1 …∈∑ ω It is a collection of infinite strings on Σ, denoted as σ j ＝A j A j+1 …。
GPoLTL path semantics with policy: for a GPDP M, a εAP, ζ is defined in M. In considering an uncertain decision scheme, for an atomic proposition r, a, its path semantics over M is an fuzzy set over Paths (M), i.e.,Paths(M)→[0,1]，
for any path pi on M, the following is defined:
||r||(π)＝r；
||a||(π)＝L(s 0 ,a).
For path formulasIts semantics are policy dependent, its path semantics on M are +.>ζ-Paths(M)→[0,1]For->The recursion is defined as follows:
the uiil operator can generally derive the temporal tense o and ≡,(here true=1). Wherein, o is an eventuality operator, which indicates that in future time; and ∈i.e. the always operator, representing from now to forever.
Since r is each r.epsilon.0, 1]GPoLTL formula of (2) using the conjunction ∈andObtain fuzzy proposition logic 11]Is a whole power set of (c). GPoLTL is based on fuzzy logic on the atomic proposition set AP. In fact, the GPoLTL equation represents the blurry nature of the GPDP path.
In the uncertainty CPS system model Q, the infinite path is represented as pi=s 0 s 1 s 2 …∈S ω The method comprises the steps of carrying out a first treatment on the surface of the The finite path is expressed as pi=s 0 s 1 ...s n (n.epsilon.N). Representing the set of infinite Paths in Q by Paths (Q), paths fin (Q) represents a set of finite paths.
For a GPDP without terminals, i.e. for any state s, there is a state t such that P (s, t)>0. Infinite path segment pi=s 0 α 0 s 1 α 1 The trace of … is defined as: trace (pi) =l(s) 0 )L(s 1 ) …. For convenience we also use the trace where L (pi) represents pi. Finite path segmentIs defined as +.>
Execution begins with an initial state and may be used to validate the system model. At each step of execution, one of the enabled tasks in the current state is selected and only one task can be executed, the order of execution of which is ambiguous. The dynamic execution trace pi of the uncertainty CPS system can be expressed as a finite or infinite sequence: Wherein s is k ＝<p k ,v k >Representing the state of the system, p k Indicating the control mode in which the system is located, v k Representing the current variable value of the system. l (L) k Indicating that the system is in state s i Residence time.
Let P be a fuzzy linear time property on the AP and M be a finite GPDP without termination state. The likelihood that M satisfies P in state s is defined as:
CPS is a complex embedded network system that fuses physical entities, computational entities, and interactive entities together. In addition, the motion process in the physical world is modeled by dynamic continuity of time, while computing system behavior in the world models event-driven discrete processes using finite state machine diagrams. The CPS system is modeled and simulated by adopting the uncertainty hybrid time automaton, so that the continuous time model can be effectively informationized and discretized, and the discrete event model can be physically and continuously physical and chemical.
Further, in this embodiment, clock invariants are introduced, and an uncertainty CPS system model is subjected to expansion modeling based on a differential equation of time and an uncertainty hybrid time automaton to obtain an uncertainty CPS expansion model, which specifically includes:
modeling the dynamic behavior of an uncertainty CPS system based on a differential equation of time, and describing the dynamic property of the system;
Introducing clock invariants and possibility into the hybrid automaton to obtain an uncertainty hybrid time automaton, and constructing an uncertainty hybrid time automaton system model based on the uncertainty hybrid time automaton;
the uncertainty hybrid time automaton is specifically a nine-tuple H P The following formula is shown:
H P ＝(I,O,T,Init,M con ,{A x |x∈I},{A y |y∈O},A,CI)
wherein I is a set of possible values for the input port; o is the set of all possible values of the output port; t is a state variable set, defining the state set as Q T The method comprises the steps of carrying out a first treatment on the surface of the Init is a likelihood initialization distribution operation defining a set of likelihood initial states [ Init]≤Q T ；M con Is a set of control modes; a is the set of internal actions; CI is a clock invariant;
and combining an uncertainty CPS system dynamic behavior modeling result and an uncertainty hybrid time automaton system model to obtain an uncertainty CPS extension model.
In an implementation, time-based differential equation modeling is first performed. In an uncertainty CPS system, the state of a physical entity has a clear dynamic continuity, and the dynamic transition of the state is based on continuous time. Taking the thermostat state model as an example, the dynamic behavior of the uncertainty CPS system is modeled as follows based on the differential equation of time:
In formula (1), the temperature variable T is a continuous time variable describing the dynamics of the system, noting that this dynamics is linear, where k 1 Is a constant; formula (2) describes the dynamics of temperature variation, where k 2 Is a constant.
Then, modeling is performed based on the uncertainty hybrid time automaton. Because of the uncertainty in the environment in which the CPS system is located, these uncertainties have a critical effect on whether CPS can function properly to some extent. The components in CPS are not completely isolated, but are mutually coupled, and the software and hardware in the traditional embedded control system are highly fused, but have sealing performance, so that the CPS cannot be modeled by a single modeling method using the embedded control system. Therefore, the invention introduces clock invariants and possibilities into the classical hybrid automaton and defines an uncertainty hybrid time automaton system model.
Wherein, uncertainty hybrid time automaton H P Represented as nine tuples
H P ＝(I,O,T,Init,M con ,{A x |x∈I},{A y Y e O, a, CI) wherein:
(1) I is a set of possible values of the input port, and is an input set of xv, wherein x is E I, and one value of x is v;
(2) O is the set of all possible values of the output port, shaped as x-! v, wherein y e O, one value of y is v;
(3) T is a state variable set, defining the state set as Q T ；
(4) Init is a likelihood initialization distribution operation defining a set of likelihood initial states [ Init]≤Q T ；
(5)M con Is a set of control modes;
(6){A x i x ε I, for each input port x, input task set A x Each input task is defined by a guard condition on T and from a read set T { x } to a write set T withThe updating of the set of formal input actions, i.e. +.>
(7){A y I y ε O, for each output port y, output the set of tasks A y Is read from the set T U by the guard condition on T{ y } defines a write set T withUpdate description of the set of formal output actions, i.e
(8) A is the set of internal actions. That is, each internal action is updated by a guard condition on T and from read set T to write set T, withOutput actions in the form of descriptions;
(9) CI is a clock invariant. It is a boolean expression on a state variable T given a state T and a real value time delta>0, if the state t+delta satisfies the expression CI for all values 0.ltoreq.t'.ltoreq.delta, thenIs a time action.
For a reactive CPS system, not only the input and output of the computation and fairness issues are relied upon, but the correctness is dependent on the execution of the system. Sequential logic is a very efficient formalization method of handling these aspects, which extends proposition or predicate logic by allowing patterns of infinite behavior that are referenced to a feedback uncertainty CPS system. Mathematically, however, they provide a very intuitive, accurate representation of the nature of the relationships between the state labels in relation to the expression execution. For example, LT (sequential logic) attribute.
Further, in this embodiment, based on the CPS grammar and semantics of the likelihood measure theory and the generalized likelihood linear sequential logic, dynamically verifying the activity and the security attribute of the uncertainty CPS extension model, and optimizing the execution path of the uncertainty CPS extension model according to the dynamic verification result specifically includes:
describing the activity of the uncertainty CPS expansion model between state labels in the expression execution process by utilizing CPS grammar and semantics of generalized likelihood linear sequential logic; the activities include final reachability, total reachability, repeated reachability, and persistent reachability;
based on the likelihood measure, calculating the likelihood that the execution path with the policy in the uncertainty CPS extension model satisfies the final reachability, always reachability, duplicate reachability, and persistent reachability of the CPS grammar and semantic depiction description of the generalized likelihood linear sequential logic, the process specifically comprising:
the generalized likelihood measure that the calculation model satisfies the final reachability is expressed as:
the computational model satisfies a generalized likelihood measure of always reachability expressed as:
the computing system satisfies a generalized likelihood measure of repeat reachability expressed as:
the generalized likelihood measure that a computing system meets the persistent reachability is expressed as:
Wherein Po ζ A generalized likelihood measure representing an uncertainty system model Q; s is a set of countable non-empty states, S representing a state of the uncertainty CPS system; pi represents the dynamic execution trace of the uncertainty CPS system; i and j represent two positions in the execution path with the policy, respectively; s is(s) i Sum s j Respectively expressed in an uncertainty CPS systemAn ith state and a jth state in the execution path with the policy; ζ -Path represents the execution Path with policy; b represents final reachability; and ∈b represents always reachability; b represents repeat reachability; and ∈b represents persistent reachability;
fuzzy canonical security attribute P defining an uncertainty CPS extension model safe Calculating fuzzy canonical security attribute P based on likelihood measure theory safe Is used for judging the fuzzy regular safety attribute P safe If any infinite string sigma contains a bad prefix, the regular security attribute P is obscured safe Is unsafe, and optimizes the unsatisfactory behaviors of the uncertain CPS extension model; if the prefix does not contain bad, the regular security attribute P is obscured safe Is safe.
Specifically, during operation of an uncertainty CPS, activity means that "good things eventually occur". If an attribute satisfies the activity, it is checked whether a model satisfies the property described by the sequential logic. The present invention is described using generalized likelihood linear sequential logic (GPoLTL). By definition, 4 different types of activity can be obtained: final reachability (eventually reachability); always reachability (always reachability); repeat reachability (repeated reachability); persistent reachability (persistence reachability).
Wherein, 1, evetually operator is denoted by symbol o. The nested application of the eventully operator can be used to require a sequence of events in a particular order. When a certain assignment on a path satisfiesThis path satisfies the GPoLTL equation +.>For example, when path pi= (x 1 ,y 1 )(x 2 ,y 2 ) .. when a certain assignment in (x=y) satisfies the expression (i.e. for some j, x j ＝y j ) Then the path pi isSatisfying GPoLTL formula (x=y). Thus, the equation o (x=y) represents the demand: eventually, at some step, the values of variables x and y are equal.
2. Always operator, denoted by the symbol ≡. When all the assignments on a path satisfyWhen this path satisfies the GPoLTL formula +.>For example, if path pi= (x 1 ,y 1 )(x 2 ,y 2 ) .. each assignment on a table satisfies the expression (x=y) (i.e., x for each j j ＝y j ) Then the path satisfies the PoLTL formula ≡ (x=y). Thus, the formula ∈ρ (x=y) indicates the requirement that the variables x and y should always be equal.
3. Always-eventualy formulaIf->Every position i on the path is satisfied, there is a future position j.gtoreq.i for every position i, and there is a position j 1 <j 2 <j 3 .. an infinite sequence such that ∈ ->Each of these positions is satisfied. In other words, if- >Satisfied in a recursive or repetitive manner, +.o. For example, path pi= (x) 1 ,y 1 )(x 2 ,y 2 ) .. the recursive formula ∈o (x=0) is satisfied when x for an infinite number of positions j, x j When=0, this means that the requirement repeatedly assigns 0 to x.
4. Eventully-always formulaIf there is a position j such that the always formula +.>Satisfying, i.e. satisfying +.every position after j>Then->Then this is satisfied. In other words, the requirement is the formula +.>Eventually satisfying and continuing to hold in a sustained manner. For example, path pi= (x) 1 ,y 1 )(x 2 ,y 2 ) .. when for a certain position j, each k is ≡j, there is x k When =0 (or if not equal to 0 at a limited number of positions), the persistence formula o is satisfied (x=0).
The uncertainty CPS is a system for sensing and controlling a feedback loop, which realizes control of physical equipment on the basis of environmental awareness, thus the loop reciprocates. Each program in the system will enter its critical part an infinite number of times, here denoted system s i Form execution trace pi, i.e. a finite or infinite sequence:such a system should continue to run, guaranteeing system activity, with the primary problem being that the computing system meets the measure of the path arrival state set B.
Let Q be the uncertainty CPS system model, satisfy the properties(/>Is a GPoLTL formula) whose generalized likelihood measure is expressed as +.>And-> Is a set of states in the uncertainty CPS system model.
The reachability analysis using GPDP Q as a system model calculates the likelihood of reaching state set B, where state set B represents the likelihood of rarely accessing a bad state set or multiple accesses to a good state set, represented by mapping function B.S.fwdarw.0, 1.
Then B, +b can be considered as the fuzzy linearity property over the state set S. The definition mode is as follows:
wherein pi=s 0 s 1 …∈s ω 。
Given a GPDP and fuzzy linearity property P (i.e., activity), calculate the likelihood that the path with policy satisfies P. The present embodiment contemplates four properties, final reachability, total reachability, duplicate reachability, and persistent reachability, respectively.
Specifically, the present embodiment provides a procedure for verifying final reachability, always reachability, repeated reachability, and persistent reachability, which is specifically as follows:
1. generalized likelihood measure for system to meet final reachability
The generalized likelihood measure that the uncertainty system model Q satisfies O B is expressed as:
2. generalized likelihood measure for system satisfaction of always reachability
The generalized likelihood measure that the uncertainty system model Q satisfies ≡b is expressed as:
3. generalized likelihood measure for satisfying repeat reachability by system
The generalized likelihood measure that the uncertainty system model Q satisfies ∈b is expressed as:
4. generalized likelihood measure of persistent reachability satisfied by system
The generalized likelihood measure that uncertainty system model Q satisfies o≡b is expressed as:
specifically, for security verification of a model, the embodiment uses generalized likelihood measure of fuzzy canonical security to perform security verification. The security requirement asserts that "bad things do not occur". For security requirements, unsatisfactory behaviour can be analyzed by using limited execution to prove if the requirement is violated. In the classical case, the security attribute may be defined as: if LT attribute P safe If any infinite string σ does not contain a bad prefix, then such LT property is called secure, i.e., σ ε P safe . In general, we formalize this as follows.
Let P be safe Is a fuzzy LT attribute if P is chosen for all σ safe Are all sigma-present in a finite prefixSo that
Establishment of the fuzzy language Σ * →[0,1]P is then safe Is safe. Arbitrary finite string- >Are all referred to as P safe Is a good prefix of (a).
Set H P ＝(I,O,T,Init,M,{A x |x∈I},{A y Y e O, a, CI) is an uncertainty hybrid temporal automaton, n= (Q, Σ, δ, J, F) is a fuzzy finite automaton.
Tensor product
Wherein for any (M, Q) ∈m×q, a' (M, Q) = (M, Q),
the transfer probability of (C) is distributed as P' safe ((m,q),(m′,q′))＝P safe (m,m′)∧δ(q,A(m′),q′)
Let P be safe Is a fuzzy canonical security attribute such that Pref (P safe ) Can be accepted by a deterministic fuzzy finite automaton. H P Represents an uncertainty hybrid time automaton, m is H P In the above, there is,
wherein the method comprises the steps of
Represents, for any (M, Q) ∈m×q, B (M, Q) =f (Q)
And (3) proving:
for any j.gtoreq.0, pi=m 0 m 1 …(m 0 =m), wherein the state sequence q 0 q 1 … by q j+1 ＝δ(q j ,A(m j ) Defined by the above-mentioned method). On the other hand, likewise the state sequence q 0 q 1 … is provided with a function of,
thus, the first and second substrates are bonded together,the syndrome is known.
Specifically, the preset modeling tool is specifically a Ptolemy II simulation modeling tool. The CPS modeling analysis is carried out by taking a constant temperature control system as an example in the embodiment, and the process is specifically as follows:
1. and constructing an uncertainty hybrid time automaton model. The thermostatic control system is an automatically adjustable system involving heating and ventilation, and is a typical feedback control system in CPS, as shown in FIG. 5. Assuming the output of the thermostat model process is temperature, then the formalized model corresponding to the uncertainty hybrid time automaton is:
(1) It has no input variables;
(2) It contains an output variable T of the cont type (this type of variable can vary continuously over time);
(3) It contains an enumerated discrete state variable M con ,M con ＝{cooling, heating) and a state variable T of cont type;
(4) Variable M con The initial value of the possibility of T is any one value of 30 ℃ to 40 ℃;
(5) It does not output a task, that is to say does not transmit the value of the temperature in discrete actions;
(6) It has two internal tasks corresponding to two mode switches: one task is a guard condition (M con =cooling ∈T+.ltoreq.32℃) and updating M con The =heating; another task is a guard condition (M con =wearing ∈T+.gtoreq.38deg.C) and updating M con :＝cooling；
(7) An expression defining the value of the output variable T is equal to the state variable T;
(8) The expression defining the derivative of the state variable T is: if (M) con ＝cooling)then-k 2 else k 1 (40℃-T)
(9) The expression of the continuous time invariant CI is: [ (M) con ＝cooling)→(T≥30℃)]∧[(M con ＝heating)→(T≤40℃)]。
There are two modes of such a thermostat: if M con When=heating, the heater is turned on; if M con At=cooling, the heater operation is stopped. When the mode is heating, according to differential equationFor a given initial value of temperature, there is a unique response signal that captures how the temperature changes over time. The constraint associated with this mode (T.ltoreq.40℃ C.) states that the process can stay in this mode only if this constraint is met: the mode must be switched to mode cooling before this constraint is violated. The condition (T.gtoreq.38 ℃) ensures that the mode is switched to cooling. That is, when the temperature exceeds 38 ℃, the mode switching occurs at any time.
In mode cooling, the differential equation isThus, the temperature decreases linearly with time when the thermostat is in the cooling mode. Constraints associated with mode cooling (T.gtoreq.30℃ C.) indicate that the process must switch to mode heating when the temperature falls below 30 ℃ and guard conditions (T.gtoreq.32℃ C.) associated with switching from cooling to heating indicate that mode switching can occur whenever the temperature falls below 32 ℃. It is noted that the system temperature varies between 30 deg.c and 40 deg.c, depending not only on the temperature of the system but also on the state of the system. This strategy avoids the phenomenon of chatter caused by the heater turning on and off as the temperature approaches the set point.
In this thermostat model, the time of the mode switch is ambiguous, i.e. there are many possibilities for the process to be performed even with a fixed initial temperature. Uncertainty transfer is very useful for building an uncertainty CPS failure (possibly without failure information present) model.
2. And (5) modeling and simulating a model. Ptolemy II is an open source modeling and simulation tool, unlike other modeling tools, ptolemy II supports hierarchical modeling of heterogeneous systems, and thus, ptolemy II provides a good modeling environment for the design of an uncertainty CPS system. Ptolemy II was used herein to model a CPS thermostat with uncertainty faulty, as shown in FIG. 6. When FSMActor is in the heating state, both outgoing transfers satisfy the execution condition (their condition values are all wire), so either transfer is possible, and both uncertainty transfers are represented in FIG. 6 by the down arrow.
FIGS. 7 and 8 are results of execution of an uncertainty thermostat model, wherein FIG. 7 is a schematic diagram of the results of execution of an uncertainty CPS thermostat model temperature over time provided by the present embodiment; fig. 8 is a schematic diagram of the execution result of the time-varying rate of the uncertainty CPS thermostat model provided in the present embodiment. Note that the heater can only be turned on for a short period of time, such that the temperature, which is the threshold at which the heater is turned on, wanders around 30 ℃. Setting the initial temperature of the system as T 0 And the system is in cooling mode. The value range of the initial temperature of the system is (T is more than or equal to 30 ℃ and less than or equal to 40 ℃). When the initial temperature T of the system 0 =36 ℃, constant k 1 ＝0.1、k 2 When = -0.05, the possible execution of the thermostat process is phased as: at each stage, the mode of the system does not change, and the temperature of the system changes as a continuous function of time according to the differential equation of the current mode. When the system mode is switched, the state discontinuously changes.
If the system is at time t * Switching to mode cooling at a temperature T * Then the temperature value at time T is T until the next mode switch * -k 2 (t-t * ). Let it be assumed that the temperature T at the time of entering this state * At least 32 ℃, then the process continues at a mode cooling minimum (T * -32)/k 2 Second, at most, last (T * -30)/k 2 Second. If the system switches to the mode heating at time T when the temperature is T, then until the next mode switch, the temperature value at time T isLet it be assumed that the temperature T at the time of entering this state * At least 38 ℃, then the process continues with In (2/40-T) at least In the pattern of heating * )/k 1 Second. When the temperature does not exceed 40 ℃, the system may be in this mode indefinitely.
3. CPS dynamic execution of an uncertainty hybrid time automaton. In a CPS system, the discrete behavior model of the state machine based on event driving and the dynamic continuous model based on time are fused together, and the current state of the uncertainty hybrid time automaton is required to be refined. Refinement is a function of the dynamic behavior of the output as a function of the dynamic behavior of the next input. Most CPS systems require time-course clock variable values to measure the system dynamics at a certain moment, whose transition state is linear, for which time automation can build a simple and complex system based on the clock.
Depending on the result of execution of the uncertainty CPS thermostat model in FIG. 5, CPS likelihood execution of the hybrid temporal automaton begins at an initial state. At each step, one of an input action, an output action, an internal action, or a time action is performed. One of the execution sequences of the dynamic execution corresponding to the alternating time and internal actions in this model is as follows:
In each time action, the blending process continuously outputs a value of temperature. For example, at duration 0. 14, the temperature signal is defined byDefined, and at duration 0.1, the temperature signal is controlled by 40-9e -0.1t And (5) defining.
The refinement of the dynamic behavior output by the uncertainty CPS extension model is specifically as follows: the dynamic behavior of the uncertainty CPS extension model output is taken as a function of the dynamic behavior of the next input.
In view of complexity and uncertainty factors in real life, the invention provides a plurality of novel methods for processing uncertain data by combining uncertainty and dynamic characteristics of CPS. We first introduce the GPDP concept describing the behavior of the uncertainty CPS, making decisions on the choice of uncertainty by policy. CPS syntax and semantics of generalized likelihood linear sequential logic with decision process are defined at the same time. The activity and safety properties of the system were then validated by theory and its model detection algorithm was given. And finally, modeling by using an intelligent constant temperature system and performing simulation experiments on the model. Modeling of the uncertainty hybrid system is represented by time-based differential equations describing the dynamic continuity of the system and time-based state machines, enabling each state interior to be described by time-based state refinement. The application combines theory and experiment, and ensures consistency.
It is to be understood that the same or similar parts in the above embodiments may be referred to each other, and that in some embodiments, the same or similar parts in other embodiments may be referred to.
In the description of the present specification, a description referring to terms "one embodiment," "some embodiments," "examples," "specific examples," or "some examples," etc., means that a particular feature, structure, material, or characteristic described in connection with the embodiment or example is included in at least one embodiment or example of the present application. Although embodiments of the present application have been shown and described above, it will be understood that the above embodiments are illustrative and not to be construed as limiting the application, and that variations, modifications, alternatives, and variations may be made to the above embodiments by one of ordinary skill in the art within the scope of the application.

Claims (5)

1. An uncertainty CPS modeling and verification method based on a decision process, which is characterized by comprising the following steps:
constructing a CPS system model based on a generalized likelihood decision process, and defining CPS grammar and semantics of generalized likelihood linear sequential logic of the CPS system model, wherein CPS is an information physical fusion system; the method specifically comprises the following steps:
A CPS system model is built by taking a generalized likelihood decision process as a system model; the generalized likelihood decision process is specifically a six-tuple m= (S, act, P, I, AP, L), where S is a set of countable non-empty states; act is a set of actions; p is a likelihood transfer function, P: s x Act x T → [0,1], there is one action a e Act for each state S e S, T e T, so that P (S, a, T) > 0; i is a likelihood initial distribution function; AP is a set of atomic propositions; l is a likelihood tag function;
based on state s, determining a set Paths(s) of infinite path segments starting with state s and a set Paths of finite path segments starting with state s, respectively, in a generalized likelihood decision process fin (s)；
Presetting a strategy of the six-tuple M, and defining the strategy as a function zeta;
based on the atomic proposition set AP, CPS grammar of generalized likelihood linear sequential logic of CPS system model is defined, CPS grammar is shown as follows:
where r is the interval value of the likelihood, r ε [0,1]]，a∈AP；
According to the CPS grammar, respectively defining language semantics and path semantics of generalized likelihood linear sequential logic;
introducing a clock invariant, and performing expansion modeling on the CPS system model based on a differential equation of time and an uncertainty mixed time automaton to obtain an uncertainty CPS expansion model;
Based on CPS grammar and semantics of a likelihood measure theory and generalized likelihood linear sequential logic, dynamically verifying the activity and safety attribute of the uncertainty CPS expansion model, and optimizing the execution path of the uncertainty CPS expansion model according to a dynamic verification result;
modeling and simulating the uncertainty CPS extension model by using a preset modeling tool, analyzing the CPS dynamic execution process of the uncertainty CPS extension model, and refining the dynamic behavior output by the uncertainty CPS extension model according to the analysis result of the CPS dynamic execution process.
2. The method for modeling and verifying the uncertainty CPS based on the decision process as claimed in claim 1, wherein said introducing clock invariants, differential equation based on time and uncertainty hybrid time automaton perform extended modeling on the CPS system model to obtain an uncertainty CPS extension model, specifically comprising:
modeling the dynamic behavior of an uncertainty CPS system based on a differential equation of time, and describing the dynamic property of the system;
introducing clock invariants and possibility into the hybrid automaton to obtain an uncertainty hybrid time automaton, and constructing an uncertainty hybrid time automaton system model based on the uncertainty hybrid time automaton;
The uncertainty hybrid time automaton is specifically a nine-tuple H P The following formula is shown:
H P ＝(I,O,T,Init,M con ,{A x |x∈I},{A y |y∈O},A,CI)
wherein I is a set of possible values for the input port; o is the set of all possible values of the output port; t is a state variable set, defining the state set as Q T The method comprises the steps of carrying out a first treatment on the surface of the Init is a likelihood initialization distribution operation defining a set of likelihood initial states [ Init]≤Q T ；M con Is a set of control modes; a is the set of internal actions; CI is a clock invariant;
and combining an uncertainty CPS system dynamic behavior modeling result and an uncertainty hybrid time automaton system model to obtain an uncertainty CPS extension model.
3. The method for modeling and verifying an uncertainty CPS based on a decision process as defined in claim 1, wherein the CPS syntax and semantics based on the likelihood measure theory and generalized likelihood linear sequential logic dynamically verifies the activity and security properties of the uncertainty CPS extension model, and optimizes the execution path of the uncertainty CPS extension model according to the dynamic verification result specifically comprises:
describing the activity of the uncertainty CPS expansion model between state labels in the expression execution process by utilizing CPS grammar and semantics of generalized likelihood linear sequential logic; the activities include final reachability, total reachability, repeated reachability, and persistent reachability;
Based on the likelihood measure, calculating the likelihood that the execution path with the policy in the uncertainty CPS extension model satisfies the final reachability, always reachability, duplicate reachability, and persistent reachability of the CPS grammar and semantic depiction description of the generalized likelihood linear sequential logic, the process specifically comprising:
the generalized likelihood measure that the calculation model satisfies the final reachability is expressed as:
the computational model satisfies a generalized likelihood measure of always reachability expressed as:
the computing system satisfies a generalized likelihood measure of repeat reachability expressed as:
the generalized likelihood measure that a computing system meets the persistent reachability is expressed as:
wherein Po ζ A generalized likelihood measure representing an uncertainty system model Q; s is a set of countable non-empty states, S representing a state of the uncertainty CPS system; pi represents the dynamic execution trace of the uncertainty CPS system; i and j represent two positions in the execution path with the policy, respectively; s is(s) i Sum s j Respectively representing an ith state and a jth state in an execution path with a policy in an uncertainty CPS system; ζ -Path(s) represents execution Path s with policy; b represents final reachability; and ∈b represents always reachability; b represents repeat reachability; and ∈b represents persistent reachability;
Fuzzy canonical security attribute P defining an uncertainty CPS extension model safe Calculating fuzzy canonical security attribute P based on likelihood measure theory safe Is used for judging the fuzzy regular safety attribute P safe If any infinite string sigma contains a bad prefix, the regular security attribute P is obscured safe Is unsafe, and optimizes the unsatisfactory behaviors of the uncertain CPS extension model; if the prefix does not contain bad, the regular security attribute P is obscured safe Is safe.
4. The method for modeling and verifying uncertainty CPS based on decision process as defined in claim 1, wherein said preset modeling tool is specifically a Ptolemy II simulation modeling tool.
5. The method for modeling and verifying an uncertainty CPS based on a decision process as claimed in claim 1, wherein said refining the dynamic behavior of the uncertainty CPS extension model output is specifically: the dynamic behavior of the uncertainty CPS extension model output is taken as a function of the dynamic behavior of the next input.
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