CN113359711B - Multi-intelligent-vehicle system distributed self-triggering control method with unknown information - Google Patents
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Abstract
The invention discloses a distributed self-triggering control method for a multi-intelligent-vehicle system with unknown information. Firstly, establishing a dynamic equation of a multi-intelligent-vehicle system, wherein a communication topological relation of an intelligent vehicle is represented by a non-directional connected graph; secondly, designing a controller, so that the control input of the controller only interacts the position information of the intelligent vehicle and does not interact the speed information of the intelligent vehicle any more, and designing a proper self-triggering condition function; then, the stability of the system is proved, and the control input updating time of the intelligent vehicle controller can be determined in advance; and finally, introducing the control input of the designed controller and a self-triggering condition function into each intelligent vehicle, and realizing the distributed information interaction of each intelligent vehicle by establishing a communication topological connected graph. The multi-intelligent-vehicle system does not interact speed information any more, but only achieves state synchronization through position information interaction, and applies self-triggering control, so that the system does not need to detect and judge triggering conditions in real time, and communication cost is reduced.
Description
Technical Field
The invention belongs to the field of multi-agent systems, and relates to a distributed self-triggering control method for a multi-intelligent vehicle system with unknown information.
Background
With the development of information communication technology and embedded technology, the concept and application of multi-agent system gradually appear in the visual field of people, and related research results are widely applied to the fields of vehicle traffic management, unmanned driving and the like. Therefore, how to design a control protocol and apply a high-efficiency and reasonable control method with the aim of saving the communication cost between the intelligent agents gradually becomes a research hotspot. The following describes a method for triggering and controlling application events of a multi-intelligent-vehicle system by taking the multi-intelligent-vehicle (differentially-driven wheeled mobile intelligent vehicle) system as an example:
to analyze the complete kinetic equations of a differentially driven wheeled mobile smart vehicle, the concept of a "hand" position was introduced instead of the center position of the entire smart vehicle, which is located at a point along the wheel axis perpendicular to and on a line intersecting the center point with the wheel axis, from the wheel axis h, as shown in fig. 1. The complete kinetic equation of the multi-intelligent vehicle system is as follows:
where i denotes the ith smart car, x i (t)、v i (t)、
Respectively representing the position, the speed, the derivative of the position, the acceleration and the control input of the intelligent vehicle i,
the k-th event triggering moment of the intelligent vehicle i,
the control input u of the controller is available at the k +1 th event triggering moment of the intelligent vehicle i i (t) is of the form:
wherein k is 1 And k 2 The strength of the coupling of the system is indicated,
the latest event triggering time of the neighbor j of the intelligent vehicle i,
G＝[a ij ] N×N an adjacency matrix representing a multi-intelligent-vehicle system communication topological graph, wherein if the intelligent vehicle i and the adjacent intelligent vehicle j can perform information interaction, a ij 1 is ═ 1; otherwise, a ij ＝0。
Control input u of the above-mentioned controller i (t) triggering a condition function f based on the following event i (t) update:
wherein
e i (t)＝(e ix (t),e iv (t)) T ，||e i (t)||，
Respectively representing the norm sum of the position error, the speed error, the total error and the total error of the intelligent vehicle i at the latest triggering moment and the current moment
Norm of control input at time, gamma i E (0,1), when the intelligent vehicle meets the triggering condition of the formula (3), executing an event triggering task, and performing information interaction and control input updating on the intelligent vehicle i and the adjacent intelligent vehicle j.
The above system is analyzed, and the following two problems exist:
a) in the system, each intelligent vehicle interacts position and speed information with adjacent vehicles to enable the whole system to achieve state synchronization, but when the speed information of the intelligent vehicle in the system (1) is not easy to measure or can not be measured, the control input (2) of the controller and the event triggering condition (3) are not applicable any more.
b) The event trigger control-based multi-intelligent vehicle system reduces the update frequency of control input, but needs to detect and judge the trigger condition in real time, which goes against the design initiatives of reducing resource use.
Aiming at the problem a), the existing method needs to design an observer or a filter to estimate the speed information, the method can increase the system dimension to cause the analysis of the closed-loop dynamic system to be more complicated, and the method introduces the position information with time lag to compensate the speed information without designing the observer or the filter.
Aiming at the problem b), the invention applies a self-triggering control method on the basis of an event triggering mechanism, so that the updating time of the control input of the intelligent vehicle i can be ensured
By
The method is determined in advance, and the trigger condition does not need to be detected and judged in real time, so that the communication cost is reduced.
Disclosure of Invention
Aiming at the existing problems, the invention provides a distributed self-triggering control method of a multi-intelligent-vehicle system with unknown information, wherein the multi-intelligent-vehicle system comprises N intelligent vehicles, and N is more than or equal to 2.
The technical scheme adopted by the invention for solving the technical problem comprises the following steps:
step A: establishing a complete kinetic equation of a multi-intelligent-vehicle system, representing the communication topological relation of each intelligent vehicle by using a directionless connected graph, and describing the relation between each intelligent vehicle by using a Laplacian matrix;
designing a controller to enable the controller to control and input the position information of the interactive intelligent vehicle and not to interact the speed information of the intelligent vehicle;
and C: designing proper self-triggering condition function F for intelligent vehicle i i (t)；
Step D: according to the control requirements, the stability of the system is proved, and the coupling strength and the time lag for stabilizing the multi-intelligent-vehicle system are solved;
step E: proving control input update time of intelligent vehicle controller
Can be composed of
Determining in advance;
step F: c-based self-triggering condition function F i (t), on the basis of ensuring the consistency of the multi-intelligent vehicle system to be stable, determining that the Zeno phenomenon cannot be generated by self-triggering;
step G: the control input and the self-triggering condition function of the designed controller are written into each intelligent vehicle in the intelligent vehicle system through programming, the distributed information interaction of each intelligent vehicle is realized through establishing a communication topological connection diagram, and finally the state consistency of all intelligent vehicles is realized.
The invention has the beneficial effects that: the multi-intelligent-vehicle system does not interact speed information any more, but only achieves state synchronization through position information interaction, and a self-triggering control algorithm is applied, so that the system does not need to detect and judge triggering conditions in real time, and communication cost is reduced.
Drawings
FIG. 1 illustrates a differential-driven wheeled mobile intelligent vehicle "hand" position;
FIG. 2 is a flow chart of the method of the present invention.
Detailed Description
The invention aims to solve the two problems that the speed information of the intelligent vehicle in the multi-intelligent vehicle system based on event trigger control is difficult to measure or cannot be measured, and the triggering condition is detected and judged in real time to cause resource waste. Compared with the traditional control protocol and the event trigger control method, the following two improvements are mainly made: 1) redesigning a control protocol of the system to ensure that only position information is interacted between the intelligent vehicles; 2) on the basis of the event trigger mechanism, a self-triggering control method is applied.
The invention is further described below with reference to fig. 2, which comprises the following steps:
step A: and establishing a complete kinetic equation of the multi-intelligent-vehicle system, wherein the communication topological relation of each intelligent vehicle can be represented by a directionless connected graph, and the connection between each intelligent vehicle is described by a Laplacian matrix.
And B, aiming at the problem a), designing a corresponding controller, so that the position information of the intelligent vehicle is only interacted and the speed information of the intelligent vehicle is not interacted by the control input of the controller.
And C: designing proper self-triggering condition function F aiming at intelligent vehicle i i (t)。
Step D: and according to the control requirements, the stability of the system is proved, and the coupling strength and time lag for stabilizing the multi-intelligent vehicle system are solved.
Step E: aiming at the problem b), based on the steps, the control input updating time of the intelligent vehicle controller is proved
Can be composed of
Is determined in advance.
Step F: c-based self-triggering condition function F i (t), the consistency of multiple intelligent vehicle systems is ensuredAnd determining that the Zeno phenomenon cannot be generated by self-triggering on the basis of the stability.
Step G: the control input of the controller and the self-triggering condition function designed in the process are written into each intelligent vehicle in the intelligent vehicle system through programming, the distributed information interaction of each intelligent vehicle is realized through establishing a communication topological connection diagram, and finally the state consistency of all intelligent vehicles is realized.
And B, according to the requirements of the step A, the complete kinetic equation of the multi-intelligent-vehicle system is consistent with the formula (1). The communication topological relation of N intelligent vehicles in the system can be represented by a undirected connected graph, and a Laplacian matrix of the undirected connected graph is defined as follows:
And B, designing the control input of the controller only exchanging the position information according to the requirement of the step B:
wherein beta is more than 0 and less than alpha is the coupling strength of the system,
tau is the time lag introduced by the time,
setting initial trigger time for time interval of two continuous trigger times
In contrast to the second term of the control input (2), the above-mentioned control input does not need to directly exchange velocity information, but indirectly compensates for velocity information by introducing position information with a time lag.
Wherein, according to the requirement of step C, a proper self-triggering condition function F is designed i (t) in the specific form:
wherein: gamma ray i1 、γ i2 E (0,1) can adjust the sensitivity of the system self-triggering condition, sign (phi) is a sign function, when F i (t) is not less than 0 to achieve the self-triggering condition.
According to the requirement of the step D, solving specific parameters alpha, beta, tau, P and Q for stabilizing the multi-intelligent vehicle system
(1) The formulas (1) and (4) can be arranged into the following forms:
wherein:
I n is an n-dimensional identity matrix, I nN Is nN dimensional identity matrix, 0 nN Is an nN-dimensional zero matrix and is,
is the Kronecker product, which is defined as: if it is
The following form of Lyapunov-krasovskii equation was further constructed:
wherein: tau.>0，
And P ═ P T >0，Q＝Q T >0 is a positive definite symmetric matrix.
The derivation of equation (7) can be found:
the LMI inequalities M (alpha, beta, tau, P, Q) of alpha, beta, tau, P and Q are less than 0 by further simplifying the above formula, and the LMI inequalities can be solved by MATALB software for any given symmetric positive definite matrix Q
According to the Lyapunov theorem,
the system is stable and the certification is finished.
According to the requirement of the step E, the control input updating time of the intelligent vehicle controller is proved
Can be composed of
Is determined in advance.
Solving any two continuous controller updating time intervals, and defining the position and speed error:
wherein:
representing velocity information calculated indirectly from the position information.
Further calculations may yield:
for the convenience of calculation, the equation of equation (5) is first shifted by the square term and then shifted by the term
Then substituting the formula (10) into the formula:
the following is discussed:
when in use
Then, substituting equation (12) can obtain:
-(γ i2 ) 2 ＜0
when the temperature is within the range of t → ∞,
when the known system stability proves to be true, substitution (12) can give:
can exist by mesomeric theorem
The equation (12) is satisfied.
When in use
Then, substituting equation (12) can obtain:
when the temperature is t → ∞ infinity,
then, knowing that the system stability in step B proves to be true, substituting equation (12) to obtain:
can exist by mesomeric theorem
The expression (11) is established.
In summary, the following results are obtained
Namely the update time of the intelligent vehicle controller
Can be composed of
Is determined in advance.
Wherein the Zeno trigger behavior is excluded on the basis of the above mentioned proof according to the requirements of step F.
Given that system stability proved to be true, there is a normal quantity ρ v 、ρ u Such that the following inequality holds:
according to | | e ix (t)+e iv (t)||≤||e ix (t)||+||e iv (t) | | can be given as:
substituting into the self-triggering condition (5) may result:
the following is to be discussed:
when in use
Then, substituting equation (13) can obtain:
when in use
Then, substituting equation (13) can obtain:
in summary, any two consecutive update time intervals are greater than zero, i.e. no Zeno trigger action occurs.
Claims (1)
1. A distributed self-triggering control method for a multi-intelligent vehicle system with unknown information is characterized by comprising the following steps
Step A: establishing a complete kinetic equation of a multi-intelligent vehicle system, representing the communication topological relation of each intelligent vehicle by a directionless connected graph, and describing the relation between each intelligent vehicle by a Laplacian matrix;
designing a controller to enable the controller to control and input the position information of the interactive intelligent vehicle and not to interact the speed information of the intelligent vehicle;
and C: designing proper self-triggering condition function F aiming at intelligent vehicle i i (t)；
Step D: according to the control requirements, the stability of the system is proved, and the coupling strength and the time lag for stabilizing the multi-intelligent-vehicle system are solved;
and E, step E: proving control input update time of intelligent vehicle controller
Can be composed of
Determining in advance;
step F: self-triggering condition function F designed based on step C i (t), on the basis of ensuring the consistency of the multi-intelligent vehicle system to be stable, determining that the Zeno phenomenon cannot be generated by self-triggering;
step G: the control input and the self-triggering condition function of the designed controller are written into each intelligent vehicle in the intelligent vehicle system through programming, the distributed information interaction of each intelligent vehicle is realized through establishing a communication topological connection diagram, and finally the state consistency of all intelligent vehicles is realized;
wherein the control input u of the controller designed in step B to exchange only position information i (t) is:
wherein alpha and beta are coupling strength, tau is introduced time lag,
the k-th event triggering moment of the intelligent vehicle i,
the event triggering time of the intelligent vehicle i at the k +1 th time,
is the latest event triggering time, a, of the neighbor j of the intelligent vehicle i ij The method comprises the following steps that elements in an adjacent matrix of a communication topological graph of the multi-intelligent vehicle system are provided, and N is the number of intelligent vehicles in the multi-intelligent vehicle system;
wherein the self-triggering condition function F designed in the step C i (t) is:
wherein: gamma ray i1 、γ i2 E (0,1) can adjust the sensitivity of the system self-triggering condition, sign (phi) is a sign function, when F i (t) is not less than 0 and reaches a self-triggering condition, e i (t) is the total error between the latest triggering moment of the intelligent vehicle i and the current moment,
is composed of
Control input of the controller at the time.
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