CN113534664A - Multi-agent system event trigger control method based on closed loop state estimation - Google Patents
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Abstract
The invention provides a multi-agent system event trigger control method based on closed-loop state estimation, which obtains the predicted state quantity at the next moment according to a trigger control formula through the state quantities and control quantities of agents i and j at the current moment; and constructing a slip film surface of the agent j, calculating to obtain a sliding mode variable in the slip film surface in the controller of the agent i, constructing a slip film controller for the agent j in the controller of the agent i, obtaining a predicted sliding mode variable at the next moment, and finally obtaining the state quantity of the agent j. The method of the invention carries out distributed closed-loop solution under the action of the feedback gain matrix, reduces the triggering times of events on the premise of ensuring the state of each agent to carry out closed-loop estimation so as to ensure the accuracy of the estimated state, can obtain more accurate future state information of each agent, reduces the growth speed of state estimation errors in the event triggering function, and obviously reduces the triggering communication times among the agents.
Description
Technical Field
The invention belongs to the technical field of unmanned system cooperative control, and relates to a closed loop state estimation-based multi-agent system event trigger control method.
Background
The multi-agent system has become one of the research hotspots for controlling the subject in recent years due to its characteristics of convenient maintainability, low development and use cost, high flexibility and reliability, etc. With the continuous development of computer technology, network technology and control theory, multi-agent systems have gradually advanced towards networking, clustering, intellectualization and the like. In the face of the problem of complicated information interaction requirements among multiple intelligent agents and the resource constraint problem of network bandwidth, the traditional distributed control method based on time triggering restricts the further development of the distributed control theory and application of a multi-intelligent-agent system due to the dependence of the distributed control method on network resources. Therefore, a distributed design and analysis method based on event triggering is developed, and the core idea is to reduce the network communication frequency and the system power consumption among multiple intelligent agents on the premise of ensuring the stability of the system. Research on a related event triggering control method has become an important front-end topic in the field of distributed control of multi-agent systems.
At present, a large amount of research work has been carried out by experts and scholars at home and abroad aiming at an event trigger control method of a multi-agent system, and related research achievements have been widely applied to the fields of smart power grids, intelligent traffic systems, distributed sensor networks, multi-unmanned aerial vehicle systems, multi-mobile robot systems and the like. However, there are still some deficiencies in the research on the control performance assurance of the event-triggered control method. Most of the existing research results require that each agent keeps the control quantity constant in two adjacent trigger intervals to reduce the power consumption of the system, and meanwhile, a dynamic trigger mechanism is designed to reduce the trigger times to reduce the network communication frequency. The mechanism enables the triggering times of the intelligent system to be positively correlated with the control performance, namely the triggering times are more (approaching time triggering) the control performance of the intelligent system is better, otherwise, the triggering times are reduced to cause the control performance of the intelligent system to be reduced. The essential reason is that the control quantity invariance in the adjacent two trigger intervals of the intelligent agent brings the mutability of the control signal of the actuator end, and further influences the control performance of the system. The potential solution is to implement continuous update of the control laws of each agent based on closed-loop state prediction, however, most scholars still implement state estimation of the agents in an open-loop manner and still maintain the control quantity in two adjacent trigger intervals constant in a zero-order holding manner at present. The only research results that the closed-loop state estimation is adopted and the continuous updating of the control quantity is realized are that the theoretical analysis process is usually complex and the engineering realization is difficult in partial scenes.
Event-triggered predictive control based on closed-loop state estimation means that agent i triggers at the moment
For the next trigger moment based on available local information
And performing closed-loop estimation on the previous self state and the control quantity. Namely, the closed-loop prediction of the state sequence and the control quantity sequence is realized, and the time interval
In which control quantities at respective times are sequentially applied to actuators of agent i at time intervals
Without the need for a communication network. The control quantity of the intelligent agent i is continuously updated on the premise of not increasing the network communication times so as to improve the control performance of the system.
The core problem faced in the implementation process is that the agent i needs to know the prediction information of the neighbor agent j at each future time in the forward prediction process, and the agent i also needs the prediction information in the forward prediction process of the agent j. The contradiction of the information requirements leads to that the multi-agent system cannot carry out distributed closed-loop solution under the condition that the global information is unknown, and the known conditions of the global information are too conservative. By comprehensively analyzing the existing research results, no matter what state form is adopted, the multi-agent system can always realize state convergence under the action of an event-triggered cooperative control law (based on a properly designed feedback gain matrix, the system is isomorphic and stable), and the control quantity of all agents finally converges on a manifold (simulation) with a certain specific dimension. In other words, the present state χj(k)＝uj(k)-ui(k) Satisfy limk→∞||χj(k)||＝0。
Therefore, there is a need for a method for controlling event triggering of a multi-agent system based on closed-loop state estimation, which reduces the increase rate of state estimation errors to achieve the purpose of reducing the number of event triggering times on the premise of ensuring the state of each agent to implement closed-loop estimation to ensure the accuracy of the estimated state.
Disclosure of Invention
In view of this, the invention provides a multi-agent system event triggering control method based on closed-loop state estimation, which is used for developing distributed closed-loop solution and reducing the triggering times of events on the premise of ensuring the state of each agent to implement closed-loop estimation so as to ensure the accuracy of the estimated state.
In order to achieve the purpose, the technical scheme of the invention is as follows:
a multi-agent system event trigger control method based on closed loop state estimation comprises the following steps:
s1, at the current moment
Predicted state quantity of neighbor agent j according to agent i
Control quantity at present
Last moment control quantity
And predicted state quantity of agent i
Solving current time control quantity of agent i
And substituting the predicted state quantity into a known intelligent agent model to obtain the predicted state quantity of the intelligent agent i at the next moment through a controller of the intelligent agent i
And the next momentPredicted state quantity of carved neighbor agent j
Will be provided with
And
substituting the model of the agent to solve the predicted control quantity of the agent i at the next moment
S2, controlling quantity according to current time of agent i
And the current time control quantity of the neighbor agent j
Calculating to obtain the sliding modal variable of the neighbor agent j at the current moment
And constructing a slip film surface for the neighbor agent j in the controller of agent i
S3, utilizing a discrete time index approach formula and combining the synovial surface of the neighbor agent j at the current moment
Calculating the slide film surface of the neighbor agent j at the next moment
Therefore, a synovial membrane controller of a neighbor agent j is constructed in an agent i
Substituting the intelligent agent model to calculate the predicted sliding mode variable of the neighbor intelligent agent j at the next moment
S4, circularly executing S1-S3 in the sampling period, wherein the circulating times are h/T times, and obtaining the control quantity sequence of the intelligent agent i
Selecting the control quantity at the corresponding moment in each sampling period and applying the control quantity to an actuator of the agent i to obtain the predicted sliding modal variable of the neighbor agent j at the corresponding moment, and further calculating to obtain the predicted control quantity of the neighbor agent j at the corresponding moment; substituting the predicted control quantity into the intelligent agent model to solve the predicted state quantity of the corresponding neighbor intelligent agent j at the next moment; wherein h represents a sliding mode variable
And (4) converging from any initial position to the time when the sliding mode surface is 0, wherein T is a sampling period.
Further, at the present moment
Predicted state quantity of neighbor agent j according to agent i
Control quantity at present
Last moment control quantity
And predicted state quantity of agent i
Solving current time control quantity of agent i
The specific method comprises the following steps:
where K is a feedback gain matrix designed by the pole allocation method, aijIs the topological graph communication weight of agent i and neighbor agent j, N is the number of agents, N isiIs a neighborhood of agent i, and i, j e (1, ·, N).
Further, the amount is controlled according to the current time of agent i
And the current time control quantity of the neighbor agent j
Calculating to obtain the sliding modal variable of the neighbor agent j at the current moment
And constructing a slip film surface for the neighbor agent j in the controller of agent i
The specific method comprises the following steps:
wherein, A is a system matrix, B is an input matrix, G is a constant coefficient matrix, and K is a feedback gain matrix.
Wherein the content of the first and second substances,
further, the characteristic roots of the matrix a + BK are distributed in the unit circle.
Further, the constant coefficient matrix G needs to satisfy that GB is a non-singular matrix.
Furthermore, a discrete time index approach formula is utilized, and a synovial surface of the neighbor agent j at the current moment is combined
Calculating the slide film surface of the neighbor agent j at the next moment
Therefore, a synovial membrane controller of a neighbor agent j is constructed in an agent i
Substituting the intelligent agent model to calculate the predicted sliding mode variable of the neighbor intelligent agent j at the next moment
The specific method comprises the following steps:
the discrete time index approach formula is:
wherein q and epsilon are normal numbers, T represents a system sampling period,
is a sign function of the slide surface; sliding mode controller
Wherein B isL -1Is the left inverse of the input matrix B; substituting the model into the agent model to calculate to obtain the predicted state quantity of the neighbor agent j at the next moment
Further, the control quantity at the corresponding time is selected in each sampling period and applied to the actuator of the agent i to obtain the predicted sliding mode variable of the neighbor agent j at the corresponding time, and then the predicted control quantity of the neighbor agent j at the corresponding time is obtained through calculation, and the specific method is as follows:
the predicted control quantity of the agent i at the next moment
And predicted state quantities of neighbor agent j at the next time
Substitution formula
Solving the predicted control quantity of the agent j at the next moment
Has the advantages that: the invention provides a multi-agent system event trigger control method based on closed-loop state estimation, which obtains the predicted state quantity at the next moment according to a trigger control formula through the state quantities and control quantities of agents i and j at the current moment; the method comprises the steps of constructing a slip film surface of an intelligent agent j, calculating to obtain a sliding modal variable in the slip film surface in a controller of the intelligent agent i, constructing a slip film controller for the intelligent agent j in the controller of the intelligent agent i, substituting a discrete time index approach formula to obtain a predicted sliding modal variable at the next moment, further obtaining a control quantity of the intelligent agent j at each moment, substituting an intelligent agent model to finally obtain a state quantity of the intelligent agent j at the corresponding moment, and forming a closed loop. The method of the invention carries out distributed closed-loop solution under the action of the feedback gain matrix, reduces the triggering times of events on the premise of ensuring the state of each agent to carry out closed-loop estimation so as to ensure the accuracy of the estimated state, compared with the existing open-loop state estimation mode, the method of the invention can obtain more accurate future state information of each agent, reduces the increasing speed of state estimation errors in an event triggering function, and obviously reduces the triggering communication times among the agents.
Drawings
FIG. 1 is a flow chart of the method of the present invention.
Detailed Description
The invention is described in detail below by way of example with reference to the accompanying drawings.
As shown in fig. 1, the present invention provides a method for controlling event triggering of a multi-agent system based on closed-loop state estimation, which comprises the following steps:
s1, at the current moment
Predicted state quantity of neighbor agent j according to agent i
Control quantity at present
Last moment control quantity
And predicted state quantity of agent i
Solving current time control quantity of agent i
And substituting the predicted state quantity into a known intelligent agent model to obtain the predicted state quantity of the intelligent agent i at the next moment through a controller of the intelligent agent i
And predicted state quantities of neighbor agent j at the next time
Will be provided with
And
substituting the model of the agent to solve the predicted control quantity of the agent i at the next moment
In the embodiment of the invention, the formula is used
Solving for
Where K is a feedback gain matrix designed by the pole allocation method, aijThe communication weights of the topological graphs of the agent i and the neighbor agent j are set, and when the agent i and the neighbor agent j can communicate, the communication weight is equal to 1, and when the agent i and the neighbor agent j cannot communicate, the communication weight is 0; n is the number of agents, NiIs the neighborhood of agent i and i, j e (1, …, N).
S2, controlling quantity according to current time of agent i
And the current time control quantity of the neighbor agent j
Calculating to obtain the sliding modal variable of the neighbor agent j at the current moment
And constructing a slip film surface for the neighbor agent j in the controller of agent i
In the embodiment of the invention, the formula is used
Solving for
Wherein A is a system matrix, B is an input matrix, and G is a constant coefficient matrix.
Wherein the content of the first and second substances,
s3, utilizing a discrete time index approach formula and combining the synovial surface of the neighbor agent j at the current moment
Calculating the slide film surface of the neighbor agent j at the next moment
Therefore, a synovial membrane controller of a neighbor agent j is constructed in an agent i
Substituting the intelligent agent model to calculate the predicted sliding mode variable of the neighbor intelligent agent j at the next moment
The discrete time index approach formula is as follows:
q and epsilon are normal numbers, T represents a system sampling period,
is a sign function of the slide surface.
Construction sliding mode controller
Wherein B isL -1Is the left inverse of the input matrix B. Substituting the model into the agent model to calculate to obtain the predicted state quantity of the neighbor agent j at the next moment
S4, circularly executing S1-S3 in the sampling period, wherein the circulating times are h/T times, and obtaining the control quantity sequence of the intelligent agent i
Selecting the control quantity at the corresponding moment in each sampling period and applying the control quantity to an actuator of the agent i to obtain the predicted sliding modal variable of the neighbor agent j at the corresponding moment, and further calculating to obtain the predicted control quantity of the neighbor agent j at the corresponding moment; substituting the predicted control quantity into the intelligent agent model to solve the predicted state quantity of the corresponding neighbor intelligent agent j at the next moment; wherein h represents a sliding mode variable
And (4) converging from any initial position to the time when the sliding mode surface is 0, wherein T is a sampling period.
In the embodiment of the invention, the predicted control quantity of the intelligent agent i at the next moment is used
And the predicted state quantity of agent j at the next moment
Substitution formula
Can solve out
Substituting the predicted control quantity into the intelligent agent model to obtain the corresponding predicted state quantity.
The principle of the method of the invention is as follows:
the known agent i may calculate the state quantity using an event-triggered control formula of the form:
wherein the content of the first and second substances,
represents a closed-loop estimated state of agent i, and
k is a feedback gain matrix designed by a known pole placement method. At the time of event trigger
State of the acquirable neighbor agent j
Control quantity
And self state
At this point the control law of agent i is solvable, i.e.
One can obtain, where i, j ∈ (1, ·, N).
Based on isomorphic multi-agent system model, state prediction information of previous step can be obtained in controller of agent i
And
further obtain the
And
based on each intelligent agent
Time of day control, design sliding mode variables
Constructing a sliding form surface S for an agent j in an agent i controllerj(k) One possible form of construction is:
Sj(k)＝Gχj(k)-G(A+BK)χj(k-1)
wherein A, B is the system matrix and the input matrix, and the constant coefficient matrix G is the Rm×nGB is not singular, K is a feedback gain matrix, and characteristic roots of the matrix A + BK can be distributed in a unit circle.
Known combined discrete time index approach formula Sj(k+1)＝(1-qT)Sj(k)-εTsgn(Sj(k))；
Wherein q and epsilon are normal numbers, T represents a system sampling period, sgn (·) is a symbolic function, namely a sliding mode controller of an intelligent agent j can be constructed in an intelligent agent i
From the agent model, a predicted state is further derived
Then it is determined that,
circularly executing the prediction process h/T times to obtain the future control quantity sequence of the intelligent agent i as
And selecting the control quantity at the corresponding moment in each sampling period, applying the control quantity to an actuator of the agent i, and finally solving the state of the agent j. Wherein h represents a sliding mode
From any initial position to the slip-form surface Sj(k) Time 0, T is the system sampling period.
As can be seen from the above loop process, the actuator end of agent i continuously updates the control quantity in each sampling period, and the multiple agents are in time
And no communication is carried out before the state estimation error arrives, so that the increase speed of the state estimation error can be reduced, and the aim of reducing the number of event triggers is fulfilled.
In summary, the above description is only a preferred embodiment of the present invention, and is not intended to limit the scope of the present invention. Any modification, equivalent replacement, or improvement made within the spirit and principle of the present invention should be included in the protection scope of the present invention.
Claims (7)
1. A multi-agent system event trigger control method based on closed loop state estimation is characterized by comprising the following steps:
s1, at the current moment
Predicted state quantity of neighbor agent j according to agent i
Control quantity at present
Last moment control quantity
And predicted state quantity of agent i
Solving current time control quantity of agent i
And substituting the predicted state quantity into a known intelligent agent model to obtain the predicted state quantity of the intelligent agent i at the next moment through a controller of the intelligent agent i
And predicted state quantities of neighbor agent j at the next time
Will be provided with
And
substituting the intelligent agent model to solve the predicted control quantity of the intelligent agent i at the next moment
S2, controlling quantity according to current time of agent i
And the current time control quantity of the neighbor agent j
Calculating to obtain the sliding modal variable of the neighbor agent j at the current moment
And constructing a slip film surface for the neighbor agent j in the controller of agent i
S3, utilizing a discrete time index approach formula and combining the synovial surface of the neighbor agent j at the current moment
Calculating the slide film surface of the neighbor agent j at the next moment
Therefore, a synovial membrane controller of a neighbor agent j is constructed in an agent i
Substituting the intelligent agent model to calculate the predicted sliding mode variable of the neighbor intelligent agent j at the next moment
S4, circularly executing S1-S3 in the sampling period, wherein the circulating times are h/T times, and obtaining the control quantity sequence of the intelligent agent i
Selecting the control quantity at the corresponding moment in each sampling period and applying the control quantity to an actuator of the agent i to obtain the predicted sliding modal variable of the neighbor agent j at the corresponding moment, and further calculating to obtain the predicted control quantity of the neighbor agent j at the corresponding moment; substituting the predicted control quantity into the intelligent agent model to solve the predicted state quantity of the corresponding neighbor intelligent agent j at the next moment; wherein h represents a sliding mode variable
And (4) converging from any initial position to the time when the sliding mode surface is 0, wherein T is a sampling period.
2. The method of claim 1, wherein the at the current time instant
Predicted state quantity of neighbor agent j according to agent i
Control quantity at present
Last moment control quantity
And predicted state quantity of agent i
Solving current time control quantity of agent i
The specific method comprises the following steps:
where K is a feedback gain matrix designed by the pole allocation method, aijIs the topological graph communication weight of agent i and neighbor agent j, N is the number of agents, N isiIs a neighborhood of agent i, and i, j e (1, ·, N).
3. The method of claim 1, wherein the amount is controlled based on a current time of agent i
And the current time control quantity of the neighbor agent j
Calculating to obtain the sliding modal variable of the neighbor agent j at the current moment
And constructing a slip film surface for the neighbor agent j in the controller of agent i
The specific method comprises the following steps:
wherein, A is a system matrix, B is an input matrix, G is a constant coefficient matrix, and K is a feedback gain matrix;
wherein the content of the first and second substances,
4. a method as claimed in claim 3, characterized in that the characteristic roots of the matrix a + BK are distributed uniformly within the unit circle.
5. A method as claimed in claim 3 or 4, wherein the constant coefficient matrix G is such that GB is a non-singular matrix.
6. The method of claim 1, wherein the approximation formula using discrete time indices is combined with a synovial surface of the neighbor agent j at the current time
Calculating the slide film surface of the neighbor agent j at the next moment
Therefore, a synovial membrane controller of a neighbor agent j is constructed in an agent i
Substituting the intelligent agent model to calculate the predicted sliding mode variable of the neighbor intelligent agent j at the next moment
The specific method comprises the following steps:
the discrete time index approach formula is:
wherein q and epsilon are normal numbers, T represents a system sampling period,
is a sign function of the slide surface; sliding mode controller
Wherein B isL -1Is the left inverse of the input matrix B; substituting the model into the agent model to calculate to obtain the predicted state quantity of the neighbor agent j at the next moment
7. The method according to claim 1, wherein the control quantity at the corresponding time is selected in each sampling period and applied to an actuator of agent i to obtain the predicted sliding mode variable of neighbor agent j at the corresponding time, and the predicted control quantity of neighbor agent j at the corresponding time is calculated by:
the predicted control quantity of the agent i at the next moment
And predicted state quantities of neighbor agent j at the next time
Substitution formula
Solving the predicted control quantity of the agent j at the next moment
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