A time-specified cooperative control method for high-order multi-agent systems with unknown states

Abstract

The present invention relates to a method for specified-time cooperative control of a high-order multi-agent system with unknown states, which includes: Step 1, setting the expected total time for bounded consensus arrival as T, setting the precise reconstruction time of the agent state information as D, and satisfying D < T; Step 2, building a specified-time observer for each agent; Step 3, designing a fully distributed edge-based adaptive control protocol; Step 4, obtaining a specified-time consensus control protocol for a fully distributed multi-agent linear system based on the observer. The present invention, aiming at a high-order linear system, introduces a specified-time observer to solve the problem that the agent state information cannot be accurately obtained, and alleviates the rigid demand of the multi-agent system for high-cost sensor and other accessory equipment; introduces an edge-based adaptive control protocol to avoid the need of the control protocol for global information; successfully extends the specified-time consensus control of multi-agents to a high-order linear system, and improves the applicability of the specified-time consensus control scheme.

Description

Technical Field

[0001] This invention relates to a time-based cooperative control method for a high-order multi-agent system with an unknown state, belonging to the fields of computer science and control technology. Background Technology

[0002] Significant progress has been made in multi-agent system cooperative control over the past decade, with numerous applications including data synchronization, wireless sensor networks, multi-vehicle cooperation, and resource allocation. The primary goal of multi-agent consensus research is to design distributed control protocols that rely solely on local information, ensuring that the states of each agent converge to the same level. In practical engineering, the control performance of these consensus protocols often requires speed. For example, in the coordinated attack of swarm drones against high-performance fighters like the F-22 and T-50, efficient distributed cooperative control protocols are needed to enable the swarm drone system to achieve rapid response, high-speed tracking, and precision strike capabilities. In the collaborative operation of multiple space robot systems, designing effective distributed cooperative control protocols is crucial, ensuring that robots performing different tasks can complete a specified series of actions at given time points. In the coordinated attack of multiple missile systems, a cooperative navigation ratio must be designed to ensure that the calculated remaining time for each missile reaches consistency within a specified time, thereby achieving precise multi-missile hits. Therefore, distributed cooperative control that meets specific convergence performance requirements, especially the ability to complete tasks at specified time points, can not only improve the cooperative speed of multi-agent systems but also ensure that the multi-agent systems achieve their cooperative goals at precise convergence time points. Compared to asymptotically convergent distributed cooperative control, distributed cooperative control that achieves consensus at specified time points has significant advantages and an irreplaceable role in practical engineering. However, existing multi-agent time-consistency control techniques mainly focus on integrator-type systems, and for higher-order linear systems, only dynamic programming-based methods are available. Furthermore, most of these methods do not avoid introducing global information (such as information related to the multi-agent topology) into the control protocol, thus failing to achieve truly fully distributed control. In addition, existing time-consistency algorithms heavily rely on each agent's ability to accurately measure its own and its neighbors' states, which increases the cost requirements for agent hardware. Summary of the Invention

[0003] The purpose of this invention is to address the shortcomings of existing methods by providing a time-based cooperative control method for high-order multi-agent systems with unknown states. Compared to existing time-based consistency control methods for high-order linear multi-agent systems based on dynamic programming, this method divides the overall consistency arrival time into two summed parts: 1) the state precise reconstruction time (during which control input is 0); and 2) the consistency realization time (during which control input is injected). The former introduces a time-based observer, allowing the controller to obtain precisely reconstructed agent state information at any pre-set time point. The latter proposes a fully distributed edge-based adaptive control protocol, which effectively avoids the use of global information by the control protocol while ensuring bounded consistency at the specified time. Both of these time components can be arbitrarily pre-set.

[0004] To achieve the above objectives, the technical solution of the present invention is as follows:

[0005] A time-based cooperative control method for a high-order multi-agent system with an unknown state includes the following steps:

[0006] Step 1: Set the total time to reach the desired bounded consistency as T, and set the time for accurate reconstruction of the agent's state information as D, and satisfy D < T;

[0007] Step 2: Build a specified time observer for each agent;

[0008] Step 3: Based on the state reconstruction information from the observer in Step 2, design a fully distributed edge-based adaptive control protocol;

[0009] Step 4: Obtain the observer-based, fully distributed multi-agent linear system's specified-time consistency control protocol. This control protocol consists of two parts: 1) a specified-time observer and 2) an edge-based adaptive controller. Specifically, no control is performed during the first D time period; only state observation is conducted. During the subsequent TD time period, the observer continues to operate and begins implementing control, ultimately achieving bounded consistency of the multi-agent system at time T.

[0010] Step two specifically includes:

[0011] Step 2.1: The following is an example of a high-order linear multi-agent system with N agents:

[0012]

[0013] in, and These represent the n-dimensional state vector, p-dimensional control input vector, and q-dimensional measurement output vector of the i-th agent, respectively. and Both represent time-invariant system matrices, where (A, B) is controllable, and (A, C) is controllable.i For any It is observable; let x(t) = [x1(t)] T , ..., x N (t) T ] T And let x0 = x(0) represent the initial state;

[0014] Step 2.2: Design two Lumborghäuser observers for each agent as follows:

[0015]

[0016] in, This represents the state value of the k-th Lumborghäuser observer for the i-th agent. This represents the corresponding Lumborghäuser observer gain, and the following symbol definitions are given:

[0017]

[0018]

[0019] Where In represents the n-dimensional identity matrix, the two Lumborghäuser observers can be rewritten as:

[0020]

[0021] Step 2.3: Based on the Lumborghäuser observer state values ​​from Step 2.2, design the specified time observer as follows:

[0022]

[0023] Among them, e · Represents an exponential function. represents the reconstructed value of the true state of the i-th agent, Mi represents the observer gain of the i-th agent at a specified time, and t0 represents the initial time.

[0024] Step three specifically includes:

[0025] Step 3.1: Reconstruct the state output based on the observer from Step 2 The following symbol definitions are given:

[0026]

[0027] Where i, j∈{1,2,…,N}, Let a represent the set of agents that communicate and interact with the i-th agent. ij Let a represent the interaction relationship between the i-th agent and the j-th agent. If an interaction exists, then a ij =1, if it does not exist, then aij =0,q i This represents the consistency error between the reconstructed state value of the i-th agent and the agents with communication interactions.

[0028] Step 3.2: Design an edge-based adaptive control protocol u i as follows:

[0029]

[0030]

[0031]

[0032]

[0033] Where K represents the feedback gain matrix, Represents the time-varying control gain. ε represents the adaptive parameters based on agent interaction edges. ij θ ij , ζ ij Both represent designable control parameters, and the feedback gain matrix K is chosen as K = B. T P;

[0034] P is the Riccati equation A T P+PA-PBB T The unique symmetric positive definite solution to P + Q = 0, where Q is any symmetric positive definite matrix.

[0035] Parameter ζ ij The selection is ε ij The selection must satisfy ε ij >0, θ ij The selection satisfies θ ij If the value is greater than 0, bounded consistency will be achieved at time T, and bounded consistency will still be maintained when t > T.

[0036] Step four specifically includes:

[0037] Step 4.1: Obtain the specified time consistency control protocol for the observer-based fully distributed multi-agent linear system as follows:

[0038]

[0039] Among them, the feedback gain matrix K and the time-varying control gain Adaptive parameters and ε ij θ ij , ζ ij The design and selection of control parameters are the same as in step 3-2;

[0040] Step 4.2: Design the Lyapunov function and derive and analyze the bounds that the system consistency reaches after a specified time. The Lyapunov function V is given as follows:

[0041]

[0042] in, η0 represents global information related to the multi-agent communication topology, and ε0 represents the information for all ε ij The minimum value of the parameter. The consistency error of the agent's state is represented by the Lyapunov function V, which can represent the sum of the consistency error of the multi-agent state and the parameter adaptation error.

[0043] Step 4.3: Taking the derivative of V and scaling it, we get:

[0044]

[0045] in, Using the comparison lemma, we can further obtain:

[0046]

[0047] At time t = T:

[0048]

[0049] in, ε0 is a designable parameter ε i1 The minimum value of Φ can decrease as ε0 decreases. At a specified time T, the sum of the system's consistency error and adaptive parameter error, V(T), will also decrease as ε0 decreases.

[0050] When time t > T:

[0051]

[0052] From the above equation, it can be seen that after a specified time T, the sum of the system's consistency error and adaptive parameter error, V(t), will converge exponentially to the bound. Inside.

[0053] This invention targets high-order linear systems. First, it introduces a specified-time observer, effectively solving the problem of inaccurate acquisition of agent state information and alleviating the rigid requirement of high-cost sensors and other accessories in multi-agent systems. Second, utilizing an adaptive method, it proposes a specified-time consistency control protocol that does not rely on global topology information, a method that allows each agent controller to be designed independently. Finally, this invention successfully extends specified-time consistency control for multi-agent systems to high-order linear systems, improving the applicability of the specified-time consistency control scheme. Attached Figure Description

[0054] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0055] Figure 1 The flowchart illustrates a time-coordinated control method for a high-order multi-agent system with an unknown state, as described in this invention. Detailed Implementation

[0056] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0057] Figure 1 This is a flowchart of a time-coordinated control method for a high-order multi-agent system with an unknown state, provided in an embodiment of the present invention.

[0058] A time-based cooperative control method for a high-order multi-agent system with an unknown state includes the following steps:

[0059] Step 1: Set the total time to reach the desired bounded consistency as T, and set the time for accurate reconstruction of the agent's state information as D, and satisfy D < T;

[0060] Step 2: Build a specified time observer for each agent;

[0061] Step 2.1: The high-order linear multi-agent system with N agents targeted by this invention is as follows:

[0062]

[0063] in, and These represent the n-dimensional state vector, p-dimensional control input vector, and q-dimensional measurement output vector of the i-th agent, respectively. and Both represent time-invariant system matrices, where (A, B) is controllable, and (A, C) is controllable. i For any It is observable; let x(t) = [x1(t)] T , ..., x N (t) T ] T And let x0 = x(0) represent the initial state;

[0064] Step 2.2: Design two Lumborghäuser observers for each agent as follows:

[0065]

[0066] in, This represents the state value of the k-th Lumborghäuser observer for the i-th agent. This represents the corresponding Lumborghäuser observer gain, and the following symbol definitions are given:

[0067]

[0068]

[0069] Among them, I n Representing the n-dimensional identity matrix, the two Lumborghäuser observers can be rewritten as:

[0070]

[0071] Step 2.3: Based on the Lumborghäuser observer state values ​​from Step 2.2, design the specified time observer as follows:

[0072]

[0073] Among them, e · Represents an exponential function. M represents the reconstructed value of the true state of the i-th agent. i The gain of the observer at a specified time represents the i-th agent, and t0 represents the initial time. In this invention, given that D is determined in step 1, H... i The selection of F must satisfy the condition that F i It is Herwitz's, and the matrix If the determinant is not zero, then the time observer gain M is specified. i can be The calculation is given, where 0 n It represents an n-dimensional zero matrix.

[0074] Step 3: Based on the state reconstruction information from the observer in Step 2, design a fully distributed edge-based adaptive control protocol;

[0075] Step 3.1: Reconstruct the state output based on the observer from Step 2 The following symbol definitions are given:

[0076]

[0077] Where i, j∈{1,2,…,N}, Let a represent the set of agents that communicate and interact with the i-th agent. ij Let a represent the interaction relationship between the i-th agent and the j-th agent. If an interaction exists, then a ij =1, if it does not exist, then a ij =0,q i This represents the consistency error between the reconstructed state value of the i-th agent and the agents with communication interactions.

[0078] Step 3.2: Design an edge-based adaptive control protocol u i as follows:

[0079]

[0080]

[0081]

[0082]

[0083] Where K represents the feedback gain matrix, Represents the time-varying control gain. ε represents the adaptive parameters based on agent interaction edges. ij θ ij , ζ ij Both represent designable control parameters, and the feedback gain matrix K is chosen as K = B. T P;

[0084] P is the Riccati equation A T P+PA-PBB T The unique symmetric positive definite solution to P + Q = 0, where Q is any symmetric positive definite matrix.

[0085] Parameter ζ ij The selection is ε ij The selection must satisfy ε ij >0, θ ij The selection satisfies θ ijIf the value is greater than 0, bounded consistency will be achieved at time T, and bounded consistency will still be maintained when t > T.

[0086] It is worth noting that all the above parameters and constant gains can be designed independently in the control protocol of each agent, without relying on any global information or information from non-interactive agents.

[0087] Step 4: Obtain the observer-based, fully distributed multi-agent linear system's specified-time consistency control protocol. This control protocol consists of two parts: 1) a specified-time observer and 2) an edge-based adaptive controller. Specifically, no control is performed during the first D time period; only state observation is conducted. During the subsequent TD time period, the observer continues to operate and begins implementing control, ultimately achieving bounded consistency of the multi-agent system at time T.

[0088] Step 4.1: Obtain the specified time consistency control protocol for the observer-based fully distributed multi-agent linear system as follows:

[0089]

[0090] Among them, the feedback gain matrix K and the time-varying control gain Adaptive parameters and ε ij θ ij , ζ ij The design and selection of control parameters shall follow step 3-2;

[0091] Step 4.2: Design the Lyapunov function and derive and analyze the bounds that the system consistency reaches after a specified time. The Lyapunov function V is given as follows:

[0092]

[0093] in, η0 represents global information related to the multi-agent communication topology, and ε0 represents the information for all ε ij The minimum value of the parameter. The consistency error of the agent's state is represented by the Lyapunov function V, which can represent the sum of the consistency error of the multi-agent state and the parameter adaptation error.

[0094] Step 4.3: Taking the derivative of V and scaling it, we get:

[0095]

[0096] in, Using the comparison lemma, we can further obtain:

[0097]

[0098] At time t = T:

[0099]

[0100] in, ε0 is a designable parameter ε ij The minimum value of Φ can decrease as ε0 decreases. At a specified time T, the sum of the system's consistency error and adaptive parameter error, V(T), will also decrease as ε0 decreases.

[0101] When time t > T:

[0102]

[0103] From the above equation, it can be seen that after a specified time T, the sum of the system's consistency error and adaptive parameter error, V(t), will converge exponentially to the bound. Inside.

[0104] The embodiments of the present invention have been described in detail above with reference to the accompanying drawings, but the present invention is not limited to the described embodiments. For those skilled in the art, various changes, modifications, substitutions, and variations can be made to these embodiments without departing from the principles and spirit of the present invention, and these variations still fall within the protection scope of the present invention.

Claims

1. A method for time-based cooperative control of a high-order multi-agent system with an unknown state, characterized in that: Includes the following steps: Step 1: Set the total time to reach the desired bounded consistency as T, and set the time for accurate reconstruction of the agent's state information as D, satisfying D. <T; Step 2: Build a specified time observer for each agent; Step 3: Design a fully distributed, edge-based adaptive control protocol; Step 4: Obtain the specified time consistency control protocol for the observer-based fully distributed multi-agent linear system; Step two specifically includes: Step 2.1: The following is an example of a high-order linear multi-agent system with N agents: in, and These represent the n-dimensional state vector, p-dimensional control input vector, and q-dimensional measurement output vector of the i-th agent, respectively. and Both represent time-invariant system matrices, where (A,B) is controllable, and (A,C) is controllable. i For any It is observable; let x(t) = [x1(t)] T ,…,x N (t) T ] T And let x0 = x(0) represent the initial state; Step 2.2: Design two Lumborghäuser observers for each agent as follows: in, This represents the state value of the k-th Lumborghäuser observer for the i-th agent. This represents the corresponding Lumborghäuser observer gain, and the following symbol definitions are given: Among them, I n Representing the n-dimensional identity matrix, the two Lumborghäuser observers can be rewritten as: Step 2.3: Based on the Lumborghäuser observer state values ​​from Step 2.2, design the specified time observer as follows: Among them, e · Represents an exponential function. M represents the reconstructed value of the true state of the i-th agent. i represents the observer gain of the i-th agent at a specified time, and t0 represents the initial time. Step three specifically includes: Step 3.1: Reconstruct the state output based on the observer from Step 2 The following symbol definitions are given: Where i,j∈{1,2,…,N}, Let a represent the set of agents that communicate and interact with the i-th agent. ij Let a represent the interaction relationship between the i-th agent and the j-th agent. If an interaction exists, then a ij =1, if it does not exist, then a ij =0,q i This represents the consistency error between the reconstructed state value of the i-th agent and the agents with communication interactions. Step 3.2: Design an edge-based adaptive control protocol u i as follows: Where K represents the feedback gain matrix, Represents the time-varying control gain. ε represents the adaptive parameters based on agent interaction edges. ij θ ij , ζ ij Both represent designable control parameters, and the feedback gain matrix K is chosen as K = B. T P; P is the Riccati equation A T P+PA-PBB T The unique symmetric positive definite solution to P + Q = 0, where Q is any symmetric positive definite matrix. Parameter ζ ij The selection is ε ij The selection must satisfy ε ij >0, θ ij The selection satisfies θ ij If the value is greater than 0, bounded consistency will be achieved at time T, and bounded consistency will still be maintained when t>T. Step four specifically includes: Step 4.1: Obtain the specified time consistency control protocol for the observer-based fully distributed multi-agent linear system as follows: Among them, the feedback gain matrix K and the time-varying control gain Adaptive parameters and ε ij θ ij , ζ ij The design and selection of control parameters are the same as in step 3.2; Step 4.2: Design the Lyapunov function and derive and analyze the bounds that the system consistency reaches after a specified time. The Lyapunov function V is given as follows: in, η0 represents global information related to the multi-agent communication topology, and ε0 represents the information for all ε ij The minimum value of the parameter. The consistency error of the agent's state is represented by the Lyapunov function V, which can represent the sum of the consistency error of the multi-agent state and the parameter adaptation error. Step 4.3: Taking the derivative of V and scaling it, we get: in, Using the comparison lemma, we can further obtain: At time t = T: in, ε0 is a designable parameter ε ij The minimum value of Φ can decrease as ε0 decreases. At a specified time T, the sum of the system's consistency error and adaptive parameter error, V(T), will also decrease as ε0 decreases. When time t > T: From the above equation, it can be seen that after a specified time T, the sum of the system's consistency error and adaptive parameter error, V(t), will converge exponentially to the bound. Within η0.

2. The method for time-based cooperative control of a high-order multi-agent system with an unknown state according to claim 1, characterized in that: The control protocol in step four includes a time-specified observer and an edge-based adaptive controller.

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