Optimal Consensus Control For Uncertain Nonlinear Multi-agent Systems

The optimal consensus control of multi-agent systems is: in the case where each agent only knows information about itself and its neighbors,designing a controller for each agent not only makes the state or output of each agent consistent,but also minimizes the performance function.Since nonlinearity and uncertainty exist widely in practical control systems,it is of great practical significance to study the optimal consensus control of uncertain nonlinear multi-agent systems.This paper studies the optimal state consensus control and optimal output consensus control of uncertain nonlinear multi-agent systems.The main research of this paper is as follows:First,this paper studies the optimal state consensus control of completely unknown nonlinear multi-agent systems.For the leader--followers nonlinear multi-agent systems whose states are measurable but whose dynamic models are completely unknown,firstly,fully distributed state observers are designed under the directed graph using the backstepping method and dynamic surface control method to observe the state of the leader.Then an observer state and a follower state are combined to construct an augmented state,and based on the augmented state system,a performance function containing a discount factor is reconstructed,and the policy iteration algorithm is used to solve the optimal controller that makes the augmented state system asymptotically stable and minimizes the performance function.In order to solve the problem that the policy iteration algorithm depends on the follower dynamic model,the policy iteration algorithm uses an integral reinforcement learning algorithm that does not rely on the leader and follower dynamic model.In order to solve the problem of dimensional disasters in the calculation process of the integral reinforcement learning algorithm,the performance function and controller in the integral reinforcement learning algorithm were estimated using the critic-actor neural networks,and the weights of the critic-actor neural networks were solved by the least square method.Finally,the feasibility of the algorithm is verified by simulations.Second,this paper studies the optimal output consensus control of partially unknown nonlinear multi-agent systems.For the nonlinear multi-agent systems where the states of the followers are unmeasurable,and the dynamic model of the followers are partially unknown and the dynamic model of the leader is completely unknown,the unknown internal functions in the followers dynamic model are first reconstructed based on neural network.Then based on the output feedback,a neural network state observer is designed to observe the unmeasurable state of the follower.Next,an augmented system is constructed using the follower state observer system and the leader state observer system.Based on the augmented system,a performance function including a discount factor is reconstructed.Then the policy iteration algorithm is used to solve the optimal controller that makes the augmented system asymptotically stable and minimizes the performance function.In order to solve the problem that the policy iteration algorithm relies on the dynamic model of the follower state observer system,the policy iteration algorithm uses an integral reinforcement learning algorithm that does not rely on the dynamic model of the leader state observer system and the follower state observer system.In order to solve the problem of dimensional disasters in the calculation of the policy iteration algorithm,the performance function and controller in the policy iteration algorithm were estimated using the critic-actor neural networks,and the adaptive laws of the estimated weights of the critic-actor neural networks were designed using the gradient descent method,and in this critic-actor neural networks,two weights can be adjusted simultaneously.Finally,the feasibility of the algorithm is verified by simulation.