Distributed optimal integrated tracking control for uncertain non-holonomic mobile multi-agents

What is it about?

This paper addresses a distributed optimal integrated tracking control method with disturbance rejection for separate kinematic and dynamic uncertain nonholonomic mobile mechanical multi-agent ($\mathbf{NM^3}$) systems. Initially, based on the graph theory, the overall tracking systems of agents are defined and the distributed optimal tracking problem of separate kinematics and dynamics is transformed into an equivalent distributed optimal regulation problem of the integrated affine system. Then, neural network (NN)-based adaptive dynamic programming and cooperative differential game theory is utilized for control in which only one NN is required for each agent. The NN weight-tuning law and the online algorithm is developed to approximate the value function, and synchronously update both optimal control and worst disturbance laws in only one iterative loop. The tracking errors and function approximation errors are proven to be uniformly ultimately bounded using Lyapunov theory. Finally, as applications of the proposed method, control of the wheeled mobile multi-robot system is discussed. The effectiveness of the method is demonstrated by the results of the comparative numerical simulation.

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Why is it important?

- The distributed optimal tracking control problem of the separate kinematic and dynamic uncertain nonholonomic mobile multiagent systems is transformed into the distributed optimal regulation stabilization problem of the integrated kinematic and dynamic affine multiagent system. - Via adaptive dynamic programming and concept of cooperative differential game theory, the new algorithm for distributed optimal tracking control with disturbance rejection for all neighboring relations is proposed. This algorithm uses only one neural network (NN) for each agent. Furthermore, the algorithm does not require any knowledge of system internal dynamics. - The system parameter convergences to the approximately optimal values are guaranteed, and the distributed tracking errors, along with the NN approximation errors, are proved to be uniformly ultimately bounded by Lyapunov theory.