Distributed optimal integrated tracking control

What is it about?

1. Transforming a distributed cooperative H_\infty optimal tracking control problem of a MIMO nonlinear multi--agent system in strict-feedback form into a problem of optimally stabilizing a nonlinear multi--agent system in affine form with cooperative tracking error as the state vector. 2. Development of a novel totally distributed cooperative H_\infty optimal tracking control scheme via ADP and the theory of the multi--players zero--sum differential graphical game. Herein, only one NN for each agent is required to reduce computational complexity as well as avoid choosing appropriate initial NN weights for stabilizing controllers. 3. Design of novel NN weight-tuning laws and online control algorithms without using knowledge of cooperative internal dynamics. In the algorithms, updating the NN weights occurs in only one iterative loop. 4. Analyzing the stability of the closed-loop system and the convergence of control and disturbance policies to the Nash equilibrium by Lyapunov theory.

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Why is it important?

The design of distributed cooperative H_\infty optimal controllers for multi--agent systems is a major challenge when the agents' models are uncertain multi--input and multi--output (MIMO) nonlinear systems in strict--feedback form in the presence of external disturbances. In this paper, first, the distributed cooperative H_\infty optimal tracking problem is transformed into controlling the cooperative tracking error dynamics in affine form. Second, control schemes and online algorithms are proposed via adaptive dynamic programming (ADP) and the theory of zero--sum differential graphical games. The schemes use only one neural network (NN) for each agent instead of three from ADP to reduce computational complexity as well as avoid choosing initial NN weights for stabilizing controllers. It is shown that despite no using knowledge of cooperative internal dynamics, the proposed algorithms not only approximate values to Nash equilibrium but also guarantee all signals, such as the NN weight approximation errors and the cooperative tracking errors in the closed-loop system, to be uniformly ultimately bounded. Finally, the effectiveness of the proposed method is shown by simulation results of an application to wheeled mobile multi--robot systems.