Distributed cooperative H_∞ optimal tracking control of MIMO nonlinear multi-agent systems in strict-feedback form via adaptive dynamic programming

ABSTRACT

The design of distributed cooperative H_∞ optimal controllers for multi-agent systems is a major challenge when the agents’ models are uncertain multi-input and multi-output nonlinear systems in strict-feedback form in the presence of external disturbances. In this paper, first, the distributed cooperative H_∞ 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 stabilising controllers. It is shown that despite not 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.

KEYWORDS:

• Nonlinear systems in strict-feedback form
• cooperative H_∞ optimal control
• adaptive dynamic programming
• zero-sum differential graphical game

Disclosure statement

No potential conflict of interest was reported by the authors.