Adaptive control for parabolic PDE based multi-agent systems

Abstract

In this paper, an adaptive controller is constructed to resolve the problem of consensus for nonlinear multi-agent systems described by partial differential equations. Firstly, the nonlinear terms existed in the considered system are approximated by neural networks. Secondly, a sufficient condition on the existence of the controller for consensus is presented in terms of linear matrix inequalities. On the basis of this, the adaptive controller is designed, and the closed-loop system is proved to be stable by applying the Lyapunov stability theory. Further, the consensus is achieved for nonlinear multi-agent systems. Finally, the effectiveness of the proposed control protocol is verified by simulation examples.

Keywords:

• Partial differential equations
• multi-agent systems
• consensus
• adaptive control

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This work is supported in part by the National Natural Science Foundation of China [grant numbers 62025303 and 62273171], and in part by the Innovation Fund for Production, Education and Research in Chinese Universities [grant number 2021ZYA02004].