Adaptive neural control for a class of random nonlinear Markov jump multi-agent systems with full state constraints

Abstract

This paper proposes a consensus control protocol based on the adaptive backstepping technique for a class of random Markov jump multi-agent systems (MASs) with full state constraints. Each agent is described by the high-order random nonlinear uncertain system driven by random differential equations, where the random noise is the second-order stationary stochastic process. First, a distributed tracking controller is designed for Markov jump MASs, effectively handling the interaction and coupling terms between agents. Second, an appropriate tan-type barrier Lyapunov function is selected to keep the agents’ states from the violation of constraint boundaries, and the unknown nonlinear terms with Markov jump parameters are approximated by neural networks (NNs) theory. Moreover, to address the differential explosion problem, the extended state observer (ESO) is first introduced instead of employing NNs approximation or command filtering techniques. Finally, the exponentially noise-to-state stability in mean square is proved rigorously through the Lyapunov method, which guarantees all signals of the closed-loop system are bounded in probability and the tracking error converges to a small neighborhood around zero. Simulations are given to demonstrate the feasibility of theoretical results.