Consensus Control for High-Order Multiagent Systems With Multiple Nonconvex State Constraints

This article addresses a consensus problem for high-order multiagent systems with multiple nonconvex state constraints. The main challenge is how to deal with different kinds of nonlinearities caused by the nonconvex state constraints and the complex relevance of the multiple kinds of state constraints. To solve the consensus problem with multiple nonconvex state constraints, we propose a distributed control algorithm for the discrete-time high-order multiagent systems and introduce time-varying scaling factors to transform the original constrained system into an equivalent time-varying one. Then, by constructing a Lyapunov function and utilizing the matrix norm of the time-varying system matrix, it is proved that consensus can be reached while the states of agents are constrained to lie in the nonconvex sets. Finally, numerical examples are included to demonstrate the effectiveness of conclusions.