On the Limit Behavior for Multi-Agent Dynamical Systems

This paper dresses the optimal control of multiple linear agents in the presence of a set of adversary constraints. This type of constraints makes the convergence of the agents’ dynamics towards the “natural” equilibrium position, impossible to fulfill. Therefore, this default equilibrium point has to be replaced by a set of equilibrium points or even accept the existence of limit cycles. Furthermore, the constraints introduced in the transitory optimization problem are non convex. The present paper proposes a dual-mode control strategy which switches between an unconstrained optimum controller and a constrained control law whenever the adversary constraints are activated. The proposed method builds on invariance concepts and proves to be related to eigenstructure assignment problems. The technique exhibits effective performance and is validated here by an illustrative example.