Constrained Control Design for Linear Systems with Geometric Adversary Constraints*

Inspired by some practical applications concerning collision avoidance topics, this paper focuses on the optimal control of linear dynamical systems in the presence of a set of adversary constraints. One of the novelties is the type of constraints introduced in the receding horizon optimization problem. These constraints can be considered as “adversary” by their non convex characteristics which make the convergence of the system dynamics towards the “zero” equilibrium position an impossible task. The present paper proposes a dual-mode control strategy which builds on an optimization based controller and a fixed constrained control law whenever the adversary constraints are activated. In order to illustrate the benefits of the proposed method, typical applications involving the control of multi-agent systems are considered.