Quadratic Programming for Continuous Control of Safety-Critical Multiagent Systems Under Uncertainty

Abstract

This paper studies the control problem for safety-critical multi-agent systems based on quadratic programming (QP). Each controlled agent is modeled as a cascade connection of an integrator and an uncertain nonlinear actuation system. In particular, the integrator represents the position-velocity relation, and the actuation system describes the dynamic response of the actual velocity to the velocity reference signal. The notion of input-to-output stability (IOS) is employed to characterize the essential velocity-tracking capability of the actuation system. The standard QP algorithms for collision avoidance may be infeasible due to uncertain actuator dynamics. Even if feasible, the solutions may be non-Lipschitz because of possible violation of the full rank condition of the active constraints. Also, the interaction between the controlled integrator and the uncertain actuator dynamics may lead to significant robustness issues. Based on the current development of nonlinear control theory and numerical optimization methods, this paper first contributes a new feasible-set reshaping technique and a refined QP algorithm for feasibility, robustness, and local Lipschitz continuity. Then, we present a nonlinear small-gain analysis to handle the inherent interaction for guaranteed safety of the closed-loop multi-agent system. The proposed method is illustrated by numerical simulation and a physical experiment.