Linear-Quadratic Optimal Control for Hybrid Systems with State-driven Jumps
In this paper, we lay preliminary foundations towards the comprehensive formulation, together with some constructive results, of the Linear-Quadratic (LQ) optimal control problem for hybrid systems in the presence of state-driven jumps. This objective is achieved by introducing the notion of N-jump optimal control law in terms of a policy that minimizes a certain (quadratic) cost functional and, at the same time, is capable of inducing N (state-driven) jumps of the resulting closed-loop hybrid system.