The linear quadratic minimum-time problem for a class of discrete systems

Abstract

We consider a linear discrete-time systems controlled by inputs on L 2([0, t N ], U), where (t i )1 ≤ i ≤ N is a given sequence of times. The final time t N (or N) is considered to be free. Given an initial state x 0 and a final one x d , we investigate the optimal control which steers the system from x 0 to x d with a minimal cost J(N, u) that includes the final time and energy terms. We treat this problem for both infinte and finite dimensional state space. We use a method similar to the Hilbert Uniqueness Method. A numerical simulation is given.