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.

Keywords::

• discretes-time systems
• minimum-time
• optimal control
• HUM method

2000 Mathematics Subject Classifications::

• 93C05
• 93C55
• 49J15