Discrete Time Optimal Control Systems

Abstract

This chapter highlights discrete time optimal control systems. The optimal control system is formulated by considering a control system whose state at any time t is described by an n -dimensional vector function x (t). The coordinates of x are sometimes referred to as phase coordinates. The chapter is restricted to control functions that arise in so-called sampled-data control systems. Thus, one shall suppose that a sampling period Τ is given beforehand and that u(t) is constant for ( i — 1) T ≤ t ≤ i T ( i = 1, 2 …). The chapter describes methods for computing these optimal discrete controls. Under appropriate restrictions, time optimal discrete controls approach the continuous time optimal control if the sampling period is allowed to go to zero. To distinguish among discrete admissible controls with different sampling periods, a function given by equation is a discrete admissible control function with period T.