Design of Optimal Sampled-Data Control Systems Using the Gradient Projection Method

Abstract

This paper is concerned with the design of the optimal controller for a sampled-data control system. Supposing that the plant is linear, time-invariant, and has a saturating input, then, the system is described by its state transition equation as follows;
x_k+1=Gx_kk+hu_k
|u_k|≤1, k=0, 1, 2, ….
Consider a quadratic performance criteria of the form
J_N=x_N'Qx_N
where, _N is a given positive integer and is the final sampling instant at which the control action terminates. The problem is to find the admissible control sequence {u_k}^N-1_k=0 which minimizes J_N for a given initial state and _N.
In this paper, _N-dimentional control space is introduced, and the gradient projection method proposed by J.B. Rosen is used to find the solution in the control space. It is shown that an algorithm to find the solution can be constructed in a sample fashion by means of the gradent projection method.
Finally, a numerical example is given to illustrate the proposed algorithm.