Abstract
It is well known as the optimal control problem with discontinuity that whenever the system trajectories hit the boundary either of the state variable constraint sets or of the sub-regions on the state space, the equations describing the system change.
In this paper, a computational algorithm is given which solves this problem numerically for linear sampled-data systems. Also the theoretical background is presented to show that this algorithm is a modification of the optimization method of Vector Performances. This algorithm has two phases, referred to as Algorithms I and II. The sample instants when the system trajectories hit the boundary of the state variable constraint sets are determined by Algorithm I. Then the given objective function is optimized subject to the input and the state variable constraints by Algorithm II with the aid of the fixed sample instants using Algorithm I.
The characteristics of this algorithm are as follows. This problem is of the decomposed type, but Varaiya's decomposition algorithm can not be used here. However the singular control problem arising in problems of this type can be dealt with by iterative computation. The convergence of this algorithm is exactly the same as that of Vector Performances Optimization Algorithm.
