Numerical Solution of Linear-Quadratic Optimal Control Problems for Switching System

In this paper we obtained an approach to the optimal switching control problem with unknown switching points which it is described in reference [1, 2]. In reference [1], the authors studied the Decomposition of Linear-Quadratic Optimal Control Problems for Two-Steps Systems. In [1], the authors assumed the switching point t1 is fixed in the interval for state equation and boundary of the integral of the minimization functional an algorithm is given for solving the Linear-Quadratic Optimal Control Problem. But in present paper we assume a more general case, in the case in which the switching point is unknown and, by using transformation, the main problem is reduced to a problem with a known interval and unknown boundary of the integral in the minimization functional is reduced to the known one, which is defined in [1, 2]. This is illustrated by an example at the end of the paper. Then by using the Gradient Projection Method Algorithm, the problem is solved numerically by the authors.