In this paper, a method of synthesizing an optimal control system is presented, which has an asymptotic stability region about the objective point and performs time optimal control out of the region. Only such an optimal system seems to serve as a realizable time optimal control system taking account for unavoidable noise.
First, it is shown that the problem treated in this paper is ascribable to the optimal problem with some different criterions according to the regions in the state space and then the solution_method for the class of the optimal problem is mentioned. Next, the condition required to the criterion function so that the asymptotic stability region may be secured about the origin as well as the theoretical condition for the shape of the boundary of the asymptotic stability region is clarified. It is also shown that the asymptotic stability region is analytically given for the linear system by adopting quadratic criterion function in the region.
In the example, the optimal control law of this problem for a simple second order system is obtained and the detail of this method is shown.