Suboptimal control of minimum-time linear discrete systems†

An on-line digital computer scheme that generates time-suboptimal control policies for discrete systems is described. The scheme is based upon solving the minimum-effort discrete problem using linear programming, where the number of sampling periods used depends on the available computation time. It is established that the suboptimal control policies generated through that scheme result in transferring the discrete system from any initial state to the origin in a finite number of sampling periods. Furthermore, the time delay that resulted from the usage of an on-line digital computer is overcome by incorporating a feedback signal to control the system during the first few sampling periods. Computational results are furnished to illustrate the efficacy of the proposed suboptimal policies.