On Maximizing the Convergence Rate

Abstract

Fast response is always a desired property for control systems. The time optimal control problem was formulated for this purpose. Although it is well known that the time optimal control is a bang-bang control, this control strategy is rarely implemented in real systems. The main reason is that it is generally impossible to characterize the switching surface. For discrete-time systems, online computation has been proposed in the literature, but the computation burden is very heavy since linear programming has to be solved recursively with increasing time-horizon. Also, as the time-horizon is extended, numerical problems become more severe. Another reason is that even if the optimal control can be obtained exactly and efficiently, it results in open-loop control