Simplified Switching Functions for Time-Optimal Control Systems

摘要

A method is given to derive simplified switching functions for the design of third or higher order, time-optimal control systems. The type of system, that is considered, is characterized by small parameters which increase the order of the system. The sensitivity functions with respect to these small parameters has been the main tool of analysis. Two existing methods have been used to determine special initial conditions for the sensitivity equations because these equations are discontinuous at t = 0. It is shown that the same methods can be applied to deal with the discontinuity of the sensitivity functions at the switching time by a transformation of the original system. This investigation above all demonstrates how sensitivity functions with respect to small parameters, that change the system order, can be used to greatly simplify the analysis of higher order systems.