Design of quasi-optimal minimum-time controllers

Abstract

This paper presents and evaluates a heuristic method for designing easily implemented quasi-optimal, minimum-time controllers for high-order dynamic systems. The high-performance, or quasi-optimal, controller is obtained by least-squares fitting points on the optimal switching surface with an easily implemented, linear-segment switching surface. This method is attractive because least-squares approximation is an analytic procedure which is readily applicable to high-order dynamic systems since it requires no visualization of the surface for its application. The method is applicable to linear dynamic systems with real characteristic frequencies as well as many other dynamic systems. For evaluation, the method has been used to design the switching surface for a triple-integrator dynamic system (i.e., <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1/s^{3}</tex> plant). A third-order system has been used, instead of a more easily portrayed second-order system, since it more typically illustrates the problems encountered in the approximation of higher-order switching surfaces. Typical response times for the quasi-optimal switching surface in this example are 1.5 to 2 times those of the minimum-time optimal switching surface and roughly one-half those of the best linear switching surface.