Adaptive Pattern Classifiers Applied to Time Optimal Control

Abstract

This paper describes the adaptive methods to construct the optimal switching curves used for time optimal control of second order processes. Three types of adaptive pattern classifiers can be used, i.e.(1) gradient-variable piecewise linear, (2) zone-variable piecewise linear and (3) non-linear pattern classifiers. The adaptation logic introduced in this paper is based on the time course of geometrical relation between the state point and the switching curve in the state plane of the process and can be applied to the processes at work. The methods need neither a priori information of the process nor identifying it. Besides they are likewise applicable to both linear and nonlinear processes. It is shown that are arbitrary switching curve is adaptively optimalized, and that by the iterative application of this on-line adaptation, approximated optimal control can be realized.