Piecewise-Linear Switching Surfaces for Minimum Time Control.

• Main Author: Redderson, Roy Henry.
• Other Authors: NA
• Language: en_US
• Published: Monterey, California. U.S. Naval Postgraduate School 2013
• Online Access: http://hdl.handle.net/10945/28450

Procedures for designing piecewise-linear (PWL) switching surfaces for minimum time control are investigated. The approach is to generate the switching function using the instantaneous values of the states as inputs to easily realized PWL function generators. The design problem is then one of fitting the state space PWL surface to points defining the optimal surface. Several performance indices related to minimum-time are defined and the resulting parameter surfaces for different initial condition distributions are studied. However, because of local minima, a successful search procedure could not be found. Therefore, a heuristic method of least squares fitting is used. A combination gradient and generalized Newton-Raphson search method is employed to obtain values for the PWL parameters. Several least squares fit methods are applied to a second order problem and the results compared using response time performance to a uniform grid of initial conditions. Very close to optimal performance is achieved using a delay time design procedure.