Optimization of systems with pulse-width-modulated control

The problem of finding pulse-width-modulated signals which provide optimal control for a specified plant is considered. A set of necessary conditions which must be satisfied by the optimal control is derived using the calculus of variations. A steepest-descent procedure is developed to obtain a numerical solution to the resulting nonlinear two-point boundary value problem. Special features of the numerical procedure are automatic step size adjustment and the generation of a sequence of performance indices which is monotonic. An example which illustrates the range of application is given.