Pulse-frequency modulation and dynamic programming

The application of dynamic programming to pulse-frequency modulated (PFM) control systems is discussed. In the PFM systems considered the control function consists of a series of standard pulses. Because, in general, the peformance index is not Markovian, which is a requirement for the application of dynamic programming, a restriction is imposed upon the control function. This restriction, which specifies the allowable instants of time where pulses may occur, may cause the resulting control function to yield a less desirable performance index than the one obtained with a control function derived by means which do not impose this restriction, i.e., modified maximum principle [8], [9]. An example belonging to a class of systems in which the equations are separable and linear with respect to the state variables, with no final value constraints is presented. It is shown that for this class of systems the optimum control function is independent of the initial values of the state variables. Consequently, the search for the optimum control function is simplified.