Discrete Walsh polynomials in the optimal control of linear digital time-varying systems

Abstract

The discrete Walsh polynomials are applied to solve the digital optimal control of time-varying systems in this study. Due to the elegant properties of operational matrices of discrete Walsh polynomials, the class of digital time-varying problems can be analysed successfully. The design algorithms of digital optimal control are based on the discrete variational principle combined with the idea of a penalty function to obtain directly computational formulations for evaluating the optimal control and state trajectory. An example is given to illustrate the usefulness of the method, and the results are very accurate.