Optimal Control of Systems With Generalized Poisson Inputs

Abstract

This paper discusses the optimal control of systems having known dynamics with command and disturbance inputs which may be described as generalized Poisson processes. An engineering interpretation of the physical nature of Poisson processes is given, with brief comments on their use as mathematical models of practical situations. Representative examples of partial differential equations of optimal control are quoted. Explicit solutions of the control equations are given for the following systems with quadratic performance indexes: (a) The general linear system with linear Poisson inputs; (b) a linear regulator with a quadratically nonlinear Poisson disturbance; (c) a linear regulator with a random step-wave disturbance.