Stochastic behavior of optimum systems with jump parameters

This paper presents an analysis of an optimally controlled linear plant subjected to additive random distrubances and jump type parameter uncertainties. In practice, these jump type parameter uncertainties arise whenever the system goes through some sudden changes in the environmental conditions, or suffers a loss of some component in the plant and/or controller parameters. The dynamic behavior of the state covariance and control covariance matrices are studied following jump type uncertainties in the process parameters. It is shown that the state covariance matrix is the solution of a first-order matrix differential equation. As an example, theoretical and experimental results are obtained for the attitude control of a satellite tracking a stellar object and subjected to the following type of additive disturbing turques: (a) Gaussian white noise: (b) Gaussian colored noise, and (c) sinusoidal signals.