Linear Optimal Control of a Linear System With State and Control Dependent Noise

[+] Author and Article Information
P. J. McLane

Department of Electrical Engineering, Queen’s University, Kingston, Ontario; Department of Electrical Engineering of the University of Toronto, Toronto, Ontario, Canada

J. Dyn. Sys., Meas., Control 94(1), 34-40 (Mar 01, 1972) (7 pages) doi:10.1115/1.3426539 History: Received January 10, 1972; Online July 13, 2010


A quadratic minimization problem for a linear stochastic system is solved in this paper. Both the finite and infinite terminal time cases are considered. Also two precise representations of the controlled stochastic process are considered. In one representation we include the correction term [6] for the state and control-dependent noise and in the other we do not. For the case with no correction terms, the optimal control is shown to be a linear feedback of the system state variables. Uniqueness and stability conditions are presented for this problem. The case with correction term is much harder to solve and we only determine the linear optimal control. An example is included which illustrates many results of the paper.

Copyright © 1972 by ASME
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