
Accession Number : ADP002949
Title : On the Control of a Linear Stochastic System with Finite Horizon,
Corporate Author : WAYNE STATE UNIV DETROIT MI DEPT OF MATHEMATICS
Personal Author(s) : Chow,P. L. ; Menaldi,J. L.
Report Date : FEB 1984
Pagination or Media Count : 10
Abstract : We consider a dynamic system whose state is governed by a linear stochastic differential equation with timedependent coefficients. The control acts additively on the state of the system. Our objective is to minimize an integral cost which depends upon the evolution of the state and the total variation of the control process. It is proved that the optimal cost is the unique solution of an appropriate free boundary problem in a spacetime domain. By using some decomposition arguments, the problems of a twosided control, i.e. optimal corrections, and the case with constraints on the resources, i.e. finite fuel, can be reduced to a simpler case of only onesided control, i.e. a monotone follower. These results are applied to solving some examples by the socalled method of similarity solutions. (Author)
Descriptors : *Stochastic processes, *Linear differential equations, *Control systems, Optimization, Dynamics, Decomposition, Time dependence, Coefficients, Corrections, Problem solving, Dynamics, Stochastic control, Random variables, Theorems
Distribution Statement : APPROVED FOR PUBLIC RELEASE