Optimal Regulation of a Class of Linear Stochastic Systems Relative to Quadratic Criteria

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Abstract
A method of optimally regulating a class of stochastic linear systems relative to quadratic performance criteria is presented. The class of stochastic systems considered are those whose dynamics are described by an nth order stochastic linear differential equation. The system input is passed through a randomly varying gain. The control function is taken to be unconstrained in magnitude. The stochastic processes treated are increments of Brownian motion and generalized Poisson. A deterministic optimal feedback control is obtained. This control is a function of time, the state vector and the system parameters (both deterministic and stochastic). All results are derived using Bellman's continuous dynamic programming.

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