Optimal Stationary Control of Linear Systems with Control-dependent Noise

Authors

David L. Kleinman

Year

1969

Journal Paper

Algorithm

Stochastic LQR

Source

IEEE Transactions on Automatic Control

Identifiers

DOI 10.1109/TAC.1969.1099303

Abstract¶

Optimal stochastic control is investigated for linear systems in which the intensity of the driving noise is proportional to control input. Conditions are given under which an optimal control always exists. It is shown that the optimal control is linear in the system state. A convergent algorithm is developed for computing the optimal feedback gains.

Summary¶

Kleinman studies optimal stationary control for linear systems whose driving noise intensity depends on the control input. The paper proves that the optimal controller is linear in the state and gives a convergent algorithm for computing the feedback gains, extending LQR-style synthesis to a control-dependent multiplicative-noise setting.