Optimal stochastic control of linear systems with state- and control-dependent disturbances

A review of the solution of the linear regulator problem for linear systems with state- and control-dependent disturbances is presented. Both the finite and infinite terminal time cases are treated. The solution to the complete state feedback case is given in detail and that for the output feedback case is noted. The general conclusion is that control-dependent noise calls for conservative control (small gains) while state-dependent noise calls for vigorous control (large gains). Of course it is the degree of this behavior that is important and this is given explicitly by the algorithms in this paper.