Adaptive stochastic control for linear systems Part I: Solution method

The problem considered in this two-part paper deals with the control of linear, discrete-time, stochastic systems with unknown (possibly time-varying and random) gain parameters. The philosophy of control is based on the use of an open-loop-feedback-optimal (O.L.F.O.) control using a quadratic index of performance. In Part I it is shown that the O.L.F.O. system consists of (1) an identifier that estimates the system state variables and gain parameters, and (2) by a controller described by an "adaptive" gain and correction term. Several qualitative properties of the overall system are obtained from an interpretation of the equations. Part II deals with the asymptotic properties of the O.L.F.O. adaptive system and with simulation results dealing with the control of stable and unstable third order plants. Comparisons are carried out with the optimal system when the parameters are known. In addition, the simulation results are interpreted in the context of the qualitative conclusions reached in Part I.