Tuning of Gaussian stochastic control systems

A closed-loop system consisting of a control system and an adaptive controller is called tuning for a specified control objective if the real system and the ideal system defined below achieve the same value for the control objective. The real system is the system consisting of the unknown control system in closed loop with the adaptive controller in which the parameters of the adaptive controller have been determined by identification under feedback or in closed loop. The ideal system is the system consisting of the unknown control system in closed loop with a controller in which the controller has been synthesized with knowledge of the unknown control system and such that the closed-loop system satisfies the control objective. Both the Gaussian stochastic control system with full observations and with partial observations are considered. The approach to the problem is based on stochastic realization theory for Gaussian systems. The control objectives of minimum variance control and pole placement are also given. Necessary conditions for tuning are discussed