Structure of large stochastic optimal and suboptimal systems

The optimal stochastic regulator is derived for systems which can be decomposed into subsystems with measurable state varibles and subsystems in which only noisy output measurements are available. The solution involves direct state feedback from the former subsystems and feedback via a set of Kalman filters for the latter subsystems. The total order of the Kalman filters equals that of the unmeasurable subsystems. The use of direct state feedback rather than state-estimate feedback is very desirable: the system becomes more robust, nonlinearities have less effect and, since Kalman filter are not needed for these subsystems, modelling errors are reduced. Having decomposed a large system, it is natural to ask whether subsystems can be started and controlled independently before the complete feedback control is applied. Conditions are determined where a sequential start-up procedure for the optimal system is possible. Simplifications to the structure of the controllers for servomechanisms are also considered.