The value of plant model information available in the control design processis discussed. We design optimal state-feedback controllers for interconnecteddiscrete-time linear systems with stochastically-varying parameters. Theparameters are assumed to be independently and identically distributed randomvariables in time. The design of each controller relies only on (i) exact localplant model information and (ii) statistical beliefs about the model of therest of the system. We consider both finite-horizon and infinite-horizonquadratic cost functions. The optimal state-feedback controller is derived inboth cases. The optimal controller is shown to be linear in the state and todepend on the model parameters and their statistics in a particular way.Furthermore, we study the value of model information in optimal control designusing the performance degradation ratio which is defined as the supremum (overall possible initial conditions) of the ratio of the cost of the optimalcontroller with limited model information scaled by the cost of the optimalcontroller with full model information. An upper bound for the performancedegradation ratio is presented for the case of fully-actuated subsystems.Comparisons are made between designs based on limited, statistical, and fullmodel information. Throughout the paper, we use a power network example toillustrate concepts and results.
展开▼
