PREDICTIVE CONTROLLERS FOR FEEDBACK STABILIZATION

Predictive control is a strategy where the current control action is b ased on a prediction of the system response at some number of time ste ps into the future. This approach allows one to work directly with an input-output model of the system, in contrast to a state-space based a pproach where the state variable is involved explicitly in the control ler design and implementation. A connection is provided between the tw o design approaches by showing that simple predictive controllers can be thought of as generalizations of the observer-based deadbeat (minim um-time) controllers in discrete time state-space theory. The excessiv e and, hence, impractical control effort demanded by the standard dead beat controllers is removed in this predictive extension. By varying t he prediction horizon, controllers that range from those exhibiting th e extreme deadbeat behavior to those approximating the minimum-energy solution are subsumed in a common framework. Although these predictive controllers can be understood as observer based, no explicit observer is actually involved in the implementation. Instead, these controller s can be derived directly from the coefficients of an identified input -output model, which has been rec entry shown to subsume an implicit o bserver. It is also shown that the two primary parameters of a predict ive controller can be understood in the state-space framework as those governing the speed of an implicit observer and the speed of an impli cit state-feedback controller. This understanding allows one to select optimal choices for these parameters in practice.