Predictive Controllers for Feedback Stabilization

Predictive control is a strategy where the current control action is based on a prediction of the system response at some number of time steps 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 approach where the state variable is involved explicitly in the controller design and implementation.A connection is provided between the two design approachesby showing that simple predictive controllers can be thought of as generalizations of the observer-based deadbeat (minimumtime) controllers in discrete-time state-space theory.The excessive and, hence, impractical control effort demanded by the standard deadbeat controllers is removed in this predictive extension. By varying the prediction horizon, controllers that range from those exhibiting the extreme deadbeat behavior to those approximatingthe minimumenergy 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 controllers can be derived directly from the coefŽ cients of an identiŽ ed input–outputmodel,whichhasbeen recently shownto subsume an implicit observer. It is also shown that the two primary parameters of a predictive controller can be understood in the state-space framework as those governing the speed of an implicit observer and the speed of an implicit state-feedback controller. This understandingallows one to select optimal choices for these parameters in practice.