Receding horizon schemes for controls, estimations, and optimizations

This paper surveys some recent developments on the receding horizon scheme. We deal with mathematical models such as state space models of continuous variable systems and controlled Markov chains (CMC) of discrete event systems (DES). Common design objectives are addressed in order to achieve good properties and performance indices are described in terms of mathematical models. In this paper, we focus on the schemes with the receding horizon performance criteria and its advantages are discussed. Receding horizon schemes are introduced for both minimization and minimaximization criteria. In the case of state space models, we first start from a general nonlinear system and move to a linear system. Specially, we introduce the state feedback and the output feedback receding horizon controls with receding horizon estimators. A linear time delay and I/O systems are also discussed for applicability of the receding horizon scheme. For controlled Markov chains of discrete event systems, we also introduce receding horizon policies for average reward criteria and two person zero sum games.