Fake Riccati equations for stable receding-horizon control

In a number of engineering problems, finite-horizon schemes such as predictive control and Receding-Horizon (RH) control are more convenient than infinite-horizon optimal control because computations can be reduced and saturations and constraints are more easily allowed for. Starting from the mid eighties, the introduction of the so called fake Riccati equation together with the study of the monotonicity and cyclomonotonicity properties of the solutions of the Riccati equation provided a unifying framework for analysing the stability of linear RH controllers. The paper gives an overview of the main results concerning fake Riccati equations. In particular, a fake H_∞ Riccati equation is used to point out the prospects and pitfalls of H_∞, RH control.