A Comparison of Robust and Stochastic Receding Horizon Control

In this thesis we study receding horizon control strategies for stochastic discrete-time linear systems with additive noise. This study is divided into two parts: First, we compare the performance of different receding horizon control techniques under constrained and unconstrained control input settings for some representative systems. It appears from our simulations that while in an unconstrained setting the robust method performs worst and the infinite horizon LQ controller performs best, no concrete conclusions can be drawn in the constrained setting. Second, we provide new results on stochastic stability (in the sense of the system being mean-square bounded,) of some of the receding horizon controllers under mild assumptions. This is effected by appending “negative drift conditions” to the the optimization routines and establishing the overall feasibility. In addition, with the aid of numerical examples we substantiate our theoretical results by showing mean-square boundedness of typical systems for different controllers under our conditions.