On the Approximation of Constrained Linear Quadratic Regulator Problems and their Application to Model Predictive Control

This article is concerned with the approximation of constrained continuous-time linear quadratic regulator problems, which are, for example, encountered in model predictive control. By representing input and state trajectories using basis functions, the underlying infinite-dimensional optimal control problems are reduced to convex finite-dimensional optimization problems that can be solved efficiently. The article quantifies the suboptimality and establishes convergence of the obtained approximations. The results are applied in the context of model predictive control. In particular, it will be shown that the truncation of the prediction horizon can be avoided, leading to recursive feasibility and closed-loop stability guarantees. On a quadruple integrator system, the resulting model predictive control algorithm is shown to outperform state-of-the-art algorithms in terms of average execution time needed to achieve a certain performance