Convergence of discrete-time approximations of constrained linear-quadratic optimal control problems

Çamlıbel, Mehmet Kanat (Dogus Author) -- Conference full title: 2010 49th IEEE Conference on Decision and Control, CDC 2010; Atlanta, GA; United States; 15 December 2010 through 17 December 2010Continuous-time linear constrained optimal control problems are in practice often solved using discretization techniques, e.g. in model predictive control (MPC). This requires the discretization of the (linear time-invariant) dynamics and the cost functional leading to discrete-time optimization problems. Although the question of convergence of the sequence of optimal controls, obtained by solving the discretized problems, to the true optimal continuous-time control signal when the discretization parameter (the sampling interval) approaches zero has been addressed in the literature, we provide some new results under less restrictive assumptions for a class of constrained continuous-time linear quadratic (LQ) problems with mixed state-control constraints by exploiting results from mathematical programming extensively. As a byproduct of our analysis, a regularity result regarding the costate trajectory is also presented