Convergence of discrete-time approximations of constrained linear-quadratic optimal control problems
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KünyeHan, L., Çamlıbel, M. K., Pang, J., & Heemels, W. P. M. H. (2010). Convergence of discrete-time approximations of constrained linear-quadratic optimal control problems. In 2010 49th IEEE Conference on Decision and Control (CDC) (pp. 5210-5215). Piscataway, NJ: IEEE. http://dx.doi.org/10.1109/CDC.2010.5717381
Continuous-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.