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

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4 Author(s)
Han, L. ; Dept. of Ind. & Enterprise Syst. Eng., Univ. of Illinois at Urbana-Champaign, Urbana, IL, USA ; Camlibel, M.K. ; Pang, J.-S. ; Heemels, W.P.M.H.

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.

Published in:

Decision and Control (CDC), 2010 49th IEEE Conference on

Date of Conference:

15-17 Dec. 2010