Abstract
Recent advances in computer technology have spurred new interest in the use of feedback controllers based upon on-line minimization for the control of constrained linear systems. Still the use of computers in the feedback loop has been hampered by the fact that the amount of time available for computation in most sampled data systems is not enough to achieve a complete solution using conventional algorithms. Several “ ad hoc” techniques have been proposed, but their applicability is restricted by the lack of supporting theory. In this paper we present a theoretical framework to analyze the stability of the closed-loop system resulting from the use of on-line optimization in the feedback loop. Using these results we show that a suboptimal algorithm, based upon the use of heuristic search techniques, yields asymptotically stable systems, provided that enough computation power is available to solve at each sampling interval an optimization problem considerably simpler than the original. The controller presented in this paper is valuable for situations where the customary approaches of using Pontryagin's minimum principle or storing a family of extremal curves are not applicable due to limitations in the computational resources available.
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