Journal
IEEE TRANSACTIONS ON AUTOMATIC CONTROL
Volume 50, Issue 5, Pages 674-678Publisher
IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
DOI: 10.1109/TAC.2005.846597
Keywords
model predictive control; nonlinear control design; optimal control; receding horizon control
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We study the stability and region of attraction properties of a family of receding horizon schemes for nonlinear systems. Using Dini's theorem on the uniform convergence of functions, we show that there is always a finite horizon for which the corresponding receding horizon scheme is stabilizing without the use of a terminal cost or terminal constraints. After showing that optimal infinite horizon trajectories possess a uniform convergence property, we show that exponential stability may also be obtained with a sufficient horizon when an upper bound on the infinite horizon cost is used as terminal cost. Combining these important cases together with a sandwiching argument, we are able to conclude that exponential stability is obtained for input-constrained receding horizon schemes with a general nonnegative terminal cost for sufficiently long horizons. Region of attraction estimates are also included in each of the results.
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