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Unconstrained receding-horizon control of nonlinear systems. (English) Zbl 1009.93028
A complete analysis of the region of attraction/operation of receding horizon control strategies which utilize finite horizon approximations is provided. The important relationships between an infinite horizon optimal control problem and its finite horizon approximations are explored. It is shown that the receding horizon control strategy, which uses the control Lyapunov function (CLF) as terminal cost, and the ideal infinite-horizon control strategies are limiting cases of the proposed strategies. Furthermore, the guaranteed region of operation contains that of the CLF controller and may be made as large as desired by increasing the optimization horizon. In order to guarantee stability, it suffices to satisfy an improvement property. Also, the absence of terminal constraints allows a significant speedup in calculations. The main result is illustrated using the problem of balancing an inverted pendulum on a cart.

##### MSC:
 93B51 Design techniques (robust design, computer-aided design, etc.) 93D05 Lyapunov and other classical stabilities (Lagrange, Poisson, $$L^p, l^p$$, etc.) in control theory 93D15 Stabilization of systems by feedback
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