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Unconstrained receding-horizon control of nonlinear systems

Jadbabaie, Ali and Yu, Jie and Hauser, John (2001) Unconstrained receding-horizon control of nonlinear systems. IEEE Transactions on Automatic Control, 46 (5). pp. 776-783. ISSN 0018-9286. http://resolver.caltech.edu/CaltechAUTHORS:JADieeetac01

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Abstract

It is well known that unconstrained infinite-horizon optimal control may be used to construct a stabilizing controller for a nonlinear system. We show that similar stabilization results may be achieved using unconstrained finite horizon optimal control. The key idea is to approximate the tail of the infinite horizon cost-to-go using, as terminal cost, an appropriate control Lyapunov function. Roughly speaking, the terminal control Lyapunov function (CLF) should provide an (incremental) upper bound on the cost. In this fashion, important stability characteristics may be retained without the use of terminal constraints such as those employed by a number of other researchers. The absence of constraints allows a significant speedup in computation. Furthermore, it is shown that in order to guarantee stability, it suffices to satisfy an improvement property, thereby relaxing the requirement that truly optimal trajectories be found. We provide a complete analysis of the stability and region of attraction/operation properties of receding horizon control strategies that utilize finite horizon approximations in the proposed class. It is shown that the guaranteed region of operation contains that of the CLF controller and may be made as large as desired by increasing the optimization horizon (restricted, of course, to the infinite horizon domain). Moreover, it is easily seen that both CLF and infinite-horizon optimal control approaches are limiting cases of our receding horizon strategy. The key results are illustrated using a familiar example, the inverted pendulum, where significant improvements in guaranteed region of operation and cost are noted.


Item Type:Article
Additional Information:© Copyright 2001 IEEE. "Personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution to servers or lists, or to reuse any copyrighted component of this work in other works must be obtained from the IEEE.” Manuscript received May 5, 1999; revised February 11, 2000 and October 4, 2000. Recommended by Associate Editor G. De Nicolao. This work was supported in part by AFOSR and DARPA.
Subject Keywords:Control Lyapunov functions (CLFs), model predictive control, nonlinear control design, optimal control, receding horizon control
Issue or Number:5
Record Number:CaltechAUTHORS:JADieeetac01
Persistent URL:http://resolver.caltech.edu/CaltechAUTHORS:JADieeetac01
Alternative URL:http://dx.doi.org/10.1109/9.920800
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:1285
Collection:CaltechAUTHORS
Deposited By: Archive Administrator
Deposited On:08 Jan 2006
Last Modified:15 Jan 2015 20:41

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