## Receding Horizon Control of Nonlinear Systems: A Control . . . (2000)

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Citations: | 46 - 4 self |

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@MISC{Jadbabaie00recedinghorizon,

author = {Ali Jadbabaie},

title = {Receding Horizon Control of Nonlinear Systems: A Control . . .},

year = {2000}

}

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### Abstract

n Automatic Control, pages 898 907, 1990. J. Shamma and M. Athans. Guaranteed properties of gain scheduled control for linear parameter-varying plants. Automatica, pages 559 564, 1991. J. Shamma and M. Athans. Gain-scheduling: Potential hazards and possible remedies. IEEE Control Systems Magazine, 12(3):101 107, June 1992. [Sch96] A. Schwartz. Theory and Implementation of Numerical Methods Based on Runge-Kutta Integration for Optimal Control Problems. PhD Disser- tation, University of California, Berkeley, 1996. [SCH+00] M. Sznaier, J. Cloutier, R. Hull, D. Jacques, and C. Mracek. Reced- ing horizon control lyapunov function approach to suboptimal regula- tion of nonlinear systems. Journal of Guidance, Control, and Dynamics, 23(3):399 405, 2000. [SD90] M. Sznaier and M. J. Damborg. Heuristically enhanced feedback con- trol of constrained discrete-time linear systems. Automatica, 26:521 532, 1990. [SMR99] P. Scokaert, D. Mayne, and J. Rawlings. Suboptimal model predictive cont

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Citation Context ...uitable neighborhood of the origin and then the control law is switched to a locally stabilizing linear controller. Another approach proposed by Parsini and Zopolli [8] and later by Chen and Allgower =-=[2]-=-, is based on using a quadratic terminal cost of the form ax(t + T ) T Px(t + T ) for some a ? 0 and some positive definite matrix P . In a more recent paper by De Nicolao et al. [7] stability of the ... |

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Robust Receding Horizon Control of Constrained Nonlinear Systems
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Citation Context ...Gilbert [3] imposed a terminal state equality constraint x(t + T ) = 0. This would result in a finite-horizon optimization problem which turns out to be computationally demanding. Michalska and Mayne =-=[5]-=- ensured closed-loop stability by requiring that x(t + T ) enters a suitable neighborhood of the origin and then the control law is switched to a locally stabilizing linear controller. Another approac... |

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Citation Context ...e shown that the existence of a CLF for the system (1) is equivalent to the existence of a globally asymptotically stabilizing control law u = k(x) which is smooth everywhere except possibly at x = 0 =-=[1]-=-. Moreover, one can calculate such a control law k when the system is affine in control, i.e. f(x; u) = ~ f(x) + g(x)u, explicitly from ~ f , g and V [11]. In the next section, we assume that a CLF an... |

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Citation Context ...nt methods to guarantee the closed-loop stability of the RecedOn leave from University of Colorado at Boulder ing horizon scheme, some of which will be summarized in what follows: Keerthi and Gilbert =-=[3]-=- imposed a terminal state equality constraint x(t + T ) = 0. This would result in a finite-horizon optimization problem which turns out to be computationally demanding. Michalska and Mayne [5] ensured... |

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51 | Guaranteed properties of gain scheduled control for linear parameter varying plants. Automatica - Shamma, Athans - 1991 |

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Stabilizing RecedingHorizon Control of Nonlinear Time-Varying Systems
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Citation Context ...Chen and Allgower [2], is based on using a quadratic terminal cost of the form ax(t + T ) T Px(t + T ) for some a ? 0 and some positive definite matrix P . In a more recent paper by De Nicolao et al. =-=[7]-=- stability of the receding horizon controller is guaranteed by using a possibly non quadratic end point penalty which is the cost incurred if a locally stabilizing linear control law is applied at the... |

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Citation Context ... such as F18-HARV or X-31 in forward flight [9]. This system has been used for a number of studies and papers. In particular, a comparison of several linear and nonlinear controllers was performed in =-=[4, 2, 11]-=-. In this section we describe the simple planar model of the fan shown in Figure 1 which ignores the stand dynamics. This model is useful for initial controller design and would serve as a good testbe... |

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