Abstract
In this paper robustness analysis and synthesis of state-feedback nonlinear Receding-Horizon (RH) control schemes is considered. In particular, robustness properties based on the monotonicity of the cost function and on inverse optimality are discussed. A particular attention is devoted to a new RH synthesis approach based on the solution of a finite-horizon dynamic game. This control law guarantees that the L 2 gain of the closed-loop is less than or equal to a given number γ in a prescribed neighbourhood of the equilibrium state.
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R. Bitmead, M. Gevers, I. Petersen, and R.J. Kaye. Monotonicity and stabilizability properties of solutions of the Riccati difference equation: Propositions, lemmas, theorems, fallacious conjectures and counterexamples. System & Control Letters, 5:309–315, 1985.
R. Bitmead, M. Gevers, and V. Wertz. Adaptive Optimal Control: The Thinking Man's GPC. Prentice Hall, 1990.
C. Chen and L. Shaw. On receding horizon feedback control. Automatica, 18(3):349–352, 1982.
H. Chen and F. Algöwer. A quasi-infinite horizon nonlinear model predictive control scheme with guaranteed stability. Automatica, 34:1205–1217, 1998.
H. Chen, C. Scherer, and F. Allgöwer. A game theoretical approach to nonlinear robust receding horizon control of constrained systems. In American Control Conference’ 97, 1997.
H. Chen, C. Scherer, and F. Allgöwer. A robust model predictive control scheme for constrained linear systems. In Proc. DYCOPS 5, Corfu, Greece, 1998.
D. Chmielewski and V. Manousiouthakis. On constrained infinite-time linear quadratic optimal control. System & Control Letters, 29:121–129, 1996.
D. Clarke, C. Mothadi, and P. Tuffs. Generalized predictive control-part I and II. Automatica, 23:137–160, 1987.
D. Clarke and R. Scattolini. Constrained receding horizon predictive control. Proc. IEE Part D, 138:347–354, 1991.
C. Cuttler and B. Ramaker. Dynamic matrix control-a computer control algorithm. In Automatic Control Conference, 1980.
G. De Nicolao, L. Magni, and R. Scattolini. On the robustness of receding-horizon control with terminal constraints. IEEE Trans. Automatic Control, 41:451–453, 1996.
G. De Nicolao, L. Magni, and R. Scattolini. Stabilizing predictive control of nonlinear ARX models. Automatica, 33:1691–1697, 1997.
G. De Nicolao, L. Magni, and R. Scattolini. Stability and robustness of nonlinear receding-horizon control. In NMPC Workshop — Assessment and Future Directions, pages 77–90, Ascona, Switzerland, 1998.
G. De Nicolao, L. Magni, and R. Scattolini. Stabilizing receding-horizon control of nonlinear time-varying systems. IEEE Trans. on Automatic Control, AC-43:1030–1036, 1998.
S. Glad. Robustness of nonlinear state feedback-a survey. Automatica, 23:425–435, 1987.
S. Keerthi and E. Gilbert. Optimal, infinite-horizon feedback laws for a general class of constrained discrete-time systems. J. Optimiz. Th. Appl., 57:265–293, 1988.
W. Kwon and A. Pearson. On feedback stabilization of time-varying discrete-linear systems. IEEE Trans. on Automatic Control, 23:479–481, 1978.
S. Lall and K. Glover. A game theoretic approach to moving horizon control. In D. Clarke, editor, Advances in Model-Based Predictive Control, pages 131–144. Oxford University Press, 1994.
W. Lin and C. Byrnes. H ∞-control of discrete-time nonlinear systems. IEEE Trans. on Automatic Control, pages 494–510, 1996.
L. Magni, G. De Nicolao, and R. Scattolini. Output feedback receding-horizon control of discrete-time nonlinear systems. In IFAC Nonlinear Control Systems Design Symposium. Enschede, The Netherlands, 1998.
L. Magni, G. De Nicolao, R. Scattolini, and F. Allgöwer. H ∞ receding horizon control for nonlinear discrete-time systems. Submitted to Systems & Control Letters.
L. Magni, H. Nijmeijer, and A. van der Schaft. A receding-horizon approach to the nonlinear H ∞ control problem. Submitted to Automatica.
L. Magni and R. Sepulchre. Stability margins of nonlinear receding horizon control via inverse optimality. System & Control Letters, 32:241–245, 1997.
D. Mayne and H. Michalska. Receding horizon control of nonlinear systems. IEEE Trans. on automatic Control, 35:814–824, 1990.
H. Michalska and D. Mayne. Robust receding horizon control of constrained nonlinear systems. IEEE Trans on Automatic Control, 38:1512–1516, 1993.
E. Mosca and J. Zhang. Stable redesign of predictive control. Automatica, 28:1229–1233, 1992.
T. Parisini and R. Zoppoli. A receding-horizon regulator for nonlinear systems and a neural approximation. Automatica, 31:1443–1451, 1995.
M. Poubelle, R. Bitmead, and M. Gevers. Fake algebraic riccati technique and stability. IEEE Trans. on Automatic Control, (33):379–381, 1988.
J. Rawlings and K. Muske. The stability of constrained receding horizon control. IEEE Trans on Automatic Control, 38:1512–1516, 1993.
P. Scokaert and D. Mayne. Min-max feedback model predictive control for constrained linear systems. IEEE Trans. on Automatic Control, 43:1136–1142, 1998.
P. Scokaert and J. Rawlings. Constrained linear quadratic regulation. IEEE Transactions on Automatic Control, 43:1163–1169, 1998.
P. Scokaert, J. Rawlings, and E. Meadows. Discrete-time stability with perturbations: Application to model predictive control. Automatica, 33:463–470, 1997.
R. Sepulchre, M. Jankovic, and P. Kokotovic. Constructive Nonlinear Control. Springer-Verlag, 1996.
M. Sznaier and M. Damborg. Control of constrained discrete time linear systems using quantized controls. Automatica, 25:623–628, 1989.
G. Tadmor. Receding horizon revisited: An easy way to robustly stabilize an LTV system. System & Control Letters, 18:285–294, 1992.
T. Vincent and W. Grantham. Nonlinear and Optimal Control Systems. John Wiley & Sons, 1997.
T. Yang and E. Polak. Moving horizon control of nonlinear systems with input saturation, disturbances and plant uncertainty. Int. J. Control, 58:875–903, 1993.
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De Nicolao, G., Magni, L., Scattolini, R. (1999). Robustness of receding horizon control for nonlinear discrete-time systems. In: Garulli, A., Tesi, A. (eds) Robustness in identification and control. Lecture Notes in Control and Information Sciences, vol 245. Springer, London. https://doi.org/10.1007/BFb0109883
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DOI: https://doi.org/10.1007/BFb0109883
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