Assessment and Future Directions of Nonlinear Model Predictive ...

On Disturbance Attenuation of Nonlinear Moving Horizon Control 293performance level when large disturbances inclusive of reference changes vanish.Moreover, we observe the clear and large violation of x e (t) T P k x e (t) ≤ r c inthe bottom right of Fig. 1. This confirms the advantages of the suggested movinghorizon tracking algorithm in avoiding infeasibility and reducing conservatismin handling time-domain constraints.5 ConclusionsIn this paper, the disturbance attenuation issue of nonlinear moving horizoncontrol has been addressed. By extending the dissipation constraint in a generalnon-quadratic form, a conceptual minimax moving horizon formulation issuggested and theoretical results on closed-loop dissipation, L 2 disturbance attenuationand stability are discussed. The implementation issue is attacked withrespect to tracking a reference trajectory in the presence of external disturbancesand control constraints. A computationally tractable algorithm is given in theframework of LMI optimization and applied to the reference tracking control ofthe CSTR. As revealed in the title, the results of this paper might be preliminary.Further works are required either to build a rigorous theoretical basis orto achieve non-conservative and computationally tractable algorithms.AcknowledgementThe work is supported by the National Nature Science Foundation China (No60374027) and by Program for New Century Excellent Talents in University.References[ABQ99] F. Allgöwer, T. A. Badgwell, J. S. Qin, J. B. Rawlings, and S. J. Wright,“Nonlinear predictive control and moving horizon estimation - An introductoryoverview,” in Advances in Control, Highlights of ECC’99 (P. Frank, ed.),pp. 391–449, Springer Verlag, (1999).[BM99] A. Bemporad and M. Morari, “Robust model predictive control: A survey,”in Robustness in Identification and Control, Lecture Notes in Control andInformation Sciences, vol. 245 (A. V. A. Garulli, A. Tesi, ed.), pp. 207–226,Springer-Verlag, (1999).[MRR00] D. Q. Mayne, J. B. Rawlings, C. V. Rao, and P. O. M. Scokaert, “Constrainedmodel predictive control: Stability and optimality,” Automatica,vol. 36, no. 6, pp. 789–814, (2000).[SM98] P. O. M. Scokaert and D. Q. Mayne, “Min-max feedback model predictivecontrol for constrained linear systems,” IEEE Trans. Automat. Contr.,vol. 43, no. 8, pp. 1136–1142, (1998).[BBM01] A. Bemporad, F. Borrelli, and M. Morari, “Robust model predictive control:piecewise linear explicit solution,” in Proc. European Control Conf., (Porto,Portugal), pp. 939–944, (2001).[LK94] S. Lall and K. Glover, “A game theoretic approach to moving horizon control,”in Advances in Model-Based Predictive Control (D. Clarke, ed.), OxfordUniversity Press, (1994).