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“Piecewise affine observer-based robust controllers for constrained nonlinear systems”

Authors: Lars Imsland, Olav Slupphaug and Bjarne A. Foss,
Affiliation: NTNU, Department of Engineering Cybernetics and ABB
Reference: 2001, Vol 22, No 4, pp. 211-225.

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Keywords: output feedback, robust nonlinear control, observer design, constrained systems, bilinear matrix inequalities

Abstract: For a general class of constrained uncertain nonlinear discrete-time systems, and a general class of observers, it is developed bilinear matrix inequalities whose solution gives gain matrices used in a piecewise afline observer/controller structure. The closed-loop system is robustly quadratically stable with a region of attraction larger than a prescribed ellipsoidal region. It is also developed a second-order algorithm for solving these inequalities locally.

PDF PDF (1623 Kb)        DOI: 10.4173/mic.2001.4.2

DOI forward links to this article:
  [1] Ya-Hui Gao, Zhi-Yuan Liu and Hong Chen (2010), doi:10.1002/asjc.207

[1] ALIZADEH, F., HAEBERLY, J.-P.A. OVERTON, M.L. (1998). Primal-dual interior-point methods for semidefinite programming: convergence rates, stability and numerical results, SIAM J. Optim. 8(3): 746-768 (electronic) doi:10.1137/S1052623496304700
[2] APKARIAN, P. TUAN. H.D. (1999). Concave Programming in Control Theory, Journal of Global Optimization 1.4: 343-370 doi:10.1023/A:1008385006172
[3] APKARIAN, P TUAN, H.D. (2000). Robust Control via Concave Minimization-Local and Global Algorithms, IEEE Transactions on Automatic Control 4.2: 299-305 doi:10.1109/9.839953
[4] ATASSI, A.N. KHALIL, H.K. (1999). A separation principle for the stabilization of a class of nonlinear systems, IEEE Trans. Automat. Control 4.9: 1672-1687 doi:10.1109/9.788534
[5] EL GHAOUI, L., OUSTRY, F. AITRAMI, M. (1997). A Cone Complementary Linearization Algorithm for Static Output-Feedback and Related Problems, IEEE Transactions on Automatic Control 4.8: 1171-6 doi:10.1109/9.618250
[6] FARES, B., APKARIAN, P. NOLL, D. (2001). An Augmented Lagrangian Method for a Class of LMI-Constrained Problems in Robust Control Theory, International Journal of Control 7.4: 348-360 doi:10.1080/00207170010010605
[7] IMSLAND, L., SLUPPHAUG, O. FOSS, B. A. (2001). Robust observer-based output feedback for nonlinear discrete-time systems with constraints, Proceedings of the 5th IFAC Nonlinear Control Systems Design Symposium.NOLCOS, St. Petersburg, Russia.
[8] KHALIL, H.K. (1996). Nonlinear Systems, 2nd edn, Prentice Hall, Upper Saddle River, NJ 07458.
[9] NESTEROV, Y. NEMIROVSKII, A. (1994). Interior-point Polynomial Algorithms in Convex Programming, vol. 13 of Studies in Applied Mathematics, SIAM, Philadelphia, PA.
[10] NOCEDAL, J. WRIGHT, S.J. (1999). Numerical optimization, Springer-Verlag, New York doi:10.1007/b98874
[11] SCOKAERT. P.O.M., RAWLINGS, J.B. MEADOWS, E.S. (1997). Discrete-time stability with perturbations: Application to model predictive control, Automatica 33(3): 463-70 doi:10.1016/S0005-1098(96)00213-0
[12] SLUPPHAUG O. FOSS, B. A. (1999). Constrained Quadratic Stabilization of Discrete-Time Uncertain Nonlinear Multi-Model Systems using Piecewise Mine State-Feedback, Int. J. of Control 7.718: 686-701.
[13] SLUPPHAUG, O., IMSLAND, L. FOSS, B.A. (2000). Uncertainty modelling and robust output feedback control of nonlinear discrete systems: a mathematical programming approach, International Journal of Robust and Nonlinear Control 1.13: 1129-1152.

  title={{Piecewise affine observer-based robust controllers for constrained nonlinear systems}},
  author={Imsland, Lars and Slupphaug, Olav and Foss, Bjarne A.},
  journal={Modeling, Identification and Control},
  publisher={Norwegian Society of Automatic Control}


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