Abstract
We present a general framework for analysis and design of optimization based numerical feedback stabilization schemes utilizing ideas from relaxed dynamic programming. The application of the framework is illustrated for a set valued and graph theoretic offline optimization algorithm and for receding horizon online optimization.
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Bardi, M., Capuzzo Dolcetta, I.: Optimal Control and Viscosity Solutions of Hamilton-Jacobi-Bellman equations. Birkhäuser, Boston (1997)
Bertsekas, D.P.: Dynamic Programming and Optimal Control, vol. 1,2. Athena Scientific, Belmont, MA (1995)
Camilli, F., Grüne, L., Wirth, F.: Control Lyapunov functions and Zubov’s method. In: SIAM J. Control Optim. (to appear, 2008)
Camilli, F., Grüne, L., Wirth, F.: A regularization of Zubov’s equation for robust domains of attraction. In: Treleaven, P.C., Nijman, A.J., de Bakker, J.W. (eds.) PARLE 1987. LNCS, vol. 258, pp. 277–290. Springer, Heidelberg (1987)
Grimm, G., Messina, M.J., Tuna, S.E., Teel, A.R.: Model predictive control: for want of a local control Lyapunov function, all is not lost. IEEE Trans. Automat. Control 50(5), 546–558 (2005)
Grüne, L.: Homogeneous state feedback stabilization of homogeneous systems. SIAM J. Control Optim. 38, 1288–1314 (2000)
Grüne, L.: An adaptive grid scheme for the discrete Hamilton–Jacobi–Bellman equation. Numer. Math. 75(3), 319–337 (1997)
Grüne, L., Junge, O.: A set oriented approach to optimal feedback stabilization. Syst. Control Lett. 54(2), 169–180 (2005)
Grüne, L., Junge, O.: Approximately optimal nonlinear stabilization with preservation of the Lyapunov function property. In: Proceedings of the 46th IEEE Conference on Decision and Control, New Orleans, Louisiana (2007)
Grüne, L., Junge, O.: Global optimal control of perturbed systems. J. Optim. Theory Appl. 136 (to appear, 2008)
Grüne, L., Nešić, D.: Optimization based stabilization of sampled–data nonlinear systems via their approximate discrete–time models. SIAM J. Control Optim. 42, 98–122 (2003)
Grüne, L., Nešić, D., Pannek, J.: Model predictive control for nonlinear sampled–data systems. In: Gianni, P. (ed.) ISSAC 1988. LNCS, vol. 358, Springer, Heidelberg (1989)
Grüne, L., Rantzer, A.: On the infinite horizon performance of receding horizon controllers. In: Preprint, Universitat Bayreuth, IEEE Trans. Automat. Control (2006) (to appear, 2008) www.math.uni-bayreuth.de/~lgruene/publ/infhorrhc.html
Jadbabaie, A., Hauser, J.: On the stability of receding horizon control with a general terminal cost. IEEE Trans. Automat. Control 50(5), 674–678 (2005)
Johansen, T.A.: Approximate explicit receding horizon control of constrained nonlinear systems. Automatica 40(2), 293–300 (2004)
Junge, O., Osinga, H.M.: A set oriented approach to global optimal control. ESAIM Control Optim. Calc. Var. 10(2), 259–270 (2004)
Kreisselmeier, G., Birkhölzer, T.: Numerical nonlinear regulator design. IEEE Trans. Autom. Control 39(1), 33–46 (1994)
Lincoln, B., Rantzer, A.: Relaxing dynamic programming. IEEE Trans. Autom. Control 51, 1249–1260 (2006)
von Lossow, M.: A min-max version of Dijkstra’s algorithm with application to perturbed optimal control problems. In: Proceedings of the GAMM Annual meeting, Zürich, Switzerland (to appear, 2007)
Rantzer, A.: Relaxed dynamic programming in switching systems. IEE Proceedings — Control Theory and Applications 153, 567–574 (2006)
Tuna, E.S.: Optimal regulation of homogeneous systems. Automatica 41(11), 1879–1890 (2005)
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Grüne, L. (2008). Optimization Based Stabilization of Nonlinear Control Systems. In: Lirkov, I., Margenov, S., Waśniewski, J. (eds) Large-Scale Scientific Computing. LSSC 2007. Lecture Notes in Computer Science, vol 4818. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-78827-0_5
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DOI: https://doi.org/10.1007/978-3-540-78827-0_5
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