Locally optimal controllers and globally inverse optimal controllers |
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| Affiliation: | 1. Université Lyon 1, Villeurbanne, France;2. CNRS, UMR 5007, LAGEP. 43 bd du 11 novembre, 69100 Villeurbanne, France;3. GIPSA-lab, Grenoble Campus, 11 rue des Mathématiques, BP 46, 38402 Saint Martin d’Hères Cedex, France;1. LaBRI UMR 5800, Université de Bordeaux F-33400 Talence, France;2. VERIMAG UMR 5104, Université Grenoble Alpes, Grenoble, France;1. Institute for Mathematics and Scientific Computing, Karl-Franzens-Universität Graz, Heinrichstr. 36, 8010 Graz, Austria;2. Institute of Mathematics, Alpen-Adria-Universität Klagenfurt, Universitätsstr. 65–67, 9020 Klagenfurt, Austria;1. INRIA Bordeaux Sud-Ouest, Campus Bordeaux 1, 33405 Talence, France;2. LIRYC, L’Institut de RYthmologie et modélisation Cardiaque, Bordeaux, France;3. LE2I CNRS UMR 6306, Université de Bourgogne, Dijon, France |
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| Abstract: | In this paper we consider the problem of global asymptotic stabilization with prescribed local behavior. We show that this problem can be formulated in terms of control Lyapunov functions. Moreover, we show that if the local control law has been synthesized employing an LQ approach, then the associated Lyapunov function can be seen as the value function of an optimal problem with some specific local properties. We illustrate these results on two specific classes of systems: backstepping and feedforward systems. Finally, we show how this framework can be employed when considering the orbital transfer problem. |
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| Keywords: | Lyapunov function Nonlinear systems Optimal control LQ |
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