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Observer design for dissipative multivalued dynamical systems

Bernard Brogliato 1 W.P. Maurice H. Heemels 2
1 BIPOP - Modelling, Simulation, Control and Optimization of Non-Smooth Dynamical Systems
Inria Grenoble - Rhône-Alpes, LJK [2007-2015] - Laboratoire Jean Kuntzmann [2007-2015], Grenoble INP [2007-2019] - Institut polytechnique de Grenoble - Grenoble Institute of Technology [2007-2019]
Abstract : This paper deals with the design of state observers for a class of systems with set-valued right-hand-sides. Two main classes of set-valued mappings are considered: maximal monotone and time-invariant; or normal cones to possibly time-varying sets (not necessarily convex). Such controlled systems can be embedded in various kinds of differential inclusions with absolutely continuous and bounded variation solutions (inclusions with maximal monotone multivalued mappings, and the perturbed Moreau's sweeping process), using a suitable state space transformation. The well-posedness properties of the observers dynamics are carefully analyzed. The stability of the observation error is proved. Then the problem of stabilization with a feedback control using the estimated state is studied in a particular case. Most of the results rely on rendering some suitable operator dissipative (or SPR in the linear case).
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https://hal.inria.fr/inria-00139576
Contributor : Bernard Brogliato <>
Submitted on : Monday, July 30, 2007 - 11:20:12 AM
Last modification on : Friday, July 17, 2020 - 11:38:57 AM
Long-term archiving on: : Tuesday, September 21, 2010 - 1:41:58 PM

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  • HAL Id : inria-00139576, version 2

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Bernard Brogliato, W.P. Maurice H. Heemels. Observer design for dissipative multivalued dynamical systems. [Research Report] 2007. ⟨inria-00139576v2⟩

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