Observability Analysis and Observer Design for Complex Dynamical Systems

Gang Zheng 1, 2
1 NON-A - Non-Asymptotic estimation for online systems
CRIStAL - Centre de Recherche en Informatique, Signal et Automatique de Lille (CRIStAL) - UMR 9189, Inria Lille - Nord Europe
Abstract : Different types of dynamical systems have been widely used to model different plants to be controlled in many different disciplines. Although control is the final goal in the control theory, given a concrete model, the designed controller sometimes could depend not only on the output, but also its internal states. This motivates us to study whether it is possible to reconstruct system’s internal states by using external measurements, named as the problem of observability analysis and observer design. This manuscript will summarize our obtained results on observability analysis and observer design for three types of dynamical systems, respectively in three parts. Part I studies the observability analysis and observer design for ordinary systems in continuous time, where the differential geometrical approach and the technique of immersion are used to study the observation problem. Finite-time and interval observers are proposed for time-continues systems. The second Part of this manuscript concerns the observability analysis and observer design for singular system. For linear singular system, the observability will be analyzed by using elementary algebraic method, while the differential geometrical method is extended to study nonlinear singular system. Luenberger-like and interval observers are studied for different types nonlinear singular systems. The observability analysis and observer design for time-delay system is considered in Part III. By introducing delay operator, the backward (causal) and forward (non-causal) unknown input observability are defined. Sufficient conditions are given to investigate the observability of a quite general linear/nonlinear time delay system with unknown inputs. Luenberger-like observer is also studied for linear time-delay systems.
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Habilitation à diriger des recherches
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Gang Zheng. Observability Analysis and Observer Design for Complex Dynamical Systems. Automatic Control Engineering. Universite Lille 1, 2015. ⟨tel-01258527v2⟩

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