Observability Analysis and Observer Design for Complex Dynamical Systems
Résumé
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.
Domaines
Automatique
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