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Abstract:
The development of set-theoretic methods and the associated theoretical concepts found applications in various domains, such as robust control, predictive control and fault diagnosis. The aim of this talk is to revisit the classical concepts and to present novel trends for the specific class of time-delay systems and further in fault diagnosis and fault-tolerant control.
The basic idea will be to use the strong concept of positive invariance for the characterization of particular classes of dynamical systems. In the case of linear discrete-time dynamical systems affected by delays, the positive invariance allow different formulations according to the state space representation. It will be shown that set-factorization represent a generalized framework for their characterization. The links with the stability will be also discussed.
The positive invariance of sets characterizing the nominal and the abnormal dynamic behavior will be shown to present a particular interest for the diagnosis of the control systems (with particular exemplification of multi-sensor systems) via set separation. From a broader theoretical perspective, we point to the link between the diagnosis and the control law design. It is shown that the Fault Tolerant Control can be enhanced by a reference governor or a predictive control scheme which adapts the state trajectory and the feedback control action in view of active fault detection.
Abstract:
Interval observers generate upper bounds and lower bounds of state
variables of dynamical systems at each time instant based on given
information about bounds of unknown disturbances and of unknown initial
conditions. The aim of this talk is to revisit a class of nonlinear systems
and to introduce new interval observer designs for that class. In the first
part of the present talk, we consider continuous-time nonlinear systems
with measurements which are available only at discrete instants. Employing
the structure of Luenberger-type observers, we construct continuous-time framers
of state variables in the presence of disturbances. Framers and state variables
converge to each other completely when the maximum time interval of
measurements is sufficiently small in the absence of disturbances.
The second part considers output feedback control design in addition to
interval observer design to simultaneously monitor and stabilize
nonlinear systems. The framework of integral input-to-state stability is
exploited to drive the estimated intervals and the state variables to the
origin asymptotically when disturbances converge to zero.
Moreover, benefit of tuning interval observers with feedback gain is discussed.
In estimating intervals, designing reduced-order observers is shown to be
useful, compared with full-order ones.
Finally, comparative simulations are given to illustrate the
theoretical results.