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Set-valued observers and optimal disturbance rejection. (English) Zbl 0958.93013

The guaranteed state estimation problem for a discrete-time linear time-varying system is studied. Based on an a priori model of initial conditions and exogenous signals, a set-valued observer is constructed. This observer computes the set of all states consistent with measured output data. It is shown that the centers of these sets provide optimal estimates in an \(l^\infty\)-induced norm sense. Next, the disturbance rejection problem is considered. It shown that an optimal controller can consist of a set-valued observer followed by a static nonlinear function defined on the observed set of possible states. An explicit construction of a controller of this type is proposed for the case of a scalar control and for the case of a full control. An illustrative example of a set-valued observer is also presented.

MSC:

93B07 Observability
93C73 Perturbations in control/observation systems
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