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We consider the stabilization of
Maxwell's equations with space-time variable coefficients
in a bounded region with a smooth boundary
by means of linear or nonlinear Silver–Müller boundary condition.
This is based on some stability estimates
that are obtained using the “standard" identity with multiplier
and appropriate properties of the feedback.
We deduce an explicit decay rate of the energy, for instance
exponential,
polynomial or logarithmic decays are available for appropriate
feedbacks.
...
We consider boundary value problems for semilinear evolution inclusions. We establish the existence of extremal solutions. Using that result, we show that the evolution inclusion has periodic extremal trajectories. These results are then applied to closed loop control systems. Finally, an example of a semilinear parabolic distributed parameter control system is worked out in detail.
We consider the differential game associated with robust control of a
system in a compact state domain, using Skorokhod dynamics on the
boundary. A specific class of problems motivated by queueing network control
is considered. A constructive approach to the Hamilton-Jacobi-Isaacs
equation is developed which is based on an appropriate family of
extremals, including boundary extremals for which the Skorokhod
dynamics are active. A number of technical lemmas and a structured
verification theorem...
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