38,697 research outputs found
Delay-dependent exponential stability of neutral stochastic delay systems (vol 54, pg 147, 2009)
In the above titled paper originally published in vol. 54, no. 1, pp. 147-152) of IEEE Transactions on Automatic Control, there were some typographical errors in inequalities. Corrections are presented here
Exponential stability of a class of boundary control systems
We study a class of partial differential equations (with variable coefficients) on a one dimensional spatial domain with control and observation at the boundary. For this class of systems we provide simple tools to check exponential stability. This class is general enough to include models of flexible structures, traveling waves, heat exchangers, and bioreactors among others. The result is based on the use of a generating function (the energy for physical systems) and an inequality condition at the boundary. Furthermore, based on the port Hamiltonian approach, we give a constructive method to reduce this inequality to a simple matrix inequality
Invariant Measures for Dissipative Dynamical Systems: Abstract Results and Applications
In this work we study certain invariant measures that can be associated to
the time averaged observation of a broad class of dissipative semigroups via
the notion of a generalized Banach limit. Consider an arbitrary complete
separable metric space which is acted on by any continuous semigroup
. Suppose that possesses a global
attractor . We show that, for any generalized Banach limit
and any distribution of initial
conditions , that there exists an invariant probability measure
, whose support is contained in , such that for all
observables living in a suitable function space of continuous mappings
on .
This work is based on a functional analytic framework simplifying and
generalizing previous works in this direction. In particular our results rely
on the novel use of a general but elementary topological observation, valid in
any metric space, which concerns the growth of continuous functions in the
neighborhood of compact sets. In the case when does not
possess a compact absorbing set, this lemma allows us to sidestep the use of
weak compactness arguments which require the imposition of cumbersome weak
continuity conditions and limits the phase space to the case of a reflexive
Banach space. Two examples of concrete dynamical systems where the semigroup is
known to be non-compact are examined in detail.Comment: To appear in Communications in Mathematical Physic
On controlled linear diffusions with delay in a model of optimal advertising under uncertainty with memory effects
We consider a class of dynamic advertising problems under uncertainty in the
presence of carryover and distributed forgetting effects, generalizing a
classical model of Nerlove and Arrow. In particular, we allow the dynamics of
the product goodwill to depend on its past values, as well as previous
advertising levels. Building on previous work of two of the authors, the
optimal advertising model is formulated as an infinite dimensional stochastic
control problem. We obtain (partial) regularity as well as approximation
results for the corresponding value function. Under specific structural
assumptions we study the effects of delays on the value function and optimal
strategy. In the absence of carryover effects, since the value function and the
optimal advertising policy can be characterized in terms of the solution of the
associated HJB equation, we obtain sharper characterizations of the optimal
policy.Comment: numerical example added; minor revision
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