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In this paper we present some mathematical analysis of dynamic (PDE) models of suspension bridges as proposed by Lazer and McKenna. Our results are illustrated by numerical simulation with physical interpretation. 1. Introduction. In [1] Lazer and McKenna studied the problem of nonlinear oscillation in a suspension bridge. They presented a (one-dimensional)(More)
The relation between nonanticipative Rate Distortion Function (RDF) and filtering theory is discussed on abstract spaces. The relation is established by imposing a realizability constraint on the reconstruction conditional distribution of the classical RDF. Existence of the extremum solution of the nonanticipative RDF is shown using weak *-convergence on(More)
In this paper, we present two methods which generalize static team theory to dynamic team theory, in the context of continuous-time stochastic nonlinear differential decentralized decision systems, with relaxed strategies, which are measurable to different noisy information structures. For both methods we apply Girsanov's measure transformation to obtain an(More)
In this second part of our two-part paper, we invoke the stochastic maximum principle, conditional Hamiltonian and the coupled backward-forward stochastic differential equations of the first part [1] to derive team optimal decentralized strategies for distributed stochastic differential systems with noiseless information structures. We present examples of(More)
This paper is concerned with optimization of uncertain stochastic systems, in which uncertainty is described by a total variation distance constraint between the measures induced by the uncertain systems and the measure induced by the nominal system, while the pay-off is a linear functional of the uncertain measure. Robustness at the abstract setting is(More)
In this paper we consider minimax games for stochastic uncertain systems with the pay-off being a nonlinear functional of the uncertain measure where the uncertainty is measured in terms of relative entropy between the uncertain and the nominal measure. The maximizing player is the uncertain measure, while the mini-mizer is the control which induces a(More)
— This paper considers minimax problems, in which the control minimizes the pay-off induced by a measure which maximizes the pay-off over the class of measures described by a relative entropy set between the uncertain and the true measure. We present several basic properties of the relative entropy on infinite dimensional spaces, and then we apply them to(More)
— In this paper we present two methods for decentralized optimization of continuous and discrete-time stochastic dynamic decision systems, with multiple decision makers having nonclassical information structures. For both methods we apply Girsanov's change of measure to transform such problems into equivalent optimization problems, under a reference(More)