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1
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Robust Control of Linear Stochastic Systems with Fully Observable State

100%
Poznyak A. S., Taksar M. I.
Applicationes Mathematicae
|
1996-1997
|
tom 24
|
nr 1
35-46
EN
We consider a multidimensional linear system with additive inputs (control) and Brownian noise. There is a cost associated with each control. The aim is to minimize the cost. However, we work with the model in which the parameters of the system may change in time and in addition the exact form of these parameters is not known, only intervals within which they vary are given. In the situation where minimization of a functional over the class of admissible controls makes no sense since the value of such a functional is different for different systems within the class, we should deal not with a single problem but with a family of problems. The objective in such a setting is twofold. First, we intend to establish existence of a state feedback linear robust control which stabilizes any system within the class. Then among all robust controls we find the one which yields the lowest bound on the cost within the class of all systems under consideration. We give the answer in terms of a solution to a matrix Riccati equation and we present necessary and sufficient conditions for such a solution to exist. We also state a criterion when the obtained bound on the cost is sharp, that is, the control we construct is actually a solution to the minimax problem.
2
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Computer-aided modeling and simulation of electrical circuits with α-stable noise

88%
Weron A.
Applicationes Mathematicae
|
1995-1996
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tom 23
|
nr 1
83-93
EN
The aim of this paper is to demonstrate how the appropriate numerical, statistical and computer techniques can be successfully applied to the construction of approximate solutions of stochastic differential equations modeling some engineering systems subject to large disturbances. In particular, the evolution in time of densities of stochastic processes solving such problems is discussed.
3
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Measure valued solutions for stochastic evolution equations on Hilbert space and their feedback control

88%
Ahmed N.
Discussiones Mathematicae, Differential Inclusions, Control and Optimization
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2005
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tom 25
|
nr 1
129-157
EN
In this paper, we consider a class of semilinear stochastic evolution equations on Hilbert space driven by a stochastic vector measure. The nonlinear terms are assumed to be merely continuous and bounded on bounded sets. We prove the existence of measure valued solutions generalizing some earlier results of the author. As a corollary, an existence result of a measure solution for a forward Kolmogorov equation with unbounded operator valued coefficients is obtained. The main result is further extended to cover Borel measurable drift and diffusion which are assumed to be bounded on bounded sets. Also we consider control problems for these systems and present several results on the existence of optimal feedback controls.
4
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Stochastic diffrential equations on Banach spaces and their optimal feedback control

75%
Discussiones Mathematicae, Differential Inclusions, Control and Optimization
|
2012
|
tom 32
|
nr 1
87-109
EN
In this paper we consider stochastic differential equations on Banach spaces (not Hilbert). The system is semilinear and the principal operator generating a C₀-semigroup is perturbed by a class of bounded linear operators considered as feedback operators from an admissible set. We consider the corresponding family of measure valued functions and present sufficient conditions for weak compactness. Then we consider applications of this result to several interesting optimal feedback control problems. We present results on existence of optimal feedback operators.
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