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LMI optimization problem of delay-dependent robust stability criteria for stochastic systems with polytopic and linear fractional uncertainties

100%
Balasubramaniam P., Lakshmanan S., Rakkiyappan R.
International Journal of Applied Mathematics and Computer Science
|
2012
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tom 22
|
nr 2
339-351
EN
This paper studies an LMI optimization problem of delay-dependent robust stability criteria for stochastic systems with polytopic and linear fractional uncertainties. The delay is assumed to be time-varying and belong to a given interval, which means that lower and upper bounds of this interval time-varying delay are available. The uncertainty under consideration includes polytopic-type uncertainty and linear fractional norm-bounded uncertainty. Based on the new Lyapunov-Krasovskii functional, some inequality techniques and stochastic stability theory, delay-dependent stability criteria are obtained in terms of Linear Matrix Inequalities (LMIs). Moreover, the derivative of time delays is allowed to take any value. Finally, four numerical examples are given to illustrate the effectiveness of the proposed method and to show an improvement over some results found in the literature.
2
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Optimal control of ∞-dimensional stochastic systems via generalized solutions of HJB equations

88%
Ahmed N.
Discussiones Mathematicae, Differential Inclusions, Control and Optimization
|
2001
|
tom 21
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nr 1
97-126
EN
In this paper, we consider optimal feedback control for stochastc infinite dimensional systems. We present some new results on the solution of associated HJB equations in infinite dimensional Hilbert spaces. In the process, we have also developed some new mathematical tools involving distributions on Hilbert spaces which may have many other interesting applications in other fields. We conclude with an application to optimal stationary feedback control.
3
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Impulsive perturbation of C₀-semigroups and stochastic evolution inclusions

75%
Ahmed N.
Discussiones Mathematicae, Differential Inclusions, Control and Optimization
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2002
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tom 22
|
nr 1
125-149
EN
In this paper, we consider a class of infinite dimensional stochastic impulsive evolution inclusions. We prove existence of solutions and study properties of the solution set. It is also indicated how these results can be used in the study of control systems driven by vector measures.
4
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Optimal control of impulsive stochastic evolution inclusions

75%
Ahmed N.
Discussiones Mathematicae, Differential Inclusions, Control and Optimization
|
2002
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tom 22
|
nr 2
155-184
EN
In this paper, we consider a class of infinite dimensional stochastic impulsive evolution inclusions driven by vector measures. We use stochastic vector measures as controls adapted to an increasing family of complete sigma algebras and prove the existence of optimal controls.
5
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Infinite dimensional uncertain dynamic systems on Banach spaces and their optimal output feedback control

75%
Ahmed N.
Discussiones Mathematicae, Differential Inclusions, Control and Optimization
|
2015
|
tom 35
|
nr 1
65-87
EN
In this paper we consider a class of partially observed semilinear dynamic systems on infinite dimensional Banach spaces subject to dynamic and measurement uncertainty. The problem is to find an output feedback control law, an operator valued function, that minimizes the maximum risk. We present a result on the existence of an optimal (output feedback) operator valued function in the presence of uncertainty in the system as well as measurement. We also consider uncertain stochastic systems and present similar results on the question of existence of optimal feedback laws.
6
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Topological dual of $B_∞(I,𝓛 ₁(X,Y))$ with application to stochastic systems on Hilbert space

63%
Ahmed N.
Discussiones Mathematicae, Differential Inclusions, Control and Optimization
|
2009
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tom 29
|
nr 1
67-90
EN
In this paper, we prove that the topological dual of the Banach space of bounded measurable functions with values in the space of nuclear operators, furnished with the natural topology, is isometrically isomorphic to the space of finitely additive linear operator-valued measures having bounded variation in a Banach space containing the space of bounded linear operators. This is then applied to a stochastic structural control problem. An optimal operator-valued measure, considered as the structural control, is to be chosen so as to minimize fluctuation (volatility). Both existence of optimal policy and necessary conditions of optimality are presented including a conceptual algorithm.
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