On Concepts of Controllability for Deterministic and Stochastic Systems

Bashirov, Agamirza E.; Mahmudov, Nazım I.

doi:10.1137/s036301299732184x

Cited by 207 publications

(96 citation statements)

References 6 publications

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“…Also, the study of stochastic differential equations has attracted great interest because of its applications in characterizing many problems in physics, biology,chemistry, mechanics, and so on. In finance and insurance, one has to deal with events such as corporate defaults, operational failures, or insured accidents, the theory and applications of stochastic differential equations in infinite-dimensional spaces have received much attention, (see [3][4][5][6][7] and the references therein).…”

Section: D Q T [Lx (T)] = (M + M) X (T) + Bu (T) + F (T X (T))mentioning

confidence: 99%

Stochastic fractional perturbed control systems with fractional Brownian motion and Sobolev stochastic non local conditions

2017

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This paper investigates the approximate controllability for Sobolev type stochastic perturbed control systems of fractional order with fractional Brownian motion and Sobolev fractional stochastic nonlocal conditions in a Hilbert space, A new set of sufficient conditions are established by using semigroup theory, fractional calculus, stochastic integrals for fractional Brownian motion, Banach's fixed point theorem. The results are obtained under the assumption that the associated linear system is approximately controllable. Finally, an example is also given to illustrate the obtained theory.

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Section: D Q T [Lx (T)] = (M + M) X (T) + Bu (T) + F (T X (T))mentioning

confidence: 99%

Stochastic fractional perturbed control systems with fractional Brownian motion and Sobolev stochastic non local conditions

2017

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“…In the papers (Bashirov and Mahmudov, 1999;Mahmudov, 2001), various kinds of controllability for stochastic systems in finite dimensional spaces were discussed. It is proved that the complete and approximate controllability notions for linear deterministic and stochastic systems are equivalent (Mahmudov, 2001).…”

Section: Dx(t) = [Ax(t) + Bu(t)] Dt +σ(T) Dw(t) T ∈ Jmentioning

confidence: 99%

“…We would like to mention that controllability questions for nonlinear systems with f i = 0, σ i = 0, I k = 0, i = 1, 2 were studied by many authors in the literature (Bashirov and Mahmudov, 1999;Mahmudov and Zorlu, 2003;Sakthivel et al, 2006). Equations (3)- (5) are of the more general form and, in particular, if f i and σ i have a varying physical meaning, it is important to note that Eqns.…”

Section: Remarkmentioning

confidence: 99%

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Controllability of nonlinear impulsive Ito type stochastic systems

Sakthivel¹

2009

International Journal of Applied Mathematics and Computer Science

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In this article, we consider finite dimensional dynamical control systems described by nonlinear impulsive Ito type stochastic integrodifferential equations. Necessary and sufficient conditions for complete controllability of nonlinear impulsive stochastic systems are formulated and proved under the natural assumption that the corresponding linear system is appropriately controllable. A fixed point approach is employed for achieving the required result.

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“…In recent years the extensions of deterministic controllability concepts to stochastic control systems have been discussed only in a limited number of publications. In the papers (Bashirov and Kerimov, 1997;Bashirov and Mahmudov, 1999;Ehrhard and Kliemann, 1982;Mahmudov, 2001;Mahmudov and Denker, 2000;Zabczyk, 1991) different kinds of stochastic controllability were discussed for linear finite dimensional stationary and nonstation-6 J. Klamka ary control systems. The papers (Fernandez-Cara et al, 1999;Kim Jong Uhn, 2004;Mahmudov, 2001; are devoted to a systematic study of approximate and exact stochastic controllability for linear infinite dimensional control systems defined in Hilbert spaces.…”

Section: Introductionmentioning

confidence: 99%

Stochastic Controllability of Linear Systems With State Delays

Klamka¹

2007

International Journal of Applied Mathematics and Computer Science

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A class of finite-dimensional stationary dynamic control systems described by linear stochastic ordinary differential state equations with a single point delay in the state variables is considered. Using a theorem and methods adopted directly from deterministic controllability problems, necessary and sufficient conditions for various kinds of stochastic relative controllability are formulated and proved. It will be demonstrated that under suitable assumptions the relative controllability of an associated deterministic linear dynamic system is equivalent to the stochastic relative exact controllability and the stochastic relative approximate controllability of the original linear stochastic dynamic system. Some remarks and comments on the existing results for the controllability of linear dynamic systems with delays are also presented. Finally, a minimum energy control problem for a stochastic dynamic system is formulated and solved.

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On Concepts of Controllability for Deterministic and Stochastic Systems

Cited by 207 publications

References 6 publications

Stochastic fractional perturbed control systems with fractional Brownian motion and Sobolev stochastic non local conditions

Stochastic fractional perturbed control systems with fractional Brownian motion and Sobolev stochastic non local conditions

Controllability of nonlinear impulsive Ito type stochastic systems

Stochastic Controllability of Linear Systems With State Delays

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