Stochastic controllability and minimum energy control of systems with multiple delays in control

Klamka, Jerzy

doi:10.1016/j.amc.2008.08.059

Cited by 57 publications

(23 citation statements)

References 19 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…It should be pointed out that the results obtained here generalize those by Klamka (2008a) as well as Shen and Sun (2012) from stochastic systems with single control delay to multiple time-varying delays. Further, they also generalize the results of Klamka (2008b) from stochastic systems with constant delays to time varying delays.…”

Section: Discussionmentioning

confidence: 96%

“…Shen and Sun (2012) extended the above results to nonlinear stochastic systems via a fixed point technique. So far, there have been very few results for stochastic systems in which multiple delays in control input are involved (Klamka, 2008b;Sikora and Klamka, 2012). Recently, Balachandran et al (2012) established global relative controllability of fractional dynamical systems with multiple delays in control.…”

Section: S Karthikeyan Et Almentioning

confidence: 99%

See 1 more Smart Citation

Controllability of nonlinear stochastic systems with multiple time-varying delays in control

Karthikeyan

Balachandran

Sathya

2015

International Journal of Applied Mathematics and Computer Science

View full text Add to dashboard Cite

This paper is concerned with the problem of controllability of semi-linear stochastic systems with time varying multiple delays in control in finite dimensional spaces. Sufficient conditions are established for the relative controllability of semilinear stochastic systems by using the Banach fixed point theorem. A numerical example is given to illustrate the application of the theoretical results. Some important comments are also presented on existing results for the stochastic controllability of fractional dynamical systems.

show abstract

Section: Discussionmentioning

confidence: 96%

Section: S Karthikeyan Et Almentioning

confidence: 99%

Controllability of nonlinear stochastic systems with multiple time-varying delays in control

Karthikeyan

Balachandran

Sathya

2015

International Journal of Applied Mathematics and Computer Science

View full text Add to dashboard Cite

show abstract

“…This problem for standard systems has been investigated in [2,[28][29][30] and in [31][32][33][34] for fractional order systems.…”

Section: Introductionmentioning

confidence: 99%

Controllability, reachability and minimum energy control of fractional discrete-time linear systems with multiple delays in state

Busłowicz¹

2014

Bulletin of the Polish Academy of Sciences Technical Sciences

View full text Add to dashboard Cite

Abstract. In the paper the problems of controllability, reachability and minimum energy control of a fractional discrete-time linear system with delays in state are addressed. A general form of solution of the state equation of the system is given and necessary and sufficient conditions for controllability, reachability and minimum energy control are established. The problems are considered for systems with unbounded and bounded inputs. The considerations are illustrated by numerical examples. Influence of a value of the fractional order on an optimal value of the performance index of the minimum energy control is examined on an example.

show abstract

“…Among them, controllability is a significant property of dynamic control systems and is of particular importance in control theory. The controllability of stochastic di¤erential equations in infinite dimensional spaces have been investigated by many authors [13,14,15,16,22]. Recently, Klamka [17] derived a set of su‰cient conditions for constrained local relative controllability for semilinear finite-dimensional dynamical control systems with multiple point delays in the control using a generalized open mapping theorem.…”

Section: Introductionmentioning

confidence: 99%

Approximate Controllability of Impulsive Stochastic Evolution Equations

Sakthivel

2009

View full text Add to dashboard Cite

Abstract. In this paper, we study the approximate controllability of nonlinear impulsive stochastic di¤erential equations in a real separable Hilbert space. We prove the approximate controllability of nonlinear impulsive stochastic control systems under the assumption that the corresponding linear system is approximately controllable. By using the stochastic analysis theory and a fixed point strategy, su‰cient conditions are formulated and proved. Moreover, an example is also provided to illustrate the e¤ectiveness of the result.

show abstract

Stochastic controllability and minimum energy control of systems with multiple delays in control

Cited by 57 publications

References 19 publications

Controllability of nonlinear stochastic systems with multiple time-varying delays in control

Controllability of nonlinear stochastic systems with multiple time-varying delays in control

Controllability, reachability and minimum energy control of fractional discrete-time linear systems with multiple delays in state

Approximate Controllability of Impulsive Stochastic Evolution Equations

Contact Info

Product

Resources

About