Controllability questions for nonlinear systems in abstract spaces

Chukwu, Ethelbert Nwakuche; Lenhart, Suzanne

doi:10.1007/bf00940064

Cited by 69 publications

(42 citation statements)

References 18 publications

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“…t∈[0,T]} (2) where x(t,0,u), (t>0) is the unique solution of the equation (2) with zero initial condition and control u ∈ U ad . Under the assumptions stated on the nonlinear mapping f, such a solution always exists [2]. Using the concept of the attainable set, we may introduce the fundamental definitions of constrained controllability for dynamical system (1) [6].…”

Section: System Descriptionmentioning

confidence: 99%

Constrained controllability of nonlinear systems

Klamka¹

1995

IMA J Math Control Info

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In the paper, infinite-dimensional, continuous-time control systems described by nonlinear abstract differential equations are considered. Using methods of functional analysis sufficient conditions for constrained exact local controllability are formulated and proved. It is generally assumed that the values of controls are in a convex and closed cone with vertex at zero. Illustrative examples are also given. Moreover, some remarks and comments on controllability problems for nonlinear dynamical systems are presented.

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Section: System Descriptionmentioning

confidence: 99%

Constrained controllability of nonlinear systems

Klamka¹

1995

IMA J Math Control Info

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“…Controllability of nonlinear systems, with different types of nonlinearity, has been studied with the help of fixed point principles [17]. Several authors have studied the problem of controllability of semilinear and nonlinear systems represented by differential and integro-differential equations in finite or infinite dimensional Banach spaces [18][19][20][21].…”

Section: Introductionmentioning

confidence: 99%

A Study of Controllability of Impulsive Neutral Evolution Integro-Differential Equations with State-Dependent Delay in Banach Spaces

Chalishajar

Anguraj²,

Malar³

et al. 2016

Mathematics

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“…The problem of controllability of linear systems represented by differential equations in Banach spaces has been extensively studied by several authors [8]. Several papers have appeared on finite dimensional controllability of linear systems [9] and infinite dimensional systems in abstract spaces [10]. Of late the controllability of nonlinear systems in finite-dimensional spaces is studeid by means of fixed point principles [11].…”

Section: Introductionmentioning

confidence: 99%