Controllability Properties of Linear and Semilinear Abstract Control Systems

Zhou, Hong

doi:10.1137/0322026

Cited by 44 publications

(29 citation statements)

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“…Hence our corollary follows. It should be mentioned, that in infinitedimensional cases, conditions for exact global controllability of linear dynamical systems which are needed in the above theorems and corollaries are known to be quite a strong requirement [4], [5], [9], [10]. However, for finite-dimensional case these conditions are not so restrictive [5].…”

Section: Constrained Controllabilitymentioning

confidence: 99%

“…It follows directly from the fact, that in infinitedimensional spaces there exist linear subspaces which are not closed. On the other hand, for nonlinear dynamical systems there exist two fundamental concepts of controllability; namely local controllability and global controllability [1], [4], [7], [10]. Therefore, for nonlinear abstract dynamical systems defined in infinite-dimensional spaces the following four main kinds of controllability are considered: local approximate controllability, global approximate controllability, local exact controllability, and global exact controllability.…”

Section: Introduction *mentioning

confidence: 99%

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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: Constrained Controllabilitymentioning

confidence: 99%

Section: Introduction *mentioning

confidence: 99%

Constrained controllability of nonlinear systems

Klamka¹

1995

IMA J Math Control Info

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“…In Naito [3] he proved Theorem 2.2 under assumptions (B) and compact operator S(t) and also Zhou in [10] showed it under assumption (B) and another condition of range of controller.…”

Section: Short Name Of First Authormentioning

confidence: 96%

Remark on the Controllability for Semilinear Evolution Equations

Jeong¹

2013

East Asian mathematical journal

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Abstract. In this paper we deal with approximate controllability for semilinear system in a Hilbert space. In order to obtain the controllability, we assume that the system of the generalized eigenspaces of the principal operator is complete in the state space, which has a simple form and can be applied to many examples. Because of its simple form, some examples of controllability of the systems governed by the semilinear equations will be given.

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“…Chukwu and Lenhart [6] have studied the controllability of nonlinear systems in abstract spaces. Do [8] and Zhou [26,27] discussed the approximate controllability for a class of semilinear abstract equations. Kwun et al [13] studied the approximate controllability for delay Volterra systems with bounded linear operators.…”

Section: Introductionmentioning

confidence: 99%