Characterization of the Controlled States in $W_2^{(1)} $ of Linear Hereditary Systems

Banks, H. T.; Jacobs, Marc Q.; Langenhop, C. E.

doi:10.1137/0313035

Cited by 72 publications

(22 citation statements)

References 17 publications

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“…The main non trivial precision is the time of controllability. We generalize the results given [6] for the case of a single input and one localized delay (see also [2,14]). The approach developed here is different from that of [9].…”

Section: Introductionmentioning

confidence: 76%

On Exact Controllability of Linear Time Delay Systems of Neutral Type

Rabah¹,

Sklyar

2007

Applications of Time Delay Systems

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To cite this version:Rabah Rabah, Grigory Sklyar. On exact controllability of linear time delay systems of neutral type. Summary. The problem of exact null controllability is considered for linear neutral type systems with distributed delay. A characterization of this problem is given. The minimal time of controllability is precised. The results are based on the analysis of the Riesz basis property of eigenspaces in Hilbert space. Recent results on the moment problem and properties of exponential families are used.

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Section: Introductionmentioning

confidence: 76%

On Exact Controllability of Linear Time Delay Systems of Neutral Type

Rabah¹,

Sklyar

2007

Applications of Time Delay Systems

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“…We devote this section to the discussion of these questions. The reader will find that the results and the direction of the arguments are essentially those found in the earlier work [4]. However, there are significant differences since we are working in different spaces.…”

Section: )-(317)) Is Given By (X U) ~ (2() --L*() -B'~( )U( ) mentioning

confidence: 83%

“…Concerning these hypotheses, we note that (H1) and (H2) are exactly those of [4] but that (H3) is considerably stronger. In fact, we can characterize those matrix functions for which (H3) …”

Section: (H3) the Map T~--~b**(t) Is Continuous On [T --R T]mentioning

confidence: 86%

“…If we make the appropriate growth assumptions and seminormality hypotheses, then the general existence theorem of [4] guarantees the existence of an optimal solution {x*, u*}, x* absolutely continuous on [0, T], u* measurable on that same interval and satisfying conditions (1.3)-(1.5), provided that admissible pairs exist. If we now consider such an optimal pair, then, since 0 …”

Section: Fa(t X U) = Ga(t X) + B(t)umentioning

confidence: 99%

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On the necessary conditions for optimal control of retarded systems

Angell

Kirsch

1990

Appl Math Optim

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Abstract. In this paper we derive necessary conditions, in the form of a maximum principle, for the optimal control of nonlinear, finitely retarded functional differential equations with function-space boundary conditions. We establish these conditions in a setting which guarantees the existence of regular multipliers, admits pointwise control constraints, and, with added restrictions, ensures nontriviality of the multipliers.

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“…This may be very important in the problem of time minimal problem and other related problems of optimal control. In this case the semigroup is not explicitly known in contrast to the situation of several discrete delays (see O'Connor and Tarn (1983);Jacobs and Langenhop (1976); Banks et al (1975);Rivera Rodas and Langenhop (1978)). To study controllability we use the moment problem approach.…”

Section: Introductionmentioning

confidence: 99%

The Exact Controllability Property of Neutral Type Systems by the Moment Problem Approach Revisited

Rabah

Sklyar

Barkhayev³

2010

IFAC Proceedings Volumes

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Abstract:In a recent paper authors gave an analysis of the exact controllability problem via the moment problem approach. Namely, the steering conditions of controllable states are formulated as a vectorial moment problem using some Riesz basis. One of the main difficulties was the choice of the basis as, in general, a basis of eigenvectors does not exist. In this contribution we use a change of control by a feedback law and modify the structure of the system in such a way that there exists a basis of eigenvectors which allows a simpler expression of the moment problem. Hence, one obtains the result on exact controllability and on the time of exact controllability.

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Characterization of the Controlled States in $W_2^{(1)} $ of Linear Hereditary Systems

Cited by 72 publications

References 17 publications

On Exact Controllability of Linear Time Delay Systems of Neutral Type

On Exact Controllability of Linear Time Delay Systems of Neutral Type

On the necessary conditions for optimal control of retarded systems

The Exact Controllability Property of Neutral Type Systems by the Moment Problem Approach Revisited

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