Time Optimal Control of Semilinear Control Systems Involving Time Delays

Jeong, Jin-Mun; Son, Sang-Jin

doi:10.1007/s10957-014-0639-y

Cited by 32 publications

(25 citation statements)

References 12 publications

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“…What is more, since the reflexivity of the state space X is no longer satisfied, we take full advantage of the compact method, and thus the time optimal pairs are still acquired. Therefore, the results here essentially generalize those in [10,11,14,26,29,32], and the references therein, where the Lipschitz continuity of nonlinear function and the reflexivity of X are all required.…”

Section: Time Optimal Control Problems Subjected To System (11)supporting

confidence: 63%

“…To our knowledge, the time optimal pairs have been derived provided that the nonlinear function is Lipschitz continuous and both the state space X and the control space Y are reflexive (see e.g. [10,11,14,26,29,32]). The Lipschitz continuity guarantees the existence and uniqueness of mild solution of the corresponding differential systems, and the reflexivity of the spaces X and Y ensure the weak convergence of solution sequences and control sequences, respectively.…”

Section: Introductionmentioning

confidence: 99%

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Time optimal controls for fractional differential systems with Riemann-Liouville derivatives

Lian

Fan

2018

FCAA

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Time optimal control problems governed by Riemann-Liouville fractional differential system are considered in this paper. Firstly, the existence results are obtained by using the theory of semigroup and Schauder’s fixed point. Secondly, the new approach of establishing time minimizing sequences twice is applied to acquire the time optimal pairs without the Lipschitz continuity of nonlinear function. Moreover, the reflexivity of state space is removed with the help of compact method. Finally, an example is given to illustrate the main conclusions. Our work essentially improves and generalizes the corresponding results in the existing literature.

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Section: Time Optimal Control Problems Subjected To System (11)supporting

confidence: 63%

Section: Introductionmentioning

confidence: 99%

Time optimal controls for fractional differential systems with Riemann-Liouville derivatives

Lian

Fan

2018

FCAA

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“…Proof The main idea of the proof comes from . Let

t_{0} = \inf {t : x (t, g, f, u) = x_{1}, where u is an admissible control}

Then, there exists a monotone decreasing sequences t n → t 0 .…”

Section: Time Optimal Controlmentioning

confidence: 99%

“…Recently, some researchers focused on the study of the solvability and optimal control of systems monitored by fractional order differential equations. For more details, we refer to the work and references therein.…”

Section: Introductionmentioning

confidence: 99%

Solvability and optimal controls of fractional delay evolution inclusions with Clarke subdifferential

Jiang

Huang

2016

Math Methods in App Sciences

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This article investigates the solvability and optimal controls of systems monitored by fractional delay evolution inclusions with Clarke subdifferential type. By applying a fixed-point theorem of condensing multivalued maps and some properties of Clarke subdifferential, an existence theorem concerned with the mild solution for the system is proved under suitable assumptions. Moreover, an existence result of optimal control pair that governed by the presented system is also obtained under some mild conditions. Finally, an example is given to illustrate our main results.(1.1) where c D0 denotes Caputo fractional time derivatives of order˛, A : D.A/ Â H ! H is the infinitesimal generator of a uniformly bounded C 0 -semigroup fT.t/g t 0 on H, fB.t/ : t 2 Ig is a family of linear operators from Y to H, g : I H ! H is a nonlinear function, @J.t, / is the Clarke's subdifferential of J.t, /, '.t/ 2 C.OE , 0; H/, and U ad denotes an admissible control set.Let A ad be a set of all admissible state control pairs .x, u/. The cost functional on the set A ad is given byThe optimal control problem of classical integer order differential equations and inclusions is of interest for aviation and space technology. It is also important in fields such as robotics, movement sequences in sports, and the control of chemical processes and power plants. In many practical cases, however, the processes to be optimized can no longer be adequately modeled by classical integer order differential equations and inclusions; instead, fractional order differential equations and inclusions have to be employed for their description. For instance, the hereditary and memory properties of viscoelasticity, electrical circuits, biomechanics, electrochemistry, biology, blood flow phenomena, signal, and image processing can be well predicted and described by some fractional order differential equations and inclusions, see [1][2][3][4][5][6][7][8][9]. Recently, some researchers focused on the study of the solvability and optimal control of systems monitored by fractional order differential equations. For more details, we refer to the work [10-16] and references therein. Very recently, Lu et al. [17] discussed the solvability and optimal control of problem (1.1) when g.t, x.t // D 0 and x.0/ D '.0/ D x 0 . However, in some practical situations, as Richard [18] pointed out that many physical processes in nature include time delay phenomena. For example, Niculescu [19] and Kolmanovskii and Myshkis [20] demonstrated that time delay arise in chemistry, biology, 3026-3039 Z t 0 .t s/ n ˛ 1 x .n/ .s/ds D I˛x .n/ .t/, t > 0, 0 Ä n 1 <˛< n; (ii) The Caputo derivative of a constant is equal to zero; (iii) If x is an abstract function which has values in H, then integrals which appear in Definitions 2.1 and 2.2 are taken in Bochner's sense.Definition 2.4 ([21, 22]) Let X be a Banach space with the dual space X and J : X ! R be a locally Lipschitz functional on X. The Clarke's generalized directional derivative of J at the point x 2 X in the direction v 2 X, denoted by ...

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“…In [13], Harrat et al established some sufficient conditions for solvability and optimal controls of an impulsive nonlinear Hilfer fractional delay evolution inclusion in Banach spaces. Mokkedem and Fu [28] discussed the standard optimal control and time optimal control problems for a class of semilinear evolution systems with infinite delay by employing the theory of fundamental solution as in papers [18,19,30]. While Tucsnak et al studied in [36], by weakening the regularity assumptions on the initial data with z 0 ∈ X, the numerical approximation of the solutions of a class of abstract parabolic time optimal control problems with unbounded control operator.…”

mentioning

confidence: 99%

Optimal control problems for a neutral integro-differential system with infinite delay

Huang¹,

Fu²

2022

EECT

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<p style='text-indent:20px;'>This work devotes to the study on problems of optimal control and time optimal control for a neutral integro-differential evolution system with infinite delay. The main technique is the theory of resolvent operators for linear neutral integro-differential evolution systems constructed recently in literature. We first establish the existence and uniqueness of mild solutions and discuss the compactness of the solution operator for the considered control system. Then, we investigate the existence of optimal controls for the both cases of bounded and unbounded admissible control sets under some assumptions. Meanwhile, the existence of time optimal control to a target set is also considered and obtained by limit arguments. An example is given at last to illustrate the applications of the obtained results.</p>

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Time Optimal Control of Semilinear Control Systems Involving Time Delays

Cited by 32 publications

References 12 publications

Time optimal controls for fractional differential systems with Riemann-Liouville derivatives

Time optimal controls for fractional differential systems with Riemann-Liouville derivatives

Solvability and optimal controls of fractional delay evolution inclusions with Clarke subdifferential

Optimal control problems for a neutral integro-differential system with infinite delay

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