On time-optimal control of fractional-order systems

Matychyn, Ivan; Onyshchenko, Viktoriia

doi:10.1016/j.cam.2017.10.016

Cited by 30 publications

(7 citation statements)

References 16 publications

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“…In the past decades, much attention has been paid to time optimal control problems governed by nonlinear differential systems [14,22,38]. Among them, the fractional time optimal control of a distributed system is an optimal control problem for which dynamic systems are defined by means of fractional differential equations and inclusions, see for example [24,27,29] and references therein. In particular, it is well known that differential equations with impulsive conditions were used to describe the evolution process with abrupt perturbation at some certain time in biology, medicine and control theory [25].…”

Section: Introductionmentioning

confidence: 99%

“…The results are obtained by using theory of fractional resolvent operators, stochastic analysis, the properties of Clarke subdifferential with a fixed-point theorem. The known results appeared in [14,18,[22][23][24]27,29,37,38] are generalized to the impulsive stochastic inclusions settings and the case of with infinite delay and multi-valued non-instantaneous impulses.…”

Section: Introductionmentioning

confidence: 99%

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Time Optimal Control of System Governed by a Fractional Stochastic Partial Differential Inclusion with Clarke Subdifferential

Zhang¹

2021

Taiwanese J. Math.

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This paper investigates the time optimal control problems to a new class of fractional non-instantaneous impulsive stochastic partial differential inclusions with Clarke subdifferential in Hilbert spaces. Firstly, using the fractional calculus, properties of fractional resolvent operators and a fixed-point theorem, the existence of mild solutions for these systems is presented. Secondly, the existence of time optimal control of system governed by fractional stochastic control inclusions with Clarke subdifferential and non-instantaneous impulses is also obtained. Finally, an example is given to illustrate our main results.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Time Optimal Control of System Governed by a Fractional Stochastic Partial Differential Inclusion with Clarke Subdifferential

Zhang¹

2021

Taiwanese J. Math.

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“…An advantage over systems with derivatives of an integer order is revealed when modeling hereditary properties and memory [16,18]. Fractional derivatives are used in optimal control problems [23,24], in risk theory [25], in research related to medicine [26,27], in solving identification problems [28] and a source problem [29].…”

Section: Introductionmentioning

confidence: 99%

Real-time reconstruction of external impact on fractional order system under measuring a part of coordinates

Сурков

2021

Journal of Computational and Applied Mathematics

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For a system of nonlinear fractional differential equations, the problem of reconstructing an unknown external impact is considered. It is complicated by the fact that only a part of system's parameters is available for measuring. An algorithm for solving this problem is proposed, which is resistant to informational noises and computational errors, and is based on regularization methods and constructions of guaranteed control theory. A numerical example illustrating the operation of the algorithm is considered.

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“…Explicit solutions to linear systems of differential equations provide a basis to solve control problems. Analytical solutions of the linear systems of fractional differential equations with constant coefficients were derived in the papers [8,9] and then applied to solving control problems and differential games in [10][11][12][13].…”

Section: Introductionmentioning

confidence: 99%

Analytical Solution of Linear Fractional Systems with Variable Coefficients Involving Riemann–Liouville and Caputo Derivatives

Matychyn

2019

Symmetry

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This paper deals with the initial value problem for linear systems of fractional differential equations (FDEs) with variable coefficients involving Riemann–Liouville and Caputo derivatives. Some basic properties of fractional derivatives and antiderivatives, including their non-symmetry w.r.t. each other, are discussed. The technique of the generalized Peano–Baker series is used to obtain the state-transition matrix. Explicit solutions are derived both in the homogeneous and inhomogeneous case. The theoretical results are supported by examples.

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On time-optimal control of fractional-order systems

Cited by 30 publications

References 16 publications

Time Optimal Control of System Governed by a Fractional Stochastic Partial Differential Inclusion with Clarke Subdifferential

Time Optimal Control of System Governed by a Fractional Stochastic Partial Differential Inclusion with Clarke Subdifferential

Real-time reconstruction of external impact on fractional order system under measuring a part of coordinates

Analytical Solution of Linear Fractional Systems with Variable Coefficients Involving Riemann–Liouville and Caputo Derivatives

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