Time-optimal control of fractional-order linear systems

Matychyn, Ivan; Onyshchenko, Viktoriia

doi:10.1515/fca-2015-0042

Cited by 19 publications

(11 citation statements)

References 9 publications

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“…which is consistent with the formulas, obtained for the systems of fractional differential equations with constant coefficients [10,18].…”

Section: Lemmasupporting

confidence: 91%

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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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“…which is consistent with the formulas, obtained for the systems of fractional differential equations with constant coefficients [10,18].…”

Section: Lemmasupporting

confidence: 91%

“…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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“…Our final objective is to establish a version of the PMP that handles Problem (OCP) with a free final time. Let us point out that some earlier works like [10,42,46,53] already deal with fractional optimal control problems with free final time.…”

Section: Work In Progressmentioning

confidence: 99%

Pontryagin maximum principle for general Caputo fractional optimal control problems with Bolza cost and terminal constraints

Bergounioux

Bourdin

2020

ESAIM: COCV

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In this paper we focus on a general optimal control problem involving a dynamical system described by a nonlinear Caputo fractional differential equation of order 0 < α ≤ 1, associated to a general Bolza cost written as the sum of a standard Mayer cost and a Lagrange cost given by a Riemann-Liouville fractional integral of order β ≥ α. In addition the present work handles general control and mixed initial/final state constraints. Adapting the standard Filippov's approach based on appropriate compactness assumptions and on the convexity of the set of augmented velocities, we give an existence result for at least one optimal solution. Then, the major contribution of this paper is the statement of a Pontryagin maximum principle which provides a first-order necessary optimality condition that can be applied to the fractional framework considered here. In particular, Hamiltonian maximization condition and transversality conditions on the adjoint vector are derived. Our proof is based on the sensitivity analysis of the Caputo fractional state equation with respect to needle-like control perturbations and on Ekeland's variational principle. The paper is concluded with two illustrating examples and with a list of several perspectives for forthcoming works.

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“…Specially it is a generalization of classical differential and integral calculus of integer order to arbitrary order. In recent times, fractional order derivatives and fractional order differential equations have been applied in several fields of science and engineering [3,4,5,6,7,8,9,10], however, initially it was treated as a topic of interest of pure mathematicians only [11]. The reason is two-fold.…”

Section: Introductionmentioning

confidence: 99%

Study of a discretized fractional-order eco-epidemiological model with prey infection

Mondal¹,

Cao²,

Bairagi³

2020

Fractional Differential Calculus

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In this paper, an attempt is made to understand the dynamics of a three-dimensional discrete fractional-order eco-epidemiological model with Holling type II functional response. We first discretize a fractional-order predator-prey-parasite system with piecewise constant arguments and then explore the system dynamics. Analytical conditions for the local stability of different fixed points have been determined using the Jury criterion. Several examples are given to substantiate the analytical results. Our analysis shows that stability of the discrete fractional order system strongly depends on the step-size and the fractional order. More specifically, the critical value of the step-size, where the switching of stability occurs, decreases as the order of the fractional derivative decreases. Simulation results explore that the discrete fractional-order system may also exhibit complex dynamics, like chaos, for higher step-size.

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Time-optimal control of fractional-order linear systems

Cited by 19 publications

References 9 publications

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

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

Pontryagin maximum principle for general Caputo fractional optimal control problems with Bolza cost and terminal constraints

Study of a discretized fractional-order eco-epidemiological model with prey infection

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