Fractional linear control systems with Caputo derivative and their optimization

Kamocki, Rafał; Majewski, Marek

doi:10.1002/oca.2150

Cited by 31 publications

(17 citation statements)

References 29 publications

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“…The FOCP refers to optimization of the performance index subject to dynamical constraints on the control and state which have fractional-order models. There has been some work done in the area of deterministic FOCPs in finite dimensional spaces [32,33] and infinite dimensional cases [34,35]. Ren and Wu [36] discussed the optimal control problem associated with multivalued SDEs with Levy jumps by using Yosida approximation theory.…”

Section: Introductionmentioning

confidence: 99%

Fractional Stochastic Differential Equations with Hilfer Fractional Derivative: Poisson Jumps and Optimal Control

Rihan

Rajivganthi

Muthukumar

2017

Discrete Dynamics in Nature and Society

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In this work, we consider a class of fractional stochastic differential system with Hilfer fractional derivative and Poisson jumps in Hilbert space. We study the existence and uniqueness of mild solutions of such a class of fractional stochastic system, using successive approximation theory, stochastic analysis techniques, and fractional calculus. Further, we study the existence of optimal control pairs for the system, using general mild conditions of cost functional. Finally, we provide an example to illustrate the obtained results.

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Section: Introductionmentioning

confidence: 99%

Fractional Stochastic Differential Equations with Hilfer Fractional Derivative: Poisson Jumps and Optimal Control

Rihan

Rajivganthi

Muthukumar

2017

Discrete Dynamics in Nature and Society

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“…However, only a few papers address optimal control problems for fractional systems (see e.g. [18], [1], [2], [12], [10], [9]) and fewer consider stochastic fractional systems [16], [3].…”

Section: Introductionmentioning

confidence: 99%

Optimal control of discrete-time linear fractional-order systems with multiplicative noise

Trujillo¹,

Ungureanu

2016

International Journal of Control

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A finite horizon linear quadratic(LQ) optimal control problem is studied for a class of discrete-time linear fractional systems (LFSs) affected by multiplicative, independent random perturbations. Based on the dynamic programming technique, two methods are proposed for solving this problem. The first one seems to be new and uses a linear, expanded-state model of the LFS. The LQ optimal control problem reduces to a similar one for stochastic linear systems and the solution is obtained by solving Riccati equations. The second method appeals to the Principle of Optimality and provides an algorithm for the computation of the optimal control and cost by using directly the fractional system. As expected, in both cases the optimal control is a linear function in the state and can be computed by a computer program. Two numerical examples proves the effectiveness of each method.

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“…These schemes lead to problems of positive integer order. In paper [15], system (1.1) with a non-zero initial condition and cost functional…”

Section: Introductionmentioning

confidence: 99%

On a linear-quadratic problem with Caputo derivative

Idczak¹,

Walczak²

2016

OpMath

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Abstract.In this paper, we study a linear-quadratic optimal control problem with a fractional control system containing a Caputo derivative of unknown function. First, we derive the formulas for the differential and gradient of the cost functional under given constraints. Next, we prove an existence result and derive a maximum principle. Finally, we describe the gradient and projection of the gradient methods for the problem under consideration.

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Fractional linear control systems with Caputo derivative and their optimization

Cited by 31 publications

References 29 publications

Fractional Stochastic Differential Equations with Hilfer Fractional Derivative: Poisson Jumps and Optimal Control

Fractional Stochastic Differential Equations with Hilfer Fractional Derivative: Poisson Jumps and Optimal Control

Optimal control of discrete-time linear fractional-order systems with multiplicative noise

On a linear-quadratic problem with Caputo derivative

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