Optimality conditions and a solution scheme for fractional optimal control problems

Jeličić, Zoran D.; Petrovacki, N.

doi:10.1007/s00158-008-0307-7

Cited by 86 publications

(86 citation statements)

References 13 publications

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“…They used this method to solve a variety of ordinary fractional differential equations (FODE). Jeličić and N. Petrovački [25] used this approach in solving fractional optimal control problems of lumped parameter systems. The main advantage of this procedure is the use of the well-known classical optimal control theory in solving fractional control problems.…”

Section: Introductionmentioning

confidence: 98%

Optimal control of a class of fractional heat diffusion systems

Rapaić

Jeličić

2010

Nonlinear Dyn

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In this paper, a solution procedure for a class of optimal control problems involving distributed parameter systems described by a generalized, fractional-order heat equation is presented. The first step in the proposed procedure is to represent the original fractional distributed parameter model as an equivalent system of fractional-order ordinary differential equations. In the second step, the necessity for solving fractional Euler-Lagrange equations is avoided completely by suitable transformation of the obtained model to a classical, although infinite-dimensional, state-space form. It is shown, however, that relatively small number of state variables are sufficient for accurate computations. The main feature of the proposed approach is that results of the classical optimal control theory can be used directly. In particular, the well-known "linear-quadratic" (LQR) and "BangBang" regulators can be designed. The proposed procedure is illustrated by a numerical example.

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Section: Introductionmentioning

confidence: 98%

Optimal control of a class of fractional heat diffusion systems

Rapaić

Jeličić

2010

Nonlinear Dyn

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“…One of the fractional discretization method has been presented in [17]. Some optimal control problems with fixed final time and a final state for continuous-time systems of the fractional order have been investigated in [18][19][20][21][22][23][24][25][26]. The fractional Kalman filter and its application have been addressed in [27][28].…”

Section: Introductionmentioning

confidence: 99%

Fixed final time and free final state optimal control problem for fractional dynamic systems – linear quadratic discrete-time case

Dzieliński¹,

Czyronis²

2013

Bulletin of the Polish Academy of Sciences: Technical Sciences

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Abstract. The optimization problem for fractional discrete-time systems with a quadratic performance index has been formulated and solved. The case of fixed final time and a free final state has been considered. A method for numerical computation of optimization problems has been presented. The presented method is a generalization of the well-known method for discrete-time systems of integer order. The efficiency of the method has been demonstrated on numerical examples and illustrated by graphs. Graphs also show the differences between the fractional and classical (standard) systems theory. Results for other cases of the fractional system order (coefficient α) and not illustrated with numerical examples have been obtained through a computer algorithm written for this purpose.

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“…They are used, among others things, to the modeling of capacitor (Westerlund and Ekstam 1994;Dzielinski et al 2011Dzielinski et al , 2010, fluid flow through porous material (Langlands 2006), viscoelastic materials (Bagley and Torvik 1986). Fractional systems are investigated in many aspects: existence and uniqueness of solutions (Daftardar-Gejji and Babakhani 2004;Delbosco and Rodino 1996;Hayek et al 1999;Idczak and Kamocki 2011;Kilbas et al 2006), stability and positivity (Buslowicz 2008(Buslowicz , 2011Kaczorek 2011a, b), calculus of variations (Agrawal 2002;Baleanu and Muslih 2005;El-Nabulusi and Torres 2007;Idczak and Majewski 2012;Riewe 1996Riewe , 1997, controllability (Kaczorek 2011c) and optimal control (Agrawal 2004;Jelicic and Petrovacki 2009;Kamocki 2012;Tricaud and Chen 2010).…”

Section: Introductionmentioning

confidence: 99%

Fractional differential repetitive processes with Riemann–Liouville and Caputo derivatives

Idczak

Kamocki

2013

Multidim Syst Sign Process

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In the paper, we study differential repetitive processes with fractional RiemannLiouville and Caputo derivatives, in the context of the existence, uniqueness and continuous dependence of solutions on controls. Some applications to controllabilty of such processes are given as well.Keywords Riemann-Liouville derivative · Caputo derivative · Differential repetitive process · Existence, uniqueness and continuous dependence of solutions on controls · Reachable set

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Optimality conditions and a solution scheme for fractional optimal control problems

Cited by 86 publications

References 13 publications

Optimal control of a class of fractional heat diffusion systems

Optimal control of a class of fractional heat diffusion systems

Fixed final time and free final state optimal control problem for fractional dynamic systems – linear quadratic discrete-time case

Fractional differential repetitive processes with Riemann–Liouville and Caputo derivatives

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