Fixed Final Time and Fixed Final State Linear Quadratic Optimal Control Problem of Fractional Order Singular System

Chiranjeevi, Tirumalasetty; Biswas, Raj Kumar; Pandey, Shashi Kant

doi:10.1007/978-981-15-2369-4_24

Cited by 3 publications

(2 citation statements)

References 22 publications

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“…In this regard, 'pseudo state space' formulation for FOCP of continuous time SS is presented in [25,26]. In literature, formulation and different solution techniques, e.g., Grünwald-Letnikov approximation based technique described by RLFD [27][28][29] or CFD [30][31][32] and reflection operator based technique described by RLFD or CFD [33,34] for FOCP of continuous time SSs are presented. Kaczorek [35] proposed coordinate transformation to convert fractional order DTSS into its equivalent non-singular form.…”

Section: Introductionmentioning

confidence: 99%

Archives of Control Sciences

Chiranjeevi,

Biswas,

Devarapalli

et al. 2021

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In this work, we present optimal control formulation and numerical algorithm for fractional order discrete time singular system (DTSS) for fixed terminal state and fixed terminal time endpoint condition. The performance index (PI) is in quadratic form, and the system dynamics is in the sense of Riemann-Liouville fractional derivative (RLFD). A coordinate transformation is used to convert the fractional-order DTSS into its equivalent non-singular form, and then the optimal control problem (OCP) is formulated. The Hamiltonian technique is used to derive the necessary conditions. A solution algorithm is presented for solving the OCP. To validate the formulation and the solution algorithm, an example for fixed terminal state and fixed terminal time case is presented.

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Section: Introductionmentioning

confidence: 99%

Archives of Control Sciences

Chiranjeevi,

Biswas,

Devarapalli

et al. 2021

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“…From the last few decades scenario has been changed. Most of the researchers from different fields are paying attention on FO systems because, the system modeling considering FO differential equations provides more accurate results compared with the integer order systems [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16]. Most of the scientists and engineers from the last few years adopted FC in various areas of science and engineering [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16].…”

Section: Introductionmentioning

confidence: 99%

Design of TID controller based on firefly algorithm for controlling the speed of a D.C. Motor

Rajput¹,

Yadav²,

Kumar³

et al. 2020

E3S Web Conf.

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Implementation of tilt integral derivative (TID) controller for controlling the speed of a D.C. Motor using meta heuristic nature inspired algorithm named by firefly algorithm (FA) is proposed in this paper. By using FA based optimization technique, we have tuned TID controller parameters. Further, comparative analysis has been done with FA based conventional PID and fractional order PID (FOPID) controllers. The performance of TID is investigated in terms of various performance indices like integral of square error (ISE), integral of time-weighted absolute error (ITAE), integral of absolute error (IAE) and integral of time-weighted square error (ITSE). Investigation carried out reveals the advantage of TID over conventional PID and FOPID in terms of reduced settling time and performance indices.

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Numerical simulation of fractional order optimal control problem

Chiranjeevi

Biswas

2020

Journal of Statistics and Management Systems

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Fixed Final Time and Fixed Final State Linear Quadratic Optimal Control Problem of Fractional Order Singular System

Cited by 3 publications

References 22 publications

Archives of Control Sciences

Archives of Control Sciences

Design of TID controller based on firefly algorithm for controlling the speed of a D.C. Motor

Numerical simulation of fractional order optimal control problem

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