Optimal Control of Time-Delay Fractional Equations via a Joint Application of Radial Basis Functions and Collocation Method
A novel approach to solve optimal control problems dealing simultaneously with fractional differential equations and time delay is proposed in this work. More precisely, a set of global radial basis functions are firstly used to approximate the states and control variables in the problem. Then, a co...
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| Abstract | A novel approach to solve optimal control problems dealing simultaneously with fractional differential equations and time delay is proposed in this work. More precisely, a set of global radial basis functions are firstly used to approximate the states and control variables in the problem. Then, a collocation method is applied to convert the time-delay fractional optimal control problem to a nonlinear programming one. By solving the resulting challenge, the unknown coefficients of the original one will be finally obtained. In this way, the proposed strategy introduces a very tunable framework for direct trajectory optimization, according to the discretization procedure and the range of arbitrary nodes. The algorithm’s performance has been analyzed for several non-trivial examples, and the obtained results have shown that this scheme is more accurate, robust, and efficient than most previous methods. |
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| AbstractList | A novel approach to solve optimal control problems dealing simultaneously with fractional differential equations and time delay is proposed in this work. More precisely, a set of global radial basis functions are firstly used to approximate the states and control variables in the problem. Then, a collocation method is applied to convert the time-delay fractional optimal control problem to a nonlinear programming one. By solving the resulting challenge, the unknown coefficients of the original one will be finally obtained. In this way, the proposed strategy introduces a very tunable framework for direct trajectory optimization, according to the discretization procedure and the range of arbitrary nodes. The algorithm’s performance has been analyzed for several non-trivial examples, and the obtained results have shown that this scheme is more accurate, robust, and efficient than most previous methods. A novel approach to solve optimal control problems dealing simultaneously with fractional differential equations and time delay is proposed in this work. More precisely, a set of global radial basis functions are firstly used to approximate the states and control variables in the problem. Then, a collocation method is applied to convert the time-delay fractional optimal control problem to a nonlinear programming one. By solving the resulting challenge, the unknown coefficients of the original one will be finally obtained. In this way, the proposed strategy introduces a very tunable framework for direct trajectory optimization, according to the discretization procedure and the range of arbitrary nodes. The algorithm's performance has been analyzed for several non-trivial examples, and the obtained results have shown that this scheme is more accurate, robust, and efficient than most previous methods.A novel approach to solve optimal control problems dealing simultaneously with fractional differential equations and time delay is proposed in this work. More precisely, a set of global radial basis functions are firstly used to approximate the states and control variables in the problem. Then, a collocation method is applied to convert the time-delay fractional optimal control problem to a nonlinear programming one. By solving the resulting challenge, the unknown coefficients of the original one will be finally obtained. In this way, the proposed strategy introduces a very tunable framework for direct trajectory optimization, according to the discretization procedure and the range of arbitrary nodes. The algorithm's performance has been analyzed for several non-trivial examples, and the obtained results have shown that this scheme is more accurate, robust, and efficient than most previous methods. |
| Author | Soradi-Zeid, Samaneh Gómez-Aguilar, José Francisco Chu, Yu-Ming Jahanshahi, Hadi Chen, Shu-Bo Alcaraz, Raúl Bekiros, Stelios |
| AuthorAffiliation | 3 Department of Mechanical Engineering, University of Manitoba, Winnipeg, MB R3T 5V6, Canada; jahanshahi.hadi90@gmail.com 7 Rimini Centre for Economic Analysis (RCEA), LH3079, Wilfrid Laurier University, 75 University Ave W., Waterloo, ON N2L3C5, Canada 2 Faculty of Industry and Mining (khash), University of Sistan and Baluchestan, Zahedan 98155-987, Iran; soradizeid@eng.usb.ac.ir 4 Research Group in Electronic, Biomedical and Telecommunication Engineering, University of Castilla-La Mancha (UCLM), 16071 Cuenca, Spain 8 Department of Mathematics, Huzhou University, Huzhou 313000, China 1 School of Science, Hunan City University, Yiyang 413000, China; shubo.chen@163.com 5 CONACyT-Tecnológico Nacional de México/CENIDET, Interior Internado Palmira S/N, Col. Palmira, Cuernavaca C.P. 62490, Morelos, Mexico; jose.ga@cenidet.tecnm.mx 9 Hunan Provincial Key Laboratory of Mathematical Modeling and Analysis in Engineering, Changsha University of Science & Technology, Changsha 410114, China 6 Department o |
| AuthorAffiliation_xml | – name: 7 Rimini Centre for Economic Analysis (RCEA), LH3079, Wilfrid Laurier University, 75 University Ave W., Waterloo, ON N2L3C5, Canada – name: 8 Department of Mathematics, Huzhou University, Huzhou 313000, China – name: 2 Faculty of Industry and Mining (khash), University of Sistan and Baluchestan, Zahedan 98155-987, Iran; soradizeid@eng.usb.ac.ir – name: 6 Department of Economics, European University Institute, Via delle Fontanelle, 18, I-50014 Florence, Italy; stelios.bekiros@eui.eu – name: 3 Department of Mechanical Engineering, University of Manitoba, Winnipeg, MB R3T 5V6, Canada; jahanshahi.hadi90@gmail.com – name: 9 Hunan Provincial Key Laboratory of Mathematical Modeling and Analysis in Engineering, Changsha University of Science & Technology, Changsha 410114, China – name: 4 Research Group in Electronic, Biomedical and Telecommunication Engineering, University of Castilla-La Mancha (UCLM), 16071 Cuenca, Spain – name: 5 CONACyT-Tecnológico Nacional de México/CENIDET, Interior Internado Palmira S/N, Col. Palmira, Cuernavaca C.P. 62490, Morelos, Mexico; jose.ga@cenidet.tecnm.mx – name: 1 School of Science, Hunan City University, Yiyang 413000, China; shubo.chen@163.com |
| Author_xml | – sequence: 1 givenname: Shu-Bo surname: Chen fullname: Chen, Shu-Bo – sequence: 2 givenname: Samaneh orcidid: 0000-0001-5918-915X surname: Soradi-Zeid fullname: Soradi-Zeid, Samaneh – sequence: 3 givenname: Hadi surname: Jahanshahi fullname: Jahanshahi, Hadi – sequence: 4 givenname: Raúl orcidid: 0000-0002-0942-3638 surname: Alcaraz fullname: Alcaraz, Raúl – sequence: 5 givenname: José Francisco orcidid: 0000-0001-9403-3767 surname: Gómez-Aguilar fullname: Gómez-Aguilar, José Francisco – sequence: 6 givenname: Stelios surname: Bekiros fullname: Bekiros, Stelios – sequence: 7 givenname: Yu-Ming orcidid: 0000-0002-0944-2134 surname: Chu fullname: Chu, Yu-Ming |
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| Cites_doi | 10.1007/s40314-013-0089-4 10.1007/978-3-319-58356-3 10.1016/j.robot.2016.10.015 10.1007/s11075-017-0363-4 10.1007/s11071-004-3744-x 10.1016/j.ces.2014.06.033 10.1002/oca.4660130103 10.1093/imamci/dnx063 10.1007/s11071-016-2983-y 10.1016/j.aej.2020.04.029 10.1109/TAC.2005.861718 10.1007/s40995-017-0420-9 10.1002/asjc.1858 10.1016/j.chaos.2019.05.008 10.1002/asjc.1371 10.1002/1099-1514(200005/06)21:3<91::AID-OCA669>3.0.CO;2-C 10.1016/j.cam.2018.10.058 10.1007/s10957-011-9932-1 10.1007/s40314-014-0142-y 10.1177/1077546317705041 10.1016/j.jmr.2007.11.007 10.1177/0142331218819048 10.1016/j.cam.2017.09.031 10.1137/0316013 10.1016/S0378-4371(02)01048-8 10.1007/s40995-017-0373-z 10.1016/j.apnum.2019.03.005 10.11121/ijocta.01.2018.00442 10.1016/j.physa.2019.123731 10.1007/s10957-009-9548-x 10.1016/j.amc.2006.06.075 10.1049/ip-d.1983.0003 10.1016/j.amc.2018.10.058 10.1016/j.jfranklin.2003.12.011 10.1007/s40314-019-1003-5 10.1007/s40314-017-0424-2 10.1016/j.cnsns.2018.04.019 10.1177/1077546318777338 10.1002/9783527622979 10.1177/1077546307087435 10.1007/s11071-007-9322-2 10.1177/1077546316687936 10.1007/978-3-642-60185-9_24 10.1007/s10092-015-0160-1 |
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| Keywords | radial basis function fractional optimal control problem direct optimization nonlinear programming problem collocation points delay system |
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| References | Youssri (ref_15) 2018; 8 Jesus (ref_9) 2008; 54 Raberto (ref_6) 2002; 314 Rahimkhani (ref_19) 2018; 77 Zeid (ref_17) 2017; 37 Wang (ref_43) 2007; 184 ref_52 Magin (ref_1) 2008; 190 Rahimkhani (ref_28) 2016; 86 Hosseinpour (ref_39) 2018; 351 Dehghan (ref_30) 2015; 34 Xu (ref_12) 2019; 142 Youssri (ref_11) 2019; 43 ref_24 Dadebo (ref_46) 1992; 13 Chen (ref_47) 2000; 21 Rahimkhani (ref_21) 2018; 42 Moradi (ref_38) 2020; 22 Diwekar (ref_10) 2014; 117 (ref_14) 2020; 39 Bhrawy (ref_26) 2016; 53 Mirinejad (ref_34) 2017; 87 Haddadi (ref_41) 2012; 153 Khellat (ref_50) 2009; 143 Bohannan (ref_8) 2008; 14 Ziaei (ref_31) 2018; 36 Banks (ref_44) 1978; 16 ref_36 ref_35 Moradi (ref_27) 2018; 25 ref_32 Basin (ref_49) 2006; 51 Wahi (ref_23) 2004; 38 Ghomanjani (ref_40) 2013; 33 Zeid (ref_16) 2019; 125 Rao (ref_45) 1983; Volume 130 Mohammadi (ref_13) 2018; 339 Tian (ref_22) 2020; 545 ref_37 Yong (ref_33) 2008; 29 Safaie (ref_25) 2014; 34 Marzban (ref_48) 2004; 341 Safaie (ref_51) 2014; 4 Rabiei (ref_29) 2017; 24 Sun (ref_3) 2018; 64 Chen (ref_20) 2019; 348 Sabermahani (ref_42) 2019; 41 ref_2 Zamani (ref_7) 2007; 10 Jajarmi (ref_53) 2017; 19 ref_5 ref_4 Ghassabzadeh (ref_18) 2020; 3 |
| References_xml | – volume: 33 start-page: 687 year: 2013 ident: ref_40 article-title: Optimal control of time-varying linear delay systems based on the Bezier curves publication-title: Comput. Appl. Math. doi: 10.1007/s40314-013-0089-4 – ident: ref_37 doi: 10.1007/978-3-319-58356-3 – ident: ref_5 – ident: ref_32 – volume: 87 start-page: 219 year: 2017 ident: ref_34 article-title: An RBF collocation method for solving optimal control problems publication-title: Robot. Auton. Syst. doi: 10.1016/j.robot.2016.10.015 – volume: 77 start-page: 1283 year: 2018 ident: ref_19 article-title: Müntz-Legendre wavelet operational matrix of fractional-order integration and its applications for solving the fractional pantograph differential equations publication-title: Numer. Algorithms doi: 10.1007/s11075-017-0363-4 – volume: 38 start-page: 3 year: 2004 ident: ref_23 article-title: Averaging oscillations with small fractional damping and delayed terms publication-title: Nonlinear Dyn. doi: 10.1007/s11071-004-3744-x – volume: 117 start-page: 239 year: 2014 ident: ref_10 article-title: A fractional calculus approach to the dynamic optimization of biological reactive systems. Part II: Numerical solution of fractional optimal control problems publication-title: Chem. Eng. Sci. doi: 10.1016/j.ces.2014.06.033 – volume: 29 start-page: 397 year: 2008 ident: ref_33 article-title: A survey of numerical methods for trajectory optimization of spacecraft publication-title: J. Astronaut. – ident: ref_35 – volume: 13 start-page: 29 year: 1992 ident: ref_46 article-title: Optimal control of time-delay systems by dynamic programming publication-title: Optim. Control Methods doi: 10.1002/oca.4660130103 – volume: 36 start-page: 713 year: 2018 ident: ref_31 article-title: The approximate solution of non-linear time-delay fractional optimal control problems by embedding process publication-title: IMA J. Math. Control Inf. doi: 10.1093/imamci/dnx063 – volume: 86 start-page: 1649 year: 2016 ident: ref_28 article-title: An efficient approximate method for solving delay fractional optimal control problems publication-title: Nonlinear Dyn. doi: 10.1007/s11071-016-2983-y – ident: ref_24 doi: 10.1016/j.aej.2020.04.029 – volume: 51 start-page: 91 year: 2006 ident: ref_49 article-title: Optimal control for linear systems with multiple time delays in control input publication-title: IEEE Trans. Autom. Control doi: 10.1109/TAC.2005.861718 – volume: 43 start-page: 543 year: 2019 ident: ref_11 article-title: Spectral tau algorithm for certain coupled system of fractional differential equations via generalized Fibonacci polynomial sequence publication-title: Iran. J. Sci. Technol. Trans. Sci. doi: 10.1007/s40995-017-0420-9 – volume: 22 start-page: 204 year: 2020 ident: ref_38 article-title: A Comparative Approach for Time-Delay Fractional Optimal Control Problems: Discrete Versus Continuous Chebyshev Polynomials publication-title: Asian J. Control doi: 10.1002/asjc.1858 – volume: 3 start-page: 127 year: 2020 ident: ref_18 article-title: Numerical Method for Approximate Solutions of Fractional Differential Equations with Time-Delay publication-title: Int. J. Ind. Electron. Control. Optim. – volume: 125 start-page: 171 year: 2019 ident: ref_16 article-title: Approximation methods for solving fractional equations publication-title: Chaos Solitons Fractals doi: 10.1016/j.chaos.2019.05.008 – volume: 4 start-page: 77 year: 2014 ident: ref_51 article-title: An approximation method for numerical solution of multi-dimensional feedback delay fractional optimal control problems by Bernstein polynomials publication-title: Iran. J. Numer. Anal. Optim. – volume: 19 start-page: 554 year: 2017 ident: ref_53 article-title: An efficient finite difference method for the time-delay optimal control problems with time-varying delay publication-title: Asian J. Control doi: 10.1002/asjc.1371 – volume: 21 start-page: 91 year: 2000 ident: ref_47 article-title: Numerical solution of time-delayed optimal control problems by iterative dynamic programming publication-title: Optim. Control Appl. Methods doi: 10.1002/1099-1514(200005/06)21:3<91::AID-OCA669>3.0.CO;2-C – volume: 351 start-page: 344 year: 2018 ident: ref_39 article-title: Müntz-Legendre spectral collocation method for solving delay fractional optimal control problems publication-title: J. Comput. Appl. Math. doi: 10.1016/j.cam.2018.10.058 – volume: 153 start-page: 338 year: 2012 ident: ref_41 article-title: Optimal control of delay systems by using a hybrid functions approximation publication-title: J. Optim. Theory Appl. doi: 10.1007/s10957-011-9932-1 – volume: 34 start-page: 831 year: 2014 ident: ref_25 article-title: An approximate method for numerically solving multidimensional delay fractional optimal control problems by Bernstein polynomials publication-title: Comput. Appl. Math. doi: 10.1007/s40314-014-0142-y – volume: 24 start-page: 3370 year: 2017 ident: ref_29 article-title: Fractional-order Boubaker functions and their applications in solving delay fractional optimal control problems publication-title: J. Vib. Control doi: 10.1177/1077546317705041 – volume: 190 start-page: 255 year: 2008 ident: ref_1 article-title: Anomalous diffusion expressed through fractional order differential operators in the Bloch-Torrey equation publication-title: J. Magn. Reson. doi: 10.1016/j.jmr.2007.11.007 – volume: 41 start-page: 2997 year: 2019 ident: ref_42 article-title: Fractional-order Lagrange polynomials: An application for solving delay fractional optimal control problems publication-title: Trans. Inst. Meas. Control doi: 10.1177/0142331218819048 – volume: 10 start-page: 169 year: 2007 ident: ref_7 article-title: FOPID controller design for robust performance using particle swarm optimization publication-title: J. Frac. Calc. Appl. Anal. – volume: 339 start-page: 306 year: 2018 ident: ref_13 article-title: A generalized fractional-order Legendre wavelet Tau method for solving fractional differential equations publication-title: J. Comput. Appl. Math. doi: 10.1016/j.cam.2017.09.031 – volume: 16 start-page: 169 year: 1978 ident: ref_44 article-title: Hereditary control problems: Numerical methods based on averaging approximations publication-title: SIAM J. Control Optim. doi: 10.1137/0316013 – volume: 314 start-page: 749 year: 2002 ident: ref_6 article-title: Waitingtimes and returns in high-frequency financial data: An empirical study publication-title: Physics A doi: 10.1016/S0378-4371(02)01048-8 – volume: 42 start-page: 2131 year: 2018 ident: ref_21 article-title: Numerical studies for fractional pantograph differential equations based on piecewise fractional-order Taylor function approximations publication-title: Iran. J. Sci. Technol. Trans. Sci. doi: 10.1007/s40995-017-0373-z – volume: 142 start-page: 122 year: 2019 ident: ref_12 article-title: Error analysis of the Legendre-Gauss collocation methods for the nonlinear distributed-order fractional differential equation publication-title: Appl. Numer. Math. doi: 10.1016/j.apnum.2019.03.005 – volume: 8 start-page: 152 year: 2018 ident: ref_15 article-title: Spectral tau algorithm for solving a class of fractional optimal control problems via Jacobi polynomials publication-title: Int. J. Optim. Control. Theor. Appl. doi: 10.11121/ijocta.01.2018.00442 – volume: 545 start-page: 123731 year: 2020 ident: ref_22 article-title: The resonance behavior in the fractional harmonic oscillator with time delay and fluctuating mass publication-title: Phys. Stat. Mech. Appl. doi: 10.1016/j.physa.2019.123731 – volume: 143 start-page: 107 year: 2009 ident: ref_50 article-title: Optimal control of linear time-delayed systems by linear Legendre multi-wavelets publication-title: J. Optim. Theory Appl. doi: 10.1007/s10957-009-9548-x – volume: 34 start-page: 77 year: 2015 ident: ref_30 article-title: A numerical approximation for delay fractional optimal control problems based on the method of moments publication-title: IMA J. Math. Control Inf. – volume: 184 start-page: 849 year: 2007 ident: ref_43 article-title: Numerical solutions of optimal control for time delay systems by hybrid of block-pulse functions and Legendre polynomials publication-title: Appl. Math. Comput. doi: 10.1016/j.amc.2006.06.075 – volume: Volume 130 start-page: 9 year: 1983 ident: ref_45 article-title: Improved algorithms for parameter identification in continuous systems via Walsh functions publication-title: IET Proceedings D-Control Theory and Applications doi: 10.1049/ip-d.1983.0003 – volume: 348 start-page: 465 year: 2019 ident: ref_20 article-title: Piecewise Picard iteration method for solving nonlinear fractional differential equation with proportional delays publication-title: Appl. Math. Comput. doi: 10.1016/j.amc.2018.10.058 – volume: 341 start-page: 279 year: 2004 ident: ref_48 article-title: Optimal control of linear delay systems via hybrid of block-pulse and Legendre polynomials publication-title: J. Frankl. Inst. doi: 10.1016/j.jfranklin.2003.12.011 – volume: 39 start-page: 20 year: 2020 ident: ref_14 article-title: Efficient radial basis functions approaches for solving a class of fractional optimal control problems publication-title: Comput. Appl. Math. doi: 10.1007/s40314-019-1003-5 – volume: 37 start-page: 158 year: 2017 ident: ref_17 article-title: Approximation methods for solving fractional optimal control problems publication-title: Comp. Appl. Math. doi: 10.1007/s40314-017-0424-2 – volume: 64 start-page: 213 year: 2018 ident: ref_3 article-title: A new collection of real world applications of fractional calculus in science and engineering publication-title: Commun. Nonlinear Sci. Numer. Simul. doi: 10.1016/j.cnsns.2018.04.019 – volume: 25 start-page: 310 year: 2018 ident: ref_27 article-title: A direct numerical solution of time-delay fractional optimal control problems by using Chelyshov wavelets publication-title: J. Vib. Control doi: 10.1177/1077546318777338 – ident: ref_2 doi: 10.1002/9783527622979 – volume: 14 start-page: 1487 year: 2008 ident: ref_8 article-title: Analog fractional order controller in temperature and motor control applications publication-title: J. Vib. Control doi: 10.1177/1077546307087435 – volume: 54 start-page: 263 year: 2008 ident: ref_9 article-title: Fractional control of heat diffusion systems publication-title: Nonlinear Dyn. doi: 10.1007/s11071-007-9322-2 – ident: ref_36 – ident: ref_52 doi: 10.1177/1077546316687936 – ident: ref_4 doi: 10.1007/978-3-642-60185-9_24 – volume: 53 start-page: 521 year: 2016 ident: ref_26 article-title: A new Legendre operational technique for delay fractional optimal control problems publication-title: Calcolo doi: 10.1007/s10092-015-0160-1 |
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| Snippet | A novel approach to solve optimal control problems dealing simultaneously with fractional differential equations and time delay is proposed in this work. More... |
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| SubjectTerms | collocation points delay system direct optimization fractional optimal control problem nonlinear programming problem radial basis function |
| Title | Optimal Control of Time-Delay Fractional Equations via a Joint Application of Radial Basis Functions and Collocation Method |
| URI | https://www.ncbi.nlm.nih.gov/pubmed/33286981 https://www.proquest.com/docview/2468336809 https://pubmed.ncbi.nlm.nih.gov/PMC7711967 https://doaj.org/article/f6630890602a46a89e596b48661d4abf |
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