{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,9,11]],"date-time":"2024-09-11T03:11:54Z","timestamp":1726024314994},"reference-count":42,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[2019,1,2]],"date-time":"2019-01-02T00:00:00Z","timestamp":1546387200000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Engineering with Computers"],"published-print":{"date-parts":[[2020,1]]},"DOI":"10.1007\/s00366-018-0688-1","type":"journal-article","created":{"date-parts":[[2019,1,2]],"date-time":"2019-01-02T06:33:53Z","timestamp":1546410833000},"page":"115-125","update-policy":"http:\/\/dx.doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":17,"title":["Collocation method to solve inequality-constrained optimal control problems of arbitrary order"],"prefix":"10.1007","volume":"36","author":[{"ORCID":"http:\/\/orcid.org\/0000-0003-0174-7328","authenticated-orcid":false,"given":"K.","family":"Rabiei","sequence":"first","affiliation":[]},{"given":"K.","family":"Parand","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2019,1,2]]},"reference":[{"key":"688_CR1","doi-asserted-by":"publisher","first-page":"479","DOI":"10.1016\/j.advwatres.2012.04.005","volume":"51","author":"DA Benson","year":"2013","unstructured":"Benson DA, Meerschaert MM, Revielle J (2013) Fractional calculus in hydrologic modeling: a numerical perspective. Adv. Water Resour 51:479\u2013497","journal-title":"Adv. Water Resour"},{"key":"688_CR2","doi-asserted-by":"publisher","first-page":"196","DOI":"10.1016\/j.cma.2014.09.018","volume":"283","author":"S Larsson","year":"2015","unstructured":"Larsson S, Racheva M, Saedpanah F (2015) Discontinuous Galerkin method for an integro-differential equation modeling dynamic fractional order viscoelasticity. Comput. Method. Appl. Mech. Eng. 283:196\u2013209","journal-title":"Comput. Method. Appl. Mech. Eng."},{"issue":"15","key":"688_CR3","doi-asserted-by":"publisher","first-page":"2218","DOI":"10.1002\/mma.2968","volume":"37","author":"G Gonzalez-Parra","year":"2014","unstructured":"Gonzalez-Parra G, Arenas AJ, Chen-Charpentier BM (2014) A fractional order epidemic model for the simulation of outbreaks of influenza A(H1N1). Math. Methods Appl. Sci. 37(15):2218\u20132226","journal-title":"Math. Methods Appl. Sci."},{"key":"688_CR4","doi-asserted-by":"publisher","first-page":"1487","DOI":"10.1177\/1077546307087435","volume":"14","author":"GW Bohannan","year":"2008","unstructured":"Bohannan GW (2008) Analog fractional order controller in temperature and motor control applications. J. Vib. Control. 14:1487\u20131498","journal-title":"J. Vib. Control."},{"issue":"17","key":"688_CR5","doi-asserted-by":"publisher","first-page":"6070","DOI":"10.1002\/mma.3765","volume":"40","author":"Xiao-Jun Yang","year":"2015","unstructured":"Yang XJ, Machado JAT (2015) A new insight into complexity from the local fractional calculus view point: modelling growths of populations, Math. Methods Appl. Sci. \nhttps:\/\/doi.org\/10.1002\/mma.3765","journal-title":"Mathematical Methods in the Applied Sciences"},{"key":"688_CR6","doi-asserted-by":"publisher","first-page":"15","DOI":"10.1115\/1.3101682","volume":"50","author":"YA Rossikhin","year":"1997","unstructured":"Rossikhin YA, Shitikova MV (1997) Applications of fractional calculus to dynamic problems of linear and nonlinear hereditary mechanics of solids. Appl. Mech. Rev. 50:15\u201367","journal-title":"Appl. Mech. Rev."},{"key":"688_CR7","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1615\/CritRevBiomedEng.v32.10","volume":"32","author":"RL Magin","year":"2004","unstructured":"Magin RL (2004) Fractional calculus in bioengineering. Crit. Rev. Biomed. Eng. 32:1\u2013104","journal-title":"Crit. Rev. Biomed. Eng."},{"key":"688_CR8","unstructured":"Kilbas AA, Srivastava HM, Trujillo JJ (2006) Theory and Applications of Fractional Differential Equations. In: North-Holland Mathematics Studies, 204, Elsevier Science B.V, Amsterdam"},{"issue":"12","key":"688_CR9","doi-asserted-by":"publisher","first-page":"1784","DOI":"10.1002\/mma.2935","volume":"37","author":"YF Pu","year":"2014","unstructured":"Pu YF, Siarry P, Zhou L, Zhang N (2014) A fractional partial differential equation based multiscale denoising model for texture image. Math. Methods Appl. Sci. 37(12):1784\u20131806","journal-title":"Math. Methods Appl. Sci."},{"issue":"3","key":"688_CR10","doi-asserted-by":"publisher","first-page":"263","DOI":"10.1007\/s11071-007-9322-2","volume":"54","author":"IS Jesus","year":"2008","unstructured":"Jesus IS, Machado JAT (2008) Fractional control of heat diffusion systems. Nonlinear Dyn. 54(3):263\u2013282","journal-title":"Nonlinear Dyn."},{"key":"688_CR11","doi-asserted-by":"publisher","first-page":"1499","DOI":"10.1177\/1077546307087434","volume":"14","author":"IJ Suarez","year":"2008","unstructured":"Suarez IJ, Vinagre BM, Chen YQ (2008) A fractional adaptation scheme for lateral control of an AGV. J. Vib. Control 14:1499\u20131511","journal-title":"J. Vib. Control"},{"key":"688_CR12","doi-asserted-by":"publisher","first-page":"323","DOI":"10.1007\/s11071-004-3764-6","volume":"38","author":"OP Agrawal","year":"2004","unstructured":"Agrawal OP (2004) A general formulation and solution scheme for fractional optimal control problems. Nonlinear Dyn. 38:323\u2013337","journal-title":"Nonlinear Dyn."},{"key":"688_CR13","doi-asserted-by":"publisher","first-page":"1269","DOI":"10.1177\/1077546307077467","volume":"13","author":"OP Agrawal","year":"2007","unstructured":"Agrawal OP (2007) A Hamiltonian formulation and a direct numerical scheme for fractional optimal control problem. J. Vib. Control. 13:1269\u20131281","journal-title":"J. Vib. Control."},{"key":"688_CR14","doi-asserted-by":"publisher","first-page":"143","DOI":"10.1016\/j.cam.2013.03.003","volume":"250","author":"A Lotfi","year":"2013","unstructured":"Lotfi A, Yousefi SA, Dehghan M (2013) Numerical solution of a class of fractional optimal control problems via the Legendre orthonormal basis combined with the operational matrix and the Gauss quadrature rule. J. Comput. Appl. Math. 250:143\u2013160","journal-title":"J. Comput. Appl. Math."},{"issue":"S1","key":"688_CR15","doi-asserted-by":"publisher","first-page":"158","DOI":"10.1007\/s40314-017-0424-2","volume":"37","author":"Samaneh Soradi Zeid","year":"2017","unstructured":"Zeid SS, Effati S, Kamyad AV (2016) Approximation methods for solving fractional optimal control problems, Computational and Applied Mathematics \nhttps:\/\/doi.org\/10.1007\/s40314-017-0424-2","journal-title":"Computational and Applied Mathematics"},{"issue":"15","key":"688_CR16","doi-asserted-by":"publisher","first-page":"3370","DOI":"10.1177\/1077546317705041","volume":"24","author":"Kobra Rabiei","year":"2017","unstructured":"Rabiei K, Ordokhani Y, Babolian E (2017) Fractional-order Boubaker functions and their applications in solving delay fractional optimal control problems, J. Vib. Control. \nhttps:\/\/doi.org\/10.1177\/1077546317705041","journal-title":"Journal of Vibration and Control"},{"issue":"4","key":"688_CR17","doi-asserted-by":"publisher","first-page":"1811","DOI":"10.1007\/s11071-014-1378-1","volume":"80","author":"Ricardo Almeida","year":"2014","unstructured":"Almeida R, Torres DFM (2015) A discrete method to solve fractional optimal control problems, Nonlinear Dyn. 2015; 80(2), 1811-1816","journal-title":"Nonlinear Dynamics"},{"issue":"3","key":"688_CR18","doi-asserted-by":"publisher","first-page":"831","DOI":"10.1007\/s40314-014-0142-y","volume":"34","author":"E. Safaie","year":"2014","unstructured":"Safaie E, Farahi M.H., Ardehaie M Farmani (2015) An approximate method for numerically solving multi-dimensional delay fractional optimal control problems by Bernstein polynomials, Computational and Applied Mathematics, 34(3) , 831-846","journal-title":"Computational and Applied Mathematics"},{"issue":"2","key":"688_CR19","doi-asserted-by":"publisher","first-page":"1013","DOI":"10.1007\/s11071-016-3291-2","volume":"88","author":"K Rabiei","year":"2017","unstructured":"Rabiei K, Ordokhani Y, Babolian E (2017) The Boubaker polynomials and their application to solve fractional optimal control problems. Nonlinear Dyn. 88(2):1013\u20131026","journal-title":"Nonlinear Dyn."},{"key":"688_CR20","first-page":"291","volume":"4","author":"SF Drefus","year":"1962","unstructured":"Drefus SF (1962) Variational problems with state variable inequality constraint. J. Math. Anal. Appl. 4:291\u2013301","journal-title":"J. Math. Anal. Appl."},{"key":"688_CR21","doi-asserted-by":"publisher","first-page":"69","DOI":"10.1109\/TAC.1972.1099881","volume":"17","author":"RK Mehra","year":"1972","unstructured":"Mehra RK, Davis RE (1972) A generalized gradiant method for optimal control problems with inequality constraint and singular arcs. IEEE Transactions on Automatic control 17:69\u201372","journal-title":"IEEE Transactions on Automatic control"},{"issue":"4","key":"688_CR22","doi-asserted-by":"publisher","first-page":"835","DOI":"10.1115\/1.2361321","volume":"128","author":"A Khalid","year":"2006","unstructured":"Khalid A, Huey J, Singhose W, Lawrence J, Frakes D (2006) Human operator performance testing using an input\n$$-$$\n\n\n\n-\n\n\n\nshaped bridge crane. J. Dyn. Sys. Meas. Control. 128(4):835\u2013841","journal-title":"J. Dyn. Sys. Meas. Control."},{"issue":"6","key":"688_CR23","doi-asserted-by":"publisher","first-page":"1863","DOI":"10.1007\/s12206-013-0437-8","volume":"27","author":"LA Tuan","year":"2013","unstructured":"Tuan LA, Lee SG (2013) Sliding mode controls of double-pendulum crane systems. Journal of Mechanical Science and Technology 27(6):1863\u20131873","journal-title":"Journal of Mechanical Science and Technology"},{"issue":"7","key":"688_CR24","doi-asserted-by":"publisher","first-page":"1115","DOI":"10.1109\/TAC.2006.878570","volume":"51","author":"Q Gong","year":"2006","unstructured":"Gong Q, Kang W, Ross IM (2006) A pseudospectral method for the optimal control of constrained feedback linearizable systems. IEEE Transactions on Automatic Control 51(7):1115\u20131129","journal-title":"IEEE Transactions on Automatic Control"},{"key":"688_CR25","doi-asserted-by":"publisher","first-page":"177","DOI":"10.1016\/j.isatra.2016.02.007","volume":"62","author":"M Li","year":"2016","unstructured":"Li M, Peng H (2016) Solutions of nonlinear constrained optimal control problems using quasilinearization and variational pseudospectral methods. ISA Transactions 62:177\u2013192","journal-title":"ISA Transactions"},{"key":"688_CR26","doi-asserted-by":"publisher","first-page":"335","DOI":"10.1016\/j.isatra.2017.02.018","volume":"68","author":"Xinwei Wang","year":"2017","unstructured":"Wang X, Peng H, Zhang S, Chen B, Zhong W (2017) A symplectic pseudospectra method for nonlinear optimal control problems with inequality constraints, ISA Transactions \nhttps:\/\/doi.org\/10.1016\/j.isatra.2017.02.018","journal-title":"ISA Transactions"},{"issue":"18","key":"688_CR27","doi-asserted-by":"publisher","first-page":"5452","DOI":"10.1002\/mma.3930","volume":"39","author":"L Lu","year":"2016","unstructured":"Lu L, Liu Z, Jiang W, Luo J (2016) Optimal controls for fractional differential evolution hemivariational inequalities. Math. Methods Appl. Sci. 39(18):5452\u20135464","journal-title":"Math. Methods Appl. Sci."},{"key":"688_CR28","doi-asserted-by":"publisher","first-page":"2523","DOI":"10.1177\/1077546312458308","volume":"19","author":"M Alipour","year":"2013","unstructured":"Alipour M, Rostamy D, Baleanu D (2013) Solving multi-dimensional fractional optimal control problems with inequality constraint by Bernstein polynomials operational matrices. J. Vib. Control. 19:2523\u20132540","journal-title":"J. Vib. Control."},{"issue":"5","key":"688_CR29","doi-asserted-by":"publisher","first-page":"541","DOI":"10.21136\/AM.2018.0083-18","volume":"63","author":"K Rabiei","year":"2018","unstructured":"Rabiei K, Ordokhani Y (2018) Boubaker hybrid functions and their application to solve fractional optimal control and fractional variational problems. Application of Mathematics. 63(5):541\u2013567","journal-title":"Application of Mathematics."},{"key":"688_CR30","doi-asserted-by":"publisher","first-page":"25","DOI":"10.1016\/j.aml.2012.01.027","volume":"26","author":"AH Bhrawy","year":"2013","unstructured":"Bhrawy AH, Alofi AS (2013) The operational matrix of fractional integration for shifted Chebyshev polynomials. Appl. Math. Letters. 26:25\u201331","journal-title":"Appl. Math. Letters."},{"issue":"1","key":"688_CR31","doi-asserted-by":"publisher","first-page":"015011","DOI":"10.1088\/0031-8949\/83\/01\/015011","volume":"83","author":"K Parand","year":"2011","unstructured":"Parand K, Abbasbandy S, Kazem S, Rezaei AR (2011) An improved numerical method for a class of astrophysics problems based on radial basis functions, Phys. Scr. 83 (11)","journal-title":"Physica Scripta"},{"key":"688_CR32","doi-asserted-by":"publisher","first-page":"2364","DOI":"10.1016\/j.camwa.2011.07.024","volume":"62","author":"EH Doha","year":"2011","unstructured":"Doha EH, Bhrawy AH, Ezz-Eldien SS (2011) A Chebyshev spectral method based on operational matrix for initial and boundary value problems of fractional order. Comput. Math. Appl. 62:2364\u20132373","journal-title":"Comput. Math. Appl."},{"issue":"1","key":"688_CR33","doi-asserted-by":"publisher","first-page":"307","DOI":"10.1007\/s11587-016-0291-y","volume":"65","author":"K Parand","year":"2016","unstructured":"Parand K, Delkhosh M (2016) Solving Volterra\u2019s population growth model of arbitrary order using the generalized fractional order of the Chebyshev functions. Ricerche Mat. 65(1):307\u2013328","journal-title":"Ricerche Mat."},{"key":"688_CR34","first-page":"96","volume":"1","author":"MA Darani","year":"2013","unstructured":"Darani MA, Nasiri M (2013) A fractional type of the Chebyshev polynomials for approximation of solution of linear fractional differential equations. Comp. Meth. Differ. Equ. 1:96\u2013107","journal-title":"Comp. Meth. Differ. Equ."},{"key":"688_CR35","volume-title":"Theory of Matrices","author":"P Lancaster","year":"1969","unstructured":"Lancaster P (1969) Theory of Matrices. Academic Press, New York"},{"key":"688_CR36","doi-asserted-by":"publisher","first-page":"479","DOI":"10.1016\/S0016-0032(02)00028-5","volume":"339","author":"H Jaddu","year":"2002","unstructured":"Jaddu H (2002) Direct solution of nonlinear optimal control problems using quasilinearization and Chebyshev polynomials. J Frank Inst 339:479\u2013498","journal-title":"J Frank Inst"},{"key":"688_CR37","doi-asserted-by":"publisher","first-page":"1831","DOI":"10.1016\/j.cnsns.2011.09.008","volume":"17","author":"S Mashayekhi","year":"2012","unstructured":"Mashayekhi S, Ordokhani Y, Razzaghi M (2012) Hybrid functions approach for nonlinear constrained optimal control problems. Commun Nonlinear Sci Numer Simulat 17:1831\u20131843","journal-title":"Commun Nonlinear Sci Numer Simulat"},{"issue":"10","key":"688_CR38","doi-asserted-by":"publisher","first-page":"1793","DOI":"10.1109\/9.467672","volume":"40","author":"G Elnagar","year":"1995","unstructured":"Elnagar G, Kazemi MA, Razzaghi M (1995) The Pseudospectral Legendre method for discretizing optimal control problems. IEEE Transactions On Automatic Control. 40(10):1793\u20131796","journal-title":"IEEE Transactions On Automatic Control."},{"issue":"1","key":"688_CR39","first-page":"1","volume":"52","author":"M Maleki","year":"2011","unstructured":"Maleki M, Tirani M Dadkhah (2011) Chebyshev finite difference method for solving constrained quadratic optimal control problems. Journal of Mathematical Extension 52(1):1\u201321","journal-title":"Journal of Mathematical Extension"},{"key":"688_CR40","doi-asserted-by":"publisher","first-page":"499","DOI":"10.1016\/0005-1098(88)90094-5","volume":"24","author":"J Vlassenbroeck","year":"1988","unstructured":"Vlassenbroeck J (1988) A Chebyshev polynomial method for optimal control with state constraints. Automatica. 24:499\u2013506","journal-title":"Automatica."},{"key":"688_CR41","unstructured":"Ordokhani Y, Razzaghi M (2005) Linear quadratic optimal control problems with inequality constraints via Rationalizes Haar functions, DCDIS Series B: Applications and Algorithms, 761-773"},{"issue":"9","key":"688_CR42","doi-asserted-by":"publisher","first-page":"1621","DOI":"10.1177\/1077546316665956","volume":"24","author":"S Mashayekhi","year":"2018","unstructured":"Mashayekhi S, Razzaghi M (2018) An approximate method for solving fractional optimal control problems by hybrid functions. J. Vib. Control. 24(9):1621\u20131631","journal-title":"J. Vib. Control."}],"container-title":["Engineering with Computers"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s00366-018-0688-1.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s00366-018-0688-1\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s00366-018-0688-1.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,10]],"date-time":"2020-01-10T05:37:30Z","timestamp":1578634650000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s00366-018-0688-1"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019,1,2]]},"references-count":42,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2020,1]]}},"alternative-id":["688"],"URL":"https:\/\/doi.org\/10.1007\/s00366-018-0688-1","relation":{},"ISSN":["0177-0667","1435-5663"],"issn-type":[{"value":"0177-0667","type":"print"},{"value":"1435-5663","type":"electronic"}],"subject":[],"published":{"date-parts":[[2019,1,2]]},"assertion":[{"value":"29 July 2018","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"17 December 2018","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"2 January 2019","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}]}}