Constrained Optimal Control of A Fractionally Damped Elastic Beam

References

[1] M. Athans and P. L. Fabl, Optimal control an introduction to the theory and its applications. Dover Publications, Inc. Mineola, NewYork, 2007.Search in Google Scholar

[2] D. E. Kirk, Optimal control theory an introduction, Dover Publications, Inc. Mineola, New York, 1998.Search in Google Scholar

[3] D. S. Naidu, Optimal control systems, CRC Press, Boca-Raton, 2002.Search in Google Scholar

[4] A. Jajarmi and D. Baleanu, Optimal control of nonlinear dynamical systems based on a new parallel eigenvalue decomposition approach, Opt. Control Appl. and Methods 39(2) (2018), 1071–1083.10.1002/oca.2397Search in Google Scholar

[5] A. Jajarmi, M. Hajipour and D. Baleanu, A new approach for the optimal control of time-varying delay systems with external persistent matched disturbances, J. Vib. and Control 24(19) (2018), 4505–4512.10.1177/1077546317727821Search in Google Scholar

[6] A. Jajarmi, M. Hajipour, S. S. Sajjadi and D. Baleanu, A robust and accurate disturbance damping control design for nonlinear dynamical systems, Opt. Control Appl. and Methods 40 (2019), 375–393.10.1002/oca.2480Search in Google Scholar

[7] O. P. Agrawal, A general formulation and solution scheme for fractional optimal control problems, Nonlinear Dynam. 38 (2004), 323–337.10.1007/s11071-004-3764-6Search in Google Scholar

[8] O. P. Agrawal, A quadratic numerical scheme for fractional optimal control problems, J. Dyn. Syst. Measur. and Control 130 (2008), 011010 1–6.10.1115/1.2814055Search in Google Scholar

[9] O. P. Agrawal and D. Baleanu, A Hamiltonian formulation and a direct numerical scheme for fractional optimal control problems, J. Vib. Control 13 (2007), 1269–1281.10.1177/1077546307077467Search in Google Scholar

[10] D. Baleanu, Fractional Hamiltonian analysis of irregular systems, Signal Processing, 86(10) (2006), 2632–2636.10.1016/j.sigpro.2006.02.008Search in Google Scholar

[11] O. P. Agrawal, Fractional optimal control of a distributed system using eigenfunctions, In Proc. of DETC2007, ASME, DETC2007/MSNDC-35921.Search in Google Scholar

[12] N. Özdemir, O. P. Agrawal, B. B. İskender and D. Karadeniz, Fractional optimal control of a 2-dimensional distributed system using eigenfunctions, Nonlinear Dynam. 55 (2009), 251–260.10.1007/s11071-008-9360-4Search in Google Scholar

[13] N. Özdemir, O. P. Agrawal, D. Karadeniz and B. B. İskender, Fractional optimal control problem of an axis-symmetric diffusion-wave propagation, Phys. Scr. T136 (2009), 014024 1–5.10.1088/0031-8949/2009/T136/014024Search in Google Scholar

[14] N. Özdemir, D. Karadeniz and B. B. İskender, Fractional optimal control problem of a distributed system in cylindrical coordinates, Phys. Lett. A 373 (2009), 221–226.10.1016/j.physleta.2008.11.019Search in Google Scholar

[15] C. Tricaud and Y.Q. Chen, Time-optimal control of systems with fractional dynamics, Int. J. Differ. Equ. 2010 (2010), 461048.10.1155/2010/461048Search in Google Scholar

[16] M. A. Zaky, J. A. Tenreiro Machado, On the formulation and numerical simulation of distributed-order fractional optimal control problems, Commun. Nonlinear Sci. Numer. Simul. 52 (2017), 177–189.10.1016/j.cnsns.2017.04.026Search in Google Scholar

[17] H. Bhrawy, S. S. Ezz-Eldien, E. H Doha, M. A. Abdelkawy and D. Baleanu, Solving fractional optimal control problems within a Chebyshev-Legendre operational technique, Internat. J. Control 90 (2017), 1230–1244.10.1080/00207179.2016.1278267Search in Google Scholar

[18] N. H. Sweilam and S. M. AL-Mekhlafi, On the optimal control for fractional multi-strain TB model, Optim. Control Appl. Meth. 37 (2016), 1355–1374.10.1002/oca.2247Search in Google Scholar

[19] N. H. Sweilam and S. M. AL-Mekhlafi, Optimal control for a nonlinear mathematical model of tumor under immune suppression, Optim. Control Appl. Meth. 39 (2018), 1581–1596.10.1002/oca.2427Search in Google Scholar

[20] A. B. Salati, M. Shamsi, D. F. M. Torres, Direct transcription methods based on fractional integral approximation formulas for solving nonlinear fractional optimal control problems, Commun. Nonlinear Sci. Numer. Simul. 67 (2019), 334–350.10.1016/j.cnsns.2018.05.011Search in Google Scholar

[21] F. Mohammadi, L. Moradi, D. Baleanu and A. Jajarmi, A hybrid functions numerical scheme for fractional optimal control problems: Application to nonanalytic dynamic systems, J. Vib. and Control 24(21) (2018), 5030–5043.10.1177/1077546317741769Search in Google Scholar

[22] D. Baleanu, J. H. Asad and A. Jajarmi, New aspects of the motion of a particle in a circular cavity, Proc. Rom. Acad. A 19 (2018), 361–367.Search in Google Scholar

[23] D. Baleanu, J. H. Asad and A. Jajarmi, The fractional model of spring pendulumml: New features within different kernels, Proc. Rom. Acad. A 19(3) (2018), 447–454.Search in Google Scholar

[24] O. P. Agrawal, An analytical scheme for stochastic dynamic systems containing fractional derivatives, Proc. of the 1999 ASME Des. Eng. Tech. Conf., Las Vegas, Nevada, (1999).10.1115/DETC99/VIB-8238Search in Google Scholar

[25] L. Yuan and O. P. Agrawal, A numerical scheme for dynamic systems containing fractional derivatives, J. Vib. Acoust. 124 (2002), 321–324.10.1115/1.1448322Search in Google Scholar

[26] B. Mbodje, G. Montseny, J. Audonet and P. Benchimol, Optimal control for fractionally damped flexible systems, The Proc. of the Third IEEE Conf. on Control Applications, The University of Strathclyde, Glasgow, 1329–1333, August 1994.10.1109/CCA.1994.381303Search in Google Scholar

[27] R. K. Biswas and T. Chiranjeevi, Formulation of optimal control problems of fractional dynamic systems with control constraints, J. Adv. Res. Dyn. Control Syst. 10 (2018), 201–212.Search in Google Scholar

[28] M. Eckert, K. Nagatou, F. Rey, O. Stark, S. Hohmann, Controllability and energy-optimal control of time-variant fractional systems, IEEE Conference on Decision and Control (CDC 2018), Miami, FL, pp. 4607–4612, December, 2018.10.1109/CDC.2018.8619785Search in Google Scholar

[29] K. S. Miller and B. Ross, An introduction to the fractional calculus and fractional differential equations, Wiley, New York, 1993.Search in Google Scholar

[30] K. B. Oldham and J. Spanier, The fractional calculus, Academic, New York, 1974.Search in Google Scholar

[31] I. Podlubny, Fractional differential equations, Academic Press, New York, (1999).Search in Google Scholar

[32] R. Hotzel and M. Flies, On linear systems with a fractional derivation: Introductory theory and examples, Math. Comput. Simulation 45 (1998), 385–395.10.1016/S0378-4754(97)00118-3Search in Google Scholar

[33] K. Diethelm, N. J. Ford and A. D. Freed, A predictor corrector approach for the numerical solution of fractional differential equations, Nonlinear Dyn. 29 (2002), 3–22.10.1023/A:1016592219341Search in Google Scholar

[34] O. P. Agrawal, A formulation and a numerical scheme for fractional optimal control problems, J. Vib. and Control 14(9–10) (2008), 1291–1299.10.1177/1077546307087451Search in Google Scholar