Numerical simulation of fractional order optimal control problem

References

• I. Podlubny, Fractional Differential Equations, Academic Press, New York, 1999.
   Google Scholar
• N. K. Jena, S. Sahoo and B. K. Sahu, Fractional order cascaded controller for AGC study in power system with PV and diesel generating units, Journal of Interdisciplinary Mathematics, 23(2) (2020), 425-434.
   Web of Science ®Google Scholar
• M. Houas and A. Saadi, Existence and uniqueness results for a coupled system of nonlinear fractional differential equations with two fractional orders, Journal of Interdisciplinary Mathematics, DOI: 10.1080/09720502.2020.1740499, (2020), 1-18.
   Web of Science ®Google Scholar
• N. R. Babu, S. K. Bhagat, L. C. Saikia and T. Chiranjeevi, Application of hybrid crow-search with particle swarm optimization algorithm in AGC studies of multi-area systems, Journal of Discrete Mathematical Sciences and Cryptography, 23 (2) (2020), 429-439.
   Web of Science ®Google Scholar
• G. Suribabu and T. Chiranjeevi, Implementation of fractional order PID controller for an AVR system using GA and ACO optimization techniques, IFAC-PapersOnLine, 49 (1) (2016), 456-461.
   Google Scholar
• D. S. Naidu, Optimal Control Systems, CRC Press, Bocaraton, Florida, 2003.
   Google Scholar
• O. P. Agrawal, A general formulation and solution scheme for fractional optimal control problems, Nonlinear Dynamics, 38 (2004), 323-337.
   Web of Science ®Google Scholar
• R. K. Biswas and S. Sen, Fractional optimal control problems with specified final time, ASME- Journal of Computational and Nonlinear Dynamics, 6 (2011), 1-6.
   Web of Science ®Google Scholar
• R. K. Biswas and S. Sen, Free final time fractional optimal control problems, Journal of the Franklin Institute, 351 (2014), 941-951.
   Web of Science ®Google Scholar
• A. Alizadeh and S. Effati, Modified Adomian decomposition method for solving fractional optimal control problems, T. I. Meas. Control, 40(6) (2018), 2054-2061.
   Web of Science ®Google Scholar
• H. Hassani, J. A. Tenreiro Machado and E. Naraghirad, Generalized shifted Chebyshev polynomials for fractional optimal control problems, Communications in Nonlinear Science and Numerical Simulation, 75 (2019), 50-61.
   Web of Science ®Google Scholar
• R. K. Biswas and S. Sen, Numerical method for solving fractional optimal control problems, Proceedings of the IDETC-CIE, San Diego, California, USA, August 30-September 02, (2009).
   Google Scholar
• A. Lotfi, A combination of variational and penalty methods for solving a class of fractional optimal control problems, J. Optim. Theory Appl., 174(1) (2017), 65-82.
   Web of Science ®Google Scholar
• M. H. Heydari, M. R. Hooshmandasl, F. M. MaalekGhaini and C. Cattani, Wavelets method for solving fractional optimal control problems, Applied Mathematics and Computation, 286 (2016), 139-154.
   Web of Science ®Google Scholar
• T. Chiranjeevi and R. K. Biswas, Closed-form solution of optimal control problem of a fractional order system, J. King Saud Univ. – Sci, 31 (4) (2019), 1042-1047.
   Web of Science ®Google Scholar
• T. Chiranjeevi and R. K. Biswas, Formulation of optimal control problems of fractional dynamic systems with control constraints, Journal of Advanced Research in Dynamical and Control Systems, 10 (2018), 201- 212.
   Google Scholar
• T. Chiranjeevi and R. K. Biswas, Discrete-time fractional optimal control, Mathematics 5(2) (2017), 1-12.
   Web of Science ®Google Scholar
• T. Chiranjeevi, R. K. Biswas and N. R. Babu, Effect of initialization on optimal control problem of fractional order discrete-time system, Journal of Interdisciplinary Mathematics, 23(1) (2020), 293-302.
   Web of Science ®Google Scholar
• L. Dai, Singular control systems, Thoma M and Wyner A (eds) Lecture Notes in Control and Information Sciences, Springer, Berlin,(1989), 1-340.
   Google Scholar
• R. K. Biswas and S. Sen, Fractional optimal controll problems: a pseudo – state - space approach, Journal of Vibration and Control, 17(7) (2010), 1034-1041.
   Web of Science ®Google Scholar
• R. K. Biswas and S. Sen, Fractional optimal control within Caputo’s derivative, Proceedings of the IDETC-CIE, Washington, DC, USA, August 28-31, (2011).
   Google Scholar
• M. R. A. Moubarak, H. F. Ahmed and O. Khorshi, Numerical solution of the optimal control for fractional order singular systems, Differ. Equ. Dyn. Syst., 26 (1-3) (2018), 279-291.
   Web of Science ®Google Scholar
• T. Chiranjeevi, R. K. Biswas and S. Chudamani, Optimal control of fractional order singular system, International Journal of Electrical Engineering & Education, DOI: 10.1177/0020720919833031, (2019), 1-17.
   Google Scholar
• T. Chiranjeevi, R. K. Biswas and S. K. Pandey, Fixed final time and fixed final state linear quadratic optimal control problem of fractional order singular system, V. K. Giri, N. K. Verma, R. K. Patel and V. P. Singh (eds.) Computing algorithms with applications in engineering, Algorithms for intelligent systems, (2020), 285-294.
   Google Scholar
• T. Chiranjeevi and R. K. Biswas, Linear quadratic optimal control problem of fractional order continuous – time singular system, Procedia Computer Science, 171 (2020), 1261-1268.
   Google Scholar
• T. Chiranjeevi and R. K. Biswas, Computational method based on reflection operator for solving a class of fractional optimal control problem, Procedia Computer Science, 171 (2020), 2030-2039.
   Google Scholar
• T. Chiranjeevi and R. K. Biswas, Numerical approach to the fractional optimal control problem of continuous-time singular system, G. Pradhan, S. Morris and N. Nayak (eds.) Advances in electrical control and signal systems, Lecture Notes in Electrical Engineering, (2020), 239-248.
   Google Scholar