Effect of initialization on optimal control problem of fractional order discrete-time system

References

• I. Podlubny , Fractional Differential Equations, Academic Press, New York , 1999.
   Google Scholar
• H. Rezazadeh , K. K. Ali , M. Eslami , M. Mirzazadeh and H. Yépez-Martínez ,On the soliton solutions to the space-time fractional simplified MCH equation, Journal of Interdisciplinary Mathematics , 22(2) (2019),149-165. doi: 10.1080/09720502.2019.1597431
   Web of Science ®Google Scholar
• D. Foukrach , Approximate solution to a Bürgers system with time and space fractional derivatives using Adomian decomposition method, Journal of Interdisciplinary Mathematics , 21(1) (2018),111-125. doi: 10.1080/09720502.2014.986914
   Web of Science ®Google Scholar
• D. Ziane and M. H. Cherif , Variational iteration transform method for fractional differential equations, Journal of Interdisciplinary Mathematics , 21(1) (2018), 185-199. doi: 10.1080/09720502.2015.1103001
   Web of Science ®Google Scholar
• V. B. L. Chaurasia and R. S. Dubey , Analytical solution for the generalized time–fractional telegraph equation, Fractional Differential Calculus 3(1) (2013), 21-29. doi: 10.7153/fdc-03-02
   Google Scholar
• R. S. Dubey , P. Goswami and F. B. M. Belgacem , Generalized time-fractional telegraph equation analytical solution by Sumudu and Fourier transforms, Journal of Fractional Calculus and Applications 5(2) (2014), 52-58.
   Google Scholar
• R. S. Dubey and P. Goswami ,Analytical solution of the nonlinear diffusion equation, Eur. Phys. J. Plus 133 (5) (2018), 1-12.
   Web of Science ®Google Scholar
• C. F. Lorenzo and T. T. Hartely , Initialization, conceptualization, and application in the generalized fractional calculus, NASA/TP , (1998), 208415.
   Google Scholar
• C. F. Lorenzo and T. T. Hartely , Initialization of fractional order operators and fractional differential equations, ASME - Journal of Computational and Nonlinear Dynamics , 3 (2008), 0211011 – 0211019.
   Web of Science ®Google Scholar
• D. Saha , D. Mondal and S. Sen , Effect of initialization on a class of fractional order systems: Experimental verification and dependence on nature of past history and system parameters, CircuitsSyst Signal Process , 32 (2013), 1501-1522. doi: 10.1007/s00034-012-9537-4
   Web of Science ®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. doi: 10.1007/s11071-004-3764-6
   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), 0210091 – 0210096.
   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. doi: 10.1016/j.jfranklin.2013.09.024
   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
• 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. doi: 10.1177/1077546310373618
   Web of Science ®Google Scholar
• E. Keshavarz , Y. Ordokhani and M. Razzaghi , A numerical solution for fractional optimal control problems via Bernoulli polynomials, Journal of Vibration and Control , (2015), 1-15.
   Web of Science ®Google Scholar
• R. Almeida and D. F. M. Torres , A discrete method to solve fractional optimal control problems, Nonlinear Dynamics , 80 (2015), 1811-1816. doi: 10.1007/s11071-014-1378-1
   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 , DOI: 10.1016/j.jksus.2019.02.010, (2019), 1-6.
   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
• A. Dzielinskiand P . M. Czyronis , Fixed final time and free final state optimal control problem for fractional dynamic systems - linear quadratic discrete - time case, Bull. Pol. Ac. : Tech . 61 (3) (2013), 681-690.
   Web of Science ®Google Scholar
• T. Chiranjeevi and R. K. Biswas , Discrete-time fractional optimal control, Mathematics 5(2) (2017), 1-12. doi: 10.3390/math5020025
   Web of Science ®Google Scholar
• P. M. Czyronis , Dynamic programming problem for fractional discrete - time dynamic systems. Quadratic index of performance case, Circuits Syst Signal Process , 33 (2014), 2131-2149. doi: 10.1007/s00034-014-9746-0
   Web of Science ®Google Scholar