Study of an approximation process of time optimal control for fractional evolution systems in Banach spaces.
Wang, Jinrong, Zhou, Yong (2011)
Advances in Difference Equations [electronic only]
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Wang, Jinrong, Zhou, Yong (2011)
Advances in Difference Equations [electronic only]
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Tadeusz Kaczorek (2014)
International Journal of Applied Mathematics and Computer Science
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A minimum energy control problem for fractional positive continuous-time linear systems with bounded inputs is formulated and solved. Sufficient conditions for the existence of a solution to the problem are established. A procedure for solving the problem is proposed and illustrated with a numerical example.
Samir Ladaci, Abdelfatah Charef, Jean Jacques Loiseau (2009)
International Journal of Applied Mathematics and Computer Science
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This paper presents a new approach to robust adaptive control, using fractional order systems as parallel feedforward in the adaptation loop. The problem is that adaptive control systems may diverge when confronted with finite sensor and actuator dynamics, or with parasitic disturbances. One of the classical robust adaptive control solutions to these problems makes use of parallel feedforward and simplified adaptive controllers based on the concept of positive realness. The proposed...
Łukasz Sajewski (2017)
International Journal of Applied Mathematics and Computer Science
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Reachability and minimum energy control of descriptor fractional discrete-time linear systems with different fractional orders are addressed. Using the Weierstrass-Kronecker decomposition theorem of the regular pencil, a solution to the state equation of descriptor fractional discrete-time linear systems with different fractional orders is given. The reachability condition of this class of systems is presented and used for solving the minimum energy control problem. The discussion is...
Gutiérrez, Ricardo Enrique, Rosário, João Maurício, Machado, José Tenreiro (2010)
Mathematical Problems in Engineering
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Rafał Kamocki (2014)
Banach Center Publications
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In the paper, a fractional continuous Roesser model is considered. Existence and uniqueness of a solution and continuous dependence of solutions on controls of the nonlinear model are investigated. Next, a theorem on the existence of an optimal solution for linear model with variable coefficients is proved.
Zakia Hammouch, Toufik Mekkaoui (2014)
Nonautonomous Dynamical Systems
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In this paper we investigate the dynamic behavior of a nonautonomous fractional-order biological system.With the stability criterion of active nonlinear fractional systems, the synchronization of the studied chaotic system is obtained. On the other hand, using a Phase-Locked-Loop (PLL) analogy we synchronize the same system. The numerical results demonstrate the effectiveness of the proposed methods.
Zhou, Ping, Kuang, Fei (2011)
Discrete Dynamics in Nature and Society
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Delshad, Saleh Sayyad, Asheghan, Mohammad Mostafa, Beheshti, Mohammadtaghi Hamidi (2010)
Advances in Difference Equations [electronic only]
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Tadeusz Kaczorek (2014)
International Journal of Applied Mathematics and Computer Science
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Ibrahima N'Doye, Mohamed Darouach, Holger Voos, Michel Zasadzinski (2013)
International Journal of Applied Mathematics and Computer Science
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This paper considers a method of designing fractional-order observers for continuous-time linear fractional-order systems with unknown inputs. Conditions for the existence of these observers are given. Sufficient conditions for the asymptotical stability of fractional-order observer errors with the fractional order α satisfying 0 < α < 2 are derived in terms of linear matrix inequalities. Two numerical examples are given to demonstrate the applicability of the proposed approach,...
Xin, Baogui, Chen, Tong, Liu, Yanqin (2010)
Mathematical Problems in Engineering
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Tadeusz Kaczorek (2014)
International Journal of Applied Mathematics and Computer Science
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Tadeusz Kaczorek (2014)
International Journal of Applied Mathematics and Computer Science
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Abd-Elouahab, Mohammed Salah, Hamri, Nasr-Eddine, Wang, Junwei (2010)
Mathematical Problems in Engineering
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Abdelbaki Djouambi, Abdelfatah Charef, Alina Voda besancon (2007)
International Journal of Applied Mathematics and Computer Science
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This paper provides an optimal approximation of the fundamental linear fractional order transfer function using a distribution of the relaxation time function. Simple methods, useful in systems and control theories, which can be used to approximate the irrational transfer function of a class of fractional systems fora given frequency band by a rational function are presented. The optimal parameters of the approximated model are obtained by minimizing simultaneously the gain and the phase...