Fractional order calculus: basic concepts and engineering applications.
Gutiérrez, Ricardo Enrique, Rosário, João Maurício, Machado, José Tenreiro (2010)
Mathematical Problems in Engineering
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Gutiérrez, Ricardo Enrique, Rosário, João Maurício, Machado, José Tenreiro (2010)
Mathematical Problems in Engineering
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Tricaud, Christophe, Chen, Yangquan (2010)
International Journal of Differential Equations
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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...
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.
Delshad, Saleh Sayyad, Asheghan, Mohammad Mostafa, Beheshti, Mohammadtaghi Hamidi (2010)
Advances in Difference Equations [electronic only]
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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,...
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...
G. M. Bahaa (2019)
Kybernetika
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In this paper, by using the classical control theory, the optimal control problem for fractional order cooperative system governed by Schrödinger operator is considered. The fractional time derivative is considered in a Riemann-Liouville and Caputo senses. The maximum principle for this system is discussed. We first study by using the Lax-Milgram Theorem, the existence and the uniqueness of the solution of the fractional differential system in a Hilbert space. Then we show that the considered...
Machado, J.A.Tenreiro (2011)
Advances in Difference Equations [electronic only]
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Kobra Rabiei, Yadollah Ordokhani (2018)
Applications of Mathematics
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A new hybrid of block-pulse functions and Boubaker polynomials is constructed to solve the inequality constrained fractional optimal control problems (FOCPs) with quadratic performance index and fractional variational problems (FVPs). First, the general formulation of the Riemann-Liouville integral operator for Boubaker hybrid function is presented for the first time. Then it is applied to reduce the problems to optimization problems, which can be solved by the existing method. In this...
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.
Xin, Baogui, Chen, Tong, Liu, Yanqin (2010)
Mathematical Problems in Engineering
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Patkar, Vivek, Stancu-Minasian, I.M. (1991)
Portugaliae mathematica
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Machado, J.A.Tenreiro, Silva, Manuel F., Barbosa, Ramiro S., Jesus, Isabel S., Reis, Cecília M., Marcos, Maria G., Galhano, Alexandra F. (2010)
Mathematical Problems in Engineering
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