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Displaying similar documents to “Time-optimal control of systems with fractional dynamics.”

Optimal control problem and maximum principle for fractional order cooperative systems

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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...

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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.

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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...

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International Journal of Applied Mathematics and Computer Science

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This paper studies distributed optimization problems of a class of agents with fractional order dynamics and unknown external disturbances. Motivated by the celebrated active disturbance rejection control (ADRC) method, a fractional order extended state observer (Frac-ESO) is first constructed, and an ADRC-based PI-like protocol is then proposed for the target distributed optimization problem. It is rigorously shown that the decision variables of the agents reach a domain of the optimal...

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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...

Fractional Roesser problem and its optimization

Rafał Kamocki (2014)

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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.

Chaos synchronization of a fractional nonautonomous system

Zakia Hammouch, Toufik Mekkaoui (2014)

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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.

Design of unknown input fractional-order observers for fractional-order systems

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,...