Time-optimal control of systems with fractional dynamics.
Tricaud, Christophe, Chen, Yangquan (2010)
International Journal of Differential Equations
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Tricaud, Christophe, Chen, Yangquan (2010)
International Journal of Differential Equations
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Wang, Jinrong, Xiang, X., Wei, W. (2009)
Electronic Journal of Qualitative Theory of Differential 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.
Noriaki Yamazaki (2009)
Banach Center Publications
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In this paper we consider optimal control problems for abstract nonlinear evolution equations associated with time-dependent subdifferentials in a real Hilbert space. We prove the existence of an optimal control that minimizes the nonlinear cost functional. Also, we study approximating control problems of our equations. Then, we show the relationship between the original optimal control problem and the approximating ones. Moreover, we give some applications of our abstract results. ...
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...
Marina L. Kleptsyna, Alain Le Breton, Michel Viot (2008)
ESAIM: Probability and Statistics
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In this paper we solve the basic fractional analogue of the classical linear-quadratic Gaussian regulator problem in continuous-time with partial observation. For a controlled linear system where both the state and observation processes are driven by fractional Brownian motions, we describe explicitly the optimal control policy which minimizes a quadratic performance criterion. Actually, we show that a separation principle holds, , the optimal control separates into two stages based...
Atle Seierstad (2013)
ESAIM: Control, Optimisation and Calculus of Variations
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Optimal nonanticipating controls are shown to exist in nonautonomous piecewise deterministic control problems with hard terminal restrictions. The assumptions needed are completely analogous to those needed to obtain optimal controls in deterministic control problems. The proof is based on well-known results on existence of deterministic optimal controls.
A. Pliś (1975)
Annales Polonici Mathematici
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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.
J. L. Gámez, J. A. Montero (1997)
ESAIM: Control, Optimisation and Calculus of Variations
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JinRong Wang, Wei Wei (2012)
Annales Polonici Mathematici
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This paper is mainly concerned with existence of mild solutions and optimal controls for nonlinear delay integrodifferential systems with Caputo fractional derivative in infinite-dimensional spaces. We do not assume that the relevant strongly continuous semigroup is compact.
Alfredo Bermudez (2010)
ESAIM: Control, Optimisation and Calculus of Variations
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In this paper we present some applications of the J.-L. Lions' optimal control theory to real life problems in engineering and environmental sciences. More precisely, we deal with the following three problems: sterilization of canned foods, optimal management of waste-water treatment plants and noise control