Barbara Bily (2002)
Applicationes Mathematicae
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Necessary conditions for some optimal control problem for a nonlinear 2-D system are considered. These conditions can be obtained in the form of a quasimaximum principle.
Kharatishvili, Guram L., Tadumadze, Tamaz A. (1997)
Memoirs on Differential Equations and Mathematical Physics
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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. ...
Chutiphon Pukdeboon (2018)
Kybernetika
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This paper presents a novel robust optimal control approach for attitude stabilization of a flexible spacecraft in the presence of external disturbances. An optimal control law is formulated by using concepts of inverse optimal control, proportional-integral-derivative control and a control Lyapunov function. A modified extended state observer is used to compensate for the total disturbances. High-gain and second order sliding mode algorithms are merged to obtain the proposed modified...
Madalina Petcu, Roger Temam (2010)
ESAIM: Control, Optimisation and Calculus of Variations
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In this article we apply the optimal and the robust control theory to the sine-Gordon equation. In our case the control is given by the boundary conditions and we work in a finite time horizon. We present at the beginning the optimal control problem and we derive a necessary condition of optimality and we continue by formulating a robust control problem for which existence and uniqueness of solutions are derived.
Jacques Louis Lions (1985)
Banach Center Publications
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V. Janković (1981)
Matematički Vesnik
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Alain Ajami, Jean-Paul Gauthier, Thibault Maillot, Ulysse Serres (2013)
ESAIM: Control, Optimisation and Calculus of Variations
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This paper is devoted to the general problem of reconstructing the cost from the observation of trajectories, in a problem of optimal control. It is motivated by the following applied problem, concerning HALE drones: one would like them to decide by themselves for their trajectories, and to behave at least as a good human pilot. This applied question is very similar to the problem of determining what is minimized in human locomotion. These starting points are the reasons for the particular...
Krishnan Balachandran, D. Somasundaram (1984)
Kybernetika
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Kenan Yildirim, Ismail Kucuk (2017)
Open Mathematics
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In this paper, an optimal vibration control problem for a nonlinear plate is considered. In order to obtain the optimal control function, wellposedness and controllability of the nonlinear system is investigated. The performance index functional of the system, to be minimized by minimum level of control, is chosen as the sum of the quadratic 10 functional of the displacement. The velocity of the plate and quadratic functional of the control function is added to the performance index...
Yuncheng You (1996)
Discussiones Mathematicae, Differential Inclusions, Control and Optimization
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Slightly below the transition temperatures, the behavior of superconducting materials is governed by the Ginzburg-Landau (GL) equation which characterizes the dynamical interaction of the density of superconducting electron pairs and the exited electromagnetic potential. In this paper, an optimal control problem of the strength of external magnetic field for one-dimensional thin film superconductors with respect to a convex criterion functional is considered. It is formulated as a nonlinear...