A collocation method for optimal control of linear systems with inequality constraints.
Razzaghi, M., Nazarzadeh, J., Nikravesh, K.Y. (1998)
Mathematical Problems in Engineering
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Razzaghi, M., Nazarzadeh, J., Nikravesh, K.Y. (1998)
Mathematical Problems in Engineering
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François Chaplais, Nicolas Petit (2008)
ESAIM: Control, Optimisation and Calculus of Variations
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This paper presents the role of vector relative degree in the formulation of stationarity conditions of optimal control problems for affine control systems. After translating the dynamics into a normal form, we study the Hamiltonian structure. Stationarity conditions are rewritten with a limited number of variables. The approach is demonstrated on two and three inputs systems, then, we prove a formal result in the general case. A mechanical system example serves as illustration. ...
Xing, An-Qing (1991)
Journal of Applied Mathematics and Stochastic Analysis
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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.
J. L. Gamez, J. A. Montero (2010)
ESAIM: Control, Optimisation and Calculus of Variations
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Uniqueness of the optimal control is obtained by assuming certain conditions on the crowding effect of the species. Moreover, an approximation procedure for the unique optimal control is developed.
Lino J. Alvarez-Vázquez, Francisco J. Fernández, Aurea Martínez (2011)
ESAIM: Control, Optimisation and Calculus of Variations
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We consider a time optimal control problem arisen from the optimal management of a bioreactor devoted to the treatment of eutrophicated water. We formulate this realistic problem as a state-control constrained time optimal control problem. After analyzing the state system (a complex system of coupled partial differential equations with non-smooth coefficients for advection-diffusion-reaction with Michaelis-Menten kinetics, modelling the eutrophication processes) we demonstrate the existence...
Leszek Mikulski (2004)
International Journal of Applied Mathematics and Computer Science
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Optimal design problems in mechanics can be mathematically formulated as optimal control tasks. The minimum principle is employed in solving such problems. This principle allows us to write down optimal design problems as Multipoint Boundary Value Problems (MPBVPs). The dimension of MPBVPs is an essential restriction that decides on numerical difficulties. Optimal control theory does not give much information about the control structure, i.e., about the sequence of the forms of the right-hand...
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
Dzhgarkava, Dimitri T. (1997)
Memoirs on Differential Equations and Mathematical Physics
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