Displaying similar documents to “Convergence rate of the solutions of singularly perturbed time-optimal control problems”

Existence of optimal nonanticipating controls in piecewise deterministic control problems

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.

Analysis of a time optimal control problem related to the management of a bioreactor

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...

Regularity along optimal trajectories of the value function of a Mayer problem

Carlo Sinestrari (2010)

ESAIM: Control, Optimisation and Calculus of Variations

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We consider an optimal control problem of Mayer type and prove that, under suitable conditions on the system, the value function is differentiable along optimal trajectories, except possibly at the endpoints. We provide counterexamples to show that this property may fail to hold if some of our conditions are violated. We then apply our regularity result to derive optimality conditions for the trajectories of the system.

Optimal control from inoculation on a continuous microalgae culture

Jorge Antonio Torres-Muñoz, Irandi Gutierrez-Carmona, Alma Rosa Dominguez-Bocanegra (2016)

Kybernetika

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The present work is centred on the problem of biomass productivity optimization of a culture of microalgae Spirulina maxima. The mathematical tools consisted of necessary and sufficient conditions for optimal control coming from the celebrated Pontryagin's Maximum Principle (PMP) as well as the Bellman's Principle of Optimality, respectively. It is shown that the optimal dilution rate turns to be a bang-singular-bang control. It turns out that, the experimental results are in accordance...

Unmaximized inclusion necessary conditions for nonconvex constrained optimal control problems

Maria do Rosário de Pinho, Maria Margarida Ferreira, Fernando Fontes (2010)

ESAIM: Control, Optimisation and Calculus of Variations

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Necessary conditions of optimality in the form of Unmaximized Inclusions (UI) are derived for optimal control problems with state constraints. The conditions presented here generalize earlier optimality conditions to problems that may be nonconvex. The derivation of UI-type conditions in the absence of the convexity assumption is of particular importance when deriving necessary conditions for constrained problems. We illustrate this feature by establishing, as an application, optimality...