Displaying similar documents to “Relaxation of optimal control problems in Lp-SPACES”

Feedback in state constrained optimal control

Francis H. Clarke, Ludovic Rifford, R. J. Stern (2010)

ESAIM: Control, Optimisation and Calculus of Variations

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An optimal control problem is studied, in which the state is required to remain in a compact set . A control feedback law is constructed which, for given ε > 0, produces -optimal trajectories that satisfy the state constraint universally with respect to all initial conditions in . The construction relies upon a constraint removal technique which utilizes geometric properties of inner approximations of and a related trajectory tracking result. The control feedback is shown to possess...

Mean-Field Optimal Control

Massimo Fornasier, Francesco Solombrino (2014)

ESAIM: Control, Optimisation and Calculus of Variations

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We introduce the concept of which is the rigorous limit process connecting finite dimensional optimal control problems with ODE constraints modeling multi-agent interactions to an infinite dimensional optimal control problem with a constraint given by a PDE of Vlasov-type, governing the dynamics of the probability distribution of interacting agents. While in the classical mean-field theory one studies the behavior of a large number of small individuals with each other, by simplifying...

Least regret control, virtual control and decomposition methods

Jacques-Louis Lions (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

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"Least regret control" consists in trying to find a control which "optimizes the situation" with the constraint of not making things too worse with respect to a known reference control, in presence of more or less significant perturbations. This notion was introduced in [7]. It is recalled on a simple example (an elliptic system, with distributed control and boundary perturbation) in Section 2. We show that the problem reduces to a standard optimal control problem for . On another...

A problem of optimal control with free initial state

Mohamed Aidene, Kahina Louadj (2012)

ESAIM: Proceedings

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We are studying an optimal control problem with free initial condition. The initial state of the optimized system is not known exactly, information on initial state is exhausted by inclusions  ∈  . Accessible controls for optimization of continuous dynamic system are discrete controls defined on quantized axes. The method presented is based on the concepts and operations of the adaptive method [9] of linear programming. The results are illustrated by a...

Spreadability, Vulnerability and Protector Control

A. Bernoussi (2010)

Mathematical Modelling of Natural Phenomena

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In this work, we present some concepts recently introduced in the analysis and control of distributed parameter systems: , and . These concepts permit to describe many biogeographical phenomena, as those of pollution, desertification or epidemics, which are characterized by a spatio-temporal evolution

New regularity results and improved error estimates for optimal control problems with state constraints

Eduardo Casas, Mariano Mateos, Boris Vexler (2014)

ESAIM: Control, Optimisation and Calculus of Variations

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In this paper we are concerned with a distributed optimal control problem governed by an elliptic partial differential equation. State constraints of box type are considered. We show that the Lagrange multiplier associated with the state constraints, which is known to be a measure, is indeed more regular under quite general assumptions. We discretize the problem by continuous piecewise linear finite elements and we are able to prove that, for the case of a linear equation, the order...

A priori error estimates for a state-constrained elliptic optimal control problem

Arnd Rösch, Simeon Steinig (2012)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

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We examine an elliptic optimal control problem with control and state constraints in ℝ. An improved error estimate of 𝒪( ) with 3/4 ≤ ≤ 1 − ε is proven for a discretisation involving piecewise constant functions for the control and piecewise linear for the state. The derived order of convergence is illustrated by a numerical example.

Viability Kernels and Control Sets

Dietmar Szolnoki (2010)

ESAIM: Control, Optimisation and Calculus of Variations

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This paper analyzes the relation of viability kernels and control sets of control affine systems. A viability kernel describes the largest closed viability domain contained in some closed subset of the state space. On the other hand, control sets are maximal regions of the state space where approximate controllability holds. It turns out that the viability kernel of can be represented by the union of domains of attraction of chain control sets, defined relative to the given set . In...