Viability Kernels and Control Sets

Dietmar Szolnoki

Displaying similar documents to “Viability Kernels and Control Sets”

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...

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...

Relaxation of optimal control problems in L-SPACES

Nadir Arada (2010)

ESAIM: Control, Optimisation and Calculus of Variations

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We consider control problems governed by semilinear parabolic equations with pointwise state constraints and controls in an -space ( < ∞). We construct a correct relaxed problem, prove some relaxation results, and derive necessary optimality conditions.

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

On asymptotic exit-time control problems lacking coercivity

M. Motta, C. Sartori (2014)

ESAIM: Control, Optimisation and Calculus of Variations

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The research on a class of asymptotic exit-time problems with a vanishing Lagrangian, begun in [M. Motta and C. Sartori, Springer (2014).] for the compact control case, is extended here to the case of unbounded controls and data, including both coercive and non-coercive problems. We give sufficient conditions to have a well-posed notion of generalized control problem and obtain regularity, characterization and approximation results for the value function of the problem.