Couples de générateurs de certaines sous-algèbres de Lie de l'algèbre de Lie symplectique affine, et applications
Dependence on the parameters of the set of trajectories of the control system described by a nonlinear Volterra integral equation
In this paper the control system with limited control resources is studied, where the behavior of the system is described by a nonlinear Volterra integral equation. The admissible control functions are chosen from the closed ball centered at the origin with radius in
Derived cones to reachable sets of a nonlinear differential inclusion
We consider a nonlinear differential inclusion defined by a set-valued map with nonconvex values and we prove that the reachable set of a certain variational inclusion is a derived cone in the sense of Hestenes to the reachable set of the initial differential inclusion. In order to obtain the continuity property in the definition of a derived cone we use a continuous version of Filippov's theorem for solutions of our differential inclusion. As an application, in finite dimensional spaces, we obtain...
Discrete-time control systems on homogeneous spaces: partition property
Domaine de victoire et stratégies viables chez les pêcheurs décrits par l'anthropologue Fredrik Barth
L'anthropologue Fredrik Barth a analysé l'émergence des formes sociales chez les pêcheurs norvégiens. Sa perspective est bien modélisée par les outils mathématiques de la théorie de la viabilité, grâce auxquels on peut calculer l'ensemble des états à partir desquels la survie du système est encore possible, ainsi que la bonne décision à prendre à chaque instant, entre explorer ou suivre les autres bateaux. En outre, il se trouve que, techniquement, la condition de compacité des images de la correspondance...
Dynamics assignment by PD state feedback in linear reachable systems
Equivalent formulation and numerical analysis of a fire confinement problem
We consider a class of variational problems for differential inclusions, related to the control of wild fires. The area burned by the fire at time t> 0 is modelled as the reachable set for a differential inclusion ∈F(x), starting from an initial set R0. To block the fire, a barrier can be constructed progressively in time. For each t> 0, the portion of the wall constructed within time t is described by a rectifiable set γ(t) ⊂. In this paper we show that the search for blocking strategies...
Evaluation of the reachability subspace of general form polynomial matrix descriptions (PMDs)
Exact controllability in short time for the wave equation
Exact controllability of the Euler-Bernoulli equation with -control only in the Dirichlet Boundary condition
The paper studies the problem of exact controllability of the Euler- Bernoulli equation in a cylinder of , via boundary controls acting on its lateral surface.
Exact controllability of the linear elasticity system with evolutive Ventcel conditions. (Contrôlabilité exacte d'un problème avec conditions de Ventcel évolutives pour le système linéaire de l'élasticité.)
Existence theorems for some optimal control problems
External reachability (reachability with pole assignment by p. d. feedback) for implicit descriptions
Externally and internally positive time-varying linear systems
The notions of externally and internally positive time-varying linear systems are introduced. Necessary and sufficient conditions for the external and internal positivities of time-varying linear systems are established. Moreover, sufficient conditions for the reachability of internally positive time-varying linear systems are presented.
Forward invariant sets, homogeneity and small-time local controllability
The property of forward invariance of a subset of with respect to a differential inclusion is characterized by using the notion of a perpendicular to a set. The obtained results are applied for investigating the dependence of the small-time local controllability of a homogeneous control system on parameters.
Global non-negative controllability of the semilinear parabolic equation governed by bilinear control
We study the global approximate controllability of the one dimensional semilinear convection-diffusion-reaction equation governed in a bounded domain via the coefficient (bilinear control) in the additive reaction term. Clearly, even in the linear case, due to the maximum principle, such system is not globally or locally controllable in any reasonable linear space. It is also well known that for the superlinear terms admitting a power growth at infinity the global approximate controllability by...
Global non-negative controllability of the semilinear parabolic equation governed by bilinear control
We study the global approximate controllability of the one dimensional semilinear convection-diffusion-reaction equation governed in a bounded domain via the coefficient (bilinear control) in the additive reaction term. Clearly, even in the linear case, due to the maximum principle, such system is not globally or locally controllable in any reasonable linear space. It is also well known that for the superlinear terms admitting a power growth at infinity the global approximate controllability by...
Interior sphere property for level sets of the value function of an exit time problem
We consider an optimal control problem for a system of the form = f(x,u), with a running cost L. We prove an interior sphere property for the level sets of the corresponding value function V. From such a property we obtain a semiconcavity result for V, as well as perimeter estimates for the attainable sets of a symmetric control system.
Interior sphere property of attainable sets and time optimal control problems
This paper studies the attainable set at time T>0 for the control system showing that, under suitable assumptions on f, such a set satisfies a uniform interior sphere condition. The interior sphere property is then applied to recover a semiconcavity result for the value function of time optimal control problems with a general target, and to deduce C1,1-regularity for boundaries of attainable sets.
Lie brackets and real analyticity in control theory