Stability analysis of solutions to an optimal control problem associated with a Goursat-Darboux problem
In the present paper, some results concerning the continuous dependence of optimal solutions and optimal values on data for an optimal control problem associated with a Goursat-Darboux problem and an integral cost functional are derived.
Stability and sensitivity analysis for optimal control problems with control-state constraints [Book]
Stability and sensitivity analysis for optimal control problems with a first-order state constraint and application to continuation methods
The paper deals with an optimal control problem with a scalar first-order state constraint and a scalar control. In presence of (nonessential) touch points, the arc structure of the trajectory is not stable. Under some reasonable assumptions, we show that boundary arcs are structurally stable, and that touch point can either remain so, vanish or be transformed into a single boundary arc. Assuming a weak second-order optimality condition (equivalent to uniform quadratic growth), stability and...
Stability of eigenvalues and eigenvectors of variational inequalities
Stability results for some nonlinear elliptic equations involving the -laplacian with critical Sobolev growth
Stability results for some nonlinear elliptic equations involving the p-Laplacian with critical Sobolev growth
This article is devoted to the study of a perturbation with a viscosity term in an elliptic equation involving the p-Laplacian operator and related to the best contant problem in Sobolev inequalities in the critical case. We prove first that this problem, together with the equation, is stable under this perturbation, assuming some conditions on the datas. In the next section, we show that the zero solution is strongly isolated in some sense, among the space of the solutions. Actually, we end the...
State space synthesis of discrete linear systems
Stationary configurations for the average distance functional and related problems
Stochastic evolution equations on Hilbert spaces with partially observed relaxed controls and their necessary conditions of optimality
In this paper we consider the question of optimal control for a class of stochastic evolution equations on infinite dimensional Hilbert spaces with controls appearing in both the drift and the diffusion operators. We consider relaxed controls (measure valued random processes) and briefly present some results on the question of existence of mild solutions including their regularity followed by a result on existence of partially observed optimal relaxed controls. Then we develop the necessary conditions...
Strong average optimality criterion for continuous-time Markov decision processes
This paper deals with continuous-time Markov decision processes with the unbounded transition rates under the strong average cost criterion. The state and action spaces are Borel spaces, and the costs are allowed to be unbounded from above and from below. Under mild conditions, we first prove that the finite-horizon optimal value function is a solution to the optimality equation for the case of uncountable state spaces and unbounded transition rates, and that there exists an optimal deterministic...
“Strong” extrema of functionals defined on Riemannian 2-manifolds.
Structural properties of solutions to total variation regularization problems
Structural Properties of Solutions to Total Variation Regularization Problems
In dimension one it is proved that the solution to a total variation-regularized least-squares problem is always a function which is "constant almost everywhere" , provided that the data are in a certain sense outside the range of the operator to be inverted. A similar, but weaker result is derived in dimension two.
Structure of optimal trajectories in a nonlinear dynamic model with endogenous delay.
Structure of stable solutions of a one-dimensional variational problem
We prove the periodicity of all H2-local minimizers with low energy for a one-dimensional higher order variational problem. The results extend and complement an earlier work of Stefan Müller which concerns the structure of global minimizer. The energy functional studied in this work is motivated by the investigation of coherent solid phase transformations and the competition between the effects from regularization and formation of small scale structures. With a special choice of a bilinear double...
Sub differentiability and trustworthiness in the light of a new variational principle of Borwein and Preiss
Subdifferential inclusions and quasi-static hemivariational inequalities for frictional viscoelastic contact problems
We survey recent results on the mathematical modeling of nonconvex and nonsmooth contact problems arising in mechanics and engineering. The approach to such problems is based on the notions of an operator subdifferential inclusion and a hemivariational inequality, and focuses on three aspects. First we report on results on the existence and uniqueness of solutions to subdifferential inclusions. Then we discuss two classes of quasi-static hemivariational ineqaulities, and finally, we present ideas...
Suboptimality Of Stochastic Systems: Structural Uncertainties And Information Constraints
Subriemannian geodesics of Carnot groups of step 3
In Carnot groups of step ≤ 3, all subriemannian geodesics are proved to be normal. The proof is based on a reduction argument and the Goh condition for minimality of singular curves. The Goh condition is deduced from a reformulation and a calculus of the end-point mapping which boils down to the graded structures of Carnot groups.