On the convergence of min/sup points in optimal control problems.
On the order reduction of optimal control systems
On the perturbations in a time-optimal closed-loop system
On the robustness of optimal solutions for combinatorial optimization problems
On the Sensivity and Relaxability of Optimal Control Problems Governed by Nonlinear Evolution Equations with State Constraints.
On the stability of Bravais lattices and their Cauchy–Born approximations
We investigate the stability of Bravais lattices and their Cauchy–Born approximations under periodic perturbations. We formulate a general interaction law and derive its Cauchy–Born continuum limit. We then analyze the atomistic and Cauchy–Born stability regions, that is, the sets of all matrices that describe a stable Bravais lattice in the atomistic and Cauchy–Born models respectively. Motivated by recent results in one dimension on the stability of atomistic/continuum coupling methods, we analyze...
On the stability of Bravais lattices and their Cauchy–Born approximations*
We investigate the stability of Bravais lattices and their Cauchy–Born approximations under periodic perturbations. We formulate a general interaction law and derive its Cauchy–Born continuum limit. We then analyze the atomistic and Cauchy–Born stability regions, that is, the sets of all matrices that describe a stable Bravais lattice in the atomistic and Cauchy–Born models respectively. Motivated by recent results in one dimension on the stability of atomistic/continuum coupling methods,...
On the stabilization problem for nonholonomic distributions
Let be a smooth connected complete manifold of dimension , and be a smooth nonholonomic distribution of rank on . We prove that if there exists a smooth Riemannian metric on1for which no nontrivial singular path is minimizing, then there exists a smooth repulsive stabilizing section of on . Moreover, in dimension three, the assumption of the absence of singular minimizing horizontal paths can be dropped in the Martinet case. The proofs are based on the study, using specific results of...
On weak sharp minima in vector optimization with applications to parametric problems
On well-posedness for parametric vector quasiequilibrium problems with moving cones
In this paper we consider weak and strong quasiequilibrium problems with moving cones in Hausdorff topological vector spaces. Sufficient conditions for well-posedness of these problems are established under relaxed continuity assumptions. All kinds of well-posedness are studied: (generalized) Hadamard well-posedness, (unique) well-posedness under perturbations. Many examples are provided to illustrate the essentialness of the imposed assumptions. As applications of the main results, sufficient conditions...
Optimal control of linear impulsive antiperiodic boundary value problem on infinite dimensional spaces.
Optimal feedback for perturbed bilinear control problems
Optimal LQ-feedback control for a class of first-order hyperbolic distributed parameter systems
The Linear-Quadratic (LQ) optimal control problem is studied for a class of first-order hyperbolic partial differential equation models by using a nonlinear infinite-dimensional (distributed parameter) Hilbert state-space description. First the dynamical properties of the linearized model around some equilibrium profile are studied. Next the LQ-feedback operator is computed by using the corresponding operator Riccati algebraic equation whose solution is obtained via a related matrix Riccati differential...
Optimality and sensitivity for semilinear bang-bang type optimal control problems
In optimal control problems with quadratic terminal cost functionals and systems dynamics linear with respect to control, the solution often has a bang-bang character. Our aim is to investigate structural solution stability when the problem data are subject to perturbations. Throughout the paper, we assume that the problem has a (possibly local) optimum such that the control is piecewise constant and almost everywhere takes extremal values. The points of discontinuity are the switching points. In...
Optimality properties of controls with bang-bang components in problems with semilinear state equation
Order-Lipschitzian properties of multifunctions with applications to stability of efficient points
Parametric problem of completely generalized quasi-variational inequalities.
Perturbation theory of duality in vector optimization via the abstract duality scheme
Porosity and models with discrete innovations.
Porosity and Variational Principles
We prove that in some classes of optimization problems, like lower semicontinuous functions which are bounded from below, lower semi-continuous or continuous functions which are bounded below by a coercive function and quasi-convex continuous functions with the topology of the uniform convergence, the complement of the set of well-posed problems is σ-porous. These results are obtained as realization of a theorem extending a variational principle of Ioffe-Zaslavski.