The construction of discontinuous controls for non-linear dynamical system with uncertainties

The properties of the solutions of a family of non-linear parametric problems are investigated in the neighbourhood of regular and irregular values of the parameter. Rules are proposed for constructing feedback-type controlling for non-linear dynamical systems with perturbations. An example is presented.     

On a constructive approach to optimality conditions for convex SIP problems with polyhedral index sets

In the paper, we consider a problem of convex Semi-Infinite Programming with an infinite index set in the form of a convex polyhedron. In study of this problem, we apply the approach suggested in our recent paper [Kostyukova OI, Tchemisova TV. Sufficient optimality conditions for convex Semi Infinite Programming. Optim. Methods Softw. 2010;25:279–297], and based on the notions of immobile indices and their immobility orders. The main result of the paper consists in explicit optimality conditions that do not use constraint qualifications and have the form of criterion. The comparison of the new optimality conditions with other known results is provided.     

Mid-IR Range Quantum-Cascade Lasers in Compact Optoacoustic Gas Analyzers

Journal of Applied Spectroscopy - The generation regimes of quantum-cascade lasers for optoacoustic sensors of methane and ammonia are examined, and the tuning and output characteristics of these...     

Properties of solutions of parametric time-optimal problems in a neighborhood of an abnormal point

We consider a linear time-optimal problem in which the initial state vector depends on a parameter. We analyze the dependence of the solutions on the parameter and justify rules for the identification of the structure of the solution under small variations of the parameter. Attention is mainly paid to the analysis of properties of solutions in a neighborhood of an abnormal value of the parameter for which the function of determining elements of solutions of the original family of problems has no finite derivatives with respect to the parameter. For the function of determining elements, we obtain an asymptotic expansion to fractional powers of the parameter increment.     

Implicit optimality criterion for convex SIP problem with box constrained index set

We consider a convex problem of Semi-Infinite Programming (SIP) with a multidimensional index set defined by a finite number of box constraints. In study of this problem we apply the approach suggested in Kostyukova et al. (Int. J. Math. Stat. 13(J08):13–33, 2008) for convex SIP problems with one-dimensional index sets and based on the notions of immobile indices and their immobility orders. For the problem under consideration we formulate optimality conditions that are explicit and have the form of criterion. We compare this criterion with other known optimality conditions for SIP and show its efficiency in the convex case.     

Selection of Optimal Phase Matching Conditions for Semiconductor Nonlinear Crystals Under Cascade Pumping at 2 μm

Russian Physics Journal - Model studies of the optimal phase matching conditions are performed for the implementation of an optical parametric oscillator (OPO) in the mid-infrared range (IR) based...     

Immobile Indices and CQ-Free Optimality Criteria for Linear Copositive Programming Problems

Set-Valued and Variational Analysis - We consider problems of linear copositive programming where feasible sets consist of vectors for which the quadratic forms induced by the corresponding linear...