Time Optimality and the Power Moment Problem

Abstract

A new critical-amplihzde relation which holds for one-dimensional guanNm groundsmte transitions is presented. The relation yields an estimate ofthe sound velocity which appears in the conformal field theov as an a priori unknown parameter. With the use of this relation, the exponent q can be explicitly determined from only the scaling fit of lhe off-critical energy gdp. The relation is confirmed in the transverse Ising model, the S = f anisotropic X Y model. and the three-state Pom model.

Time-Optimal Control Problem for a Special Class of Control Systems: Optimal Controls and Approximation in the Sense of Time Optimality

“…It is well known that the time-optimal control problem for a linear system admits an interpretation in terms of the Markov moment problem [23,24]. The results of the present paper open the following direction of the further research: find a moment interpretation for dual-to-linear systems.…”

Problem 3.8 Determining of various asymptotics of solutions of nonlinear time-optimal problems via right ideals in the moment algebra

“…We assume the initial point x 0 is steered to the origin in the time θ by the control u(t) w.r.t. system (2). Then under our assumptions for rather small θ one has…”

“…When condition (3) is not satisfied, one can try to find a nonlinear system which has rather simply form and approximates system (2) in the sense of time optimality. In [8] we claim the following result.…”

“…For linear systems, the maximum principle allows to indicate a class of optimal controls. However, the explicit form of the solution can be given only in a number of particular cases [1][2][3]. At the same time [4], an arbitrary linear time-optimal problem with analytic coefficients can be approximated (in a neighborhood of the origin) by a certain linear problem of the forṁ x i = −t qi u, i = 1, .…”

Feedback Control Design for Systems with x-Discontinuous Right-Hand Side

“…In particular, the time optimal control problem consists in constructing of a control which transfers an arbitrary point to the given one in minimal time. The analytic solution of the linear time optimal problem, by using the moment min-problem, is given in [3,4].…”