Some Algorithms for the Dynamic Reconstruction of Inputs

For some classes of systems described by ordinary differential equations, a survey of algorithms for the dynamic reconstruction of inputs is presented. The algorithms described in the paper are stable with respect to information noises and computation errors; they are based on methods from the theory of ill-posed problems as well as on appropriate modifications of N. N. Krasovskii's principle of extremal aiming, which is known in the theory of guaranteed control. © 2011 Pleiades Publishing, Ltd.This work was supported by the Russian Foundation for Basic Research (project no. 09-01-00378), by the Program for Fundamental Research of the Presidium of the Russian Academy of Sciences “Mathematical Theory of Control” (project no. 09-P-1-1014), by the Program for State Support of Leading Scientific Schools of the Russian Federation (project no. NSh-65590.2010.1), and by the Ural–Siberian Integration Project no. 09-S-1-1010

Reindeer in tundra ecosystems: the challenges of understanding system complexity

complexit

Optimization problems with convex epigraphs. Application to optimal control

For a class of infinite-dimensional minimization problems with nonlinear equality constraints, an iterative algorithm for finding global solutions is suggested. A key assumption is the convexity of the "epigraph", a set in the product of the image spaces of the constraint and objective functions. A convexification method involving randomization is used. The algorithm is based on the extremal shift control principle due to N.N. Krasovskii. An application to a problem of optimal control for a bilinear control system is described

Reconstruction of Boundary Sources through Sensor Observations

Introduction. Problem Formulation. The paper deals with a problem of reconstruction of extremal boundary disturbances in a parabolic system. The reconstruction is perfomed on the basis of inaccurate observations of linear signals on system's states. Extremality of disturbances is understood with respect to a given linear functional. The paper ajoins theory of inverse problems for distributed systems (see, e.g., [Lavrentyev et al.,1980; Banks and Kunisch, 1982; Kurzhanski and Khapalov, 1989; Barbu, 1991; Osipov et al., 1991; Maksimov, 1993; Ainseba, 1994]) and theory of ill-posed problems (see, e.g., [Tikhonov and Arsenin, 1979], [Vasiliev, 1981]). A variant of a substantial problem formulation is as follows. A flow of heat enters a solid body occupying space\Omega through boundary domains fl 1 ; : : : ; fl n . At time t the instant velocity of the heat flow coming through fl k is represented as<F3

Optimal Enforcement on a Pure Seller's Market of Illicit Drugs

An optimal control problem for the dynamic enforcement (crackdown) of dealers on a pure seller's market for illicit drugs is explored. Theorems on existence and uniqueness of the optimal synthesis are proved. Using a technique of resolution of singularities for degenerate differential equations, we design analytically an optimal enforcement policy

Numerical encoding of sampled controls and an approximation metric criterion for the solvability of a guidance game problem

A game problem of guaranteed aiming in the class of positional strategies is considered for a conflict controlled system with affine scalar controls in the equation of the system. Simplified sampled analogs of quasi-strategies, i.e., of nonanticipating program reactions of the first player to the controls of the second player, are introduced. The nonanticipating property is characterized in metric terms with the use of numerical images (codes) of argument controls and reaction controls. A class of nonanticipating transformations is introduced that is approximately equivalent by the criterion of the solvability of the game problem to the class of positional strategies. The elements of this class as transformations of the numerical codes of controls are characterized by the 1-Lipschitz property. A numerical algorithm for checking the solvability of the problem in this class is described. The complexity order of the algorithm is close to that of the approximation variant of the classical program construction