Yu. S. Osipov

On the solvability of problems of guaranteeing control for partially observable linear dynamical systems

This paper is devoted to a specification of the method of open-loop control packages, a universal instrument for verification of the solvability of problems of closed-loop control for partially observable dynamical systems. Under the assumption that the control system and observed signal are linear and the set of the admissible initial states is finite, a structure of the corresponding open-loop control packages is specified and a finite-step backward construction is described, which provides a criterion for the solvability of a problem of guaranteed closed-loop guidance onto a target set at a prescribed time.

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.

N.N. Krasovskii's extremal shift method and problems of boundary control

For the boundary-controlled dynamic system obeying a parabolic differential equation with the Neumann boundary condition, the problems of following the reference motion, following the reference control, and guaranteed control (at domination of the controller resource) were solved on the basis of the N.N. Krasovskii method of extremal shift from the theory of positional differential games.

Higher-order elastics and elastic hulls

By higher-order elastics we mean solutions of the problem to minimize integrals of quadratic forms of curvatures of multidimensional curves. Differential equations of second-order elastics (minimizing a quadratic form of the curvature and torsion of the curve) are obtained. Surfaces minimizing integrals of the squared Gaussian curvature are found.

Extremum Problems with Separable Graphs

The paper introduces a geometric feature of separability of graphs for extremum equality-type boundary problems. To find an optimal value for a problem with an almost separable graph, the paper presents an iteration algorithm, each step of which minimizes Lagrangian function for the main variable with a fixed Lagrangian multiplier. This algorithm dates back to Krasovskii extremal shift method from differential game theory.

Multidimensional generalizations of Jacobi’s envelope theorem

In the paper, the extension of a field of geodesics ℘ on a manifold N isometrically embedded in a Riemannian manifoldM is considered. The symplectic involute of the manifold N along the field ℘ is defined and a theorem is proved which gives a multidimensional analog of Jacobi’s envelope theorem.

On dynamical regularization under random noise

We consider the problem of constructing a robust dynamic approximation of a timevarying input to a control system from the results of inaccurate observation of the states of the system. In contrast to the earlier studied cases in which the observation errors are assumed to be small in the metric sense, the errors in the present case are allowed to take, generally, large values and are subject to a certain probability distribution. The observation errors occurring at different instants are supposed to be statistically independent. Under the assumption that the expected values of the observation errors are small, we construct a dynamical algorithm for approximating the normal (minimal in the sense of the mean-square norm) input; the algorithm ensures an arbitrarily high level of the mean-square approximation accuracy with an arbitrarily high probability.