ON THE PROPERTIES OF THE SOLVABILITY SET FOR A LINEAR SYSTEM WITH UNCERTAINTY

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Abstract

The work is devoted to the problem of verifying that the state of a linear controlled system of differential equations will hit the target set over a finite time interval, despite the uncertainties (noise). Some geometric, pointwise convex constraints on uncertainties are imposed. In the case of a two-dimensional state space a method is proposed for constructing a solvability set without the calculation of the convex hulls of the functions necessary to construct a support function of the geometric difference of the sets. A Hamilton–Jacobi–Bellman type equation is obtained, which is satisfied by the distance function to the solvability set.

About the authors

A. A Melnikova

Lomonosov Moscow State University;

Email: nastya.a.melnikova@gmail.com

P. A Tochilin

Lomonosov Moscow State University; V.A. Trapeznikov Institute of Control Sciences of RAS

Email: tochilin@cs.msu.ru

A. N Daryin

Lomonosov Moscow State University

Email: daryin@mail.ru

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