# Control Problem for a Piecewise Linear System with Uncertainties Based on Measurement Results

Control Problem for a Piecewise Linear System with Uncertainties Based on Measurement Results We consider the problem of control of a piecewise linear system on a finite time horizonunder uncertainty on the basis of incomplete and inaccurate information. A scheme for anapproximate solution is developed, including the construction of auxiliary piecewise quadraticvalue functions. Formulas are given for calculating such a function; this allows one to give anexternal estimate of the information set of the piecewise linear system. An algorithm forconstructing a feedback control that minimizes (in the corresponding metric) the deviation of theexternal estimate of the information set from the internal estimate of the solvability set and solvesthe problem of bringing the system trajectory to a small neighborhood of the target set in a giventime is proposed. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Differential Equations Springer Journals

# Control Problem for a Piecewise Linear System with Uncertainties Based on Measurement Results

, Volume 57 (11) – Nov 1, 2021
14 pages

/lp/springer-journals/control-problem-for-a-piecewise-linear-system-with-uncertainties-based-h271ggpikH
Publisher
Springer Journals
ISSN
0012-2661
eISSN
1608-3083
DOI
10.1134/s0012266121110082
Publisher site
See Article on Publisher Site

### Abstract

We consider the problem of control of a piecewise linear system on a finite time horizonunder uncertainty on the basis of incomplete and inaccurate information. A scheme for anapproximate solution is developed, including the construction of auxiliary piecewise quadraticvalue functions. Formulas are given for calculating such a function; this allows one to give anexternal estimate of the information set of the piecewise linear system. An algorithm forconstructing a feedback control that minimizes (in the corresponding metric) the deviation of theexternal estimate of the information set from the internal estimate of the solvability set and solvesthe problem of bringing the system trajectory to a small neighborhood of the target set in a giventime is proposed.

### Journal

Differential EquationsSpringer Journals

Published: Nov 1, 2021

### References

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