Calculating Positive Invariant Sets: A Quantifier Elimination Approach-Reference-Cited by-同舟云学术

Calculating Positive Invariant Sets: A Quantifier Elimination Approach

Published:2019-05-13 Issue:7 Volume:14 Page:
ISSN:1555-1415
Container-title:Journal of Computational and Nonlinear Dynamics
language:en
Short-container-title:

Author:

Röbenack Klaus¹,Voßwinkel Rick²,Richter Hendrik³

Affiliation:

1. Professor Faculty of Electrical and Computer Engineering, Institute of Control Theory, Technische Universität Dresden, Dresden 01062, Germany e-mail:

2. Faculty of Electrical and Computer Engineering, Institute of Control Theory, Technische Universität Dresden, Dresden 01062, Germany e-mail:

3. Professor Faculty of Electrical Engineering and Information Technology, HTWK Leipzig University of Applied Sciences, Leipzig 04107, Germany e-mail:

Abstract

A Lyapunov-based approach for calculating positive invariant sets in an automatic manner is presented. This is done using real algebraic geometry techniques, which are summed up under the term quantifier elimination (QE). Using available tools, the approach presented yields an algorithmizable procedure whose conservatism only depends on the initial choice for the Lyapunov candidate function. The performance of the approach is illustrated on a variant of the Rössler system and on the Lorenz-Haken system.

Publisher

ASME International

Subject

Applied Mathematics,Mechanical Engineering,Control and Systems Engineering,Applied Mathematics,Mechanical Engineering,Control and Systems Engineering

Link

http://asmedigitalcollection.asme.org/computationalnonlinear/article-pdf/doi/10.1115/1.4043380/6391240/cnd_014_07_074502.pdf

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