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.
Calculating Positive Invariant Sets: A Quantifier Elimination Approach
Contributed by the Design Engineering Division of ASME for publication in the JOURNAL OF COMPUTATIONAL AND NONLINEAR DYNAMICS. Manuscript received November 12, 2018; final manuscript received March 27, 2019; published online May 13, 2019. Assoc. Editor: Katrin Ellermann.
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Röbenack, K., Voßwinkel, R., and Richter, H. (May 13, 2019). "Calculating Positive Invariant Sets: A Quantifier Elimination Approach." ASME. J. Comput. Nonlinear Dynam. July 2019; 14(7): 074502. https://doi.org/10.1115/1.4043380
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