Complexity of ten decision problems in continuous time dynamical systems
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Author(s)
Ahmadi, Amir Ali
Majumdar, Anirudha
Tedrake, Russell Louis
Date Issued
June 2013
Journal
Proceedings of the 2013 American Control Conference
Publisher
Institute of Electrical and Electronics Engineers (IEEE)
Citation
Ahmadi, Amir Ali, Anirudha Majumdar, and Russ Tedrake. “Complexity of Ten Decision Problems in Continuous Time Dynamical Systems.” 2013 American Control Conference (June 2013).
Version
Author's final manuscript
Abstract
We show that for continuous time dynamical systems described by polynomial differential equations of modest degree (typically equal to three), the following decision problems which arise in numerous areas of systems and control theory cannot have a polynomial time (or even pseudo-polynomial time) algorithm unless P=NP: local attractivity of an equilibrium point, stability of an equilibrium point in the sense of Lyapunov, boundedness of trajectories, convergence of all trajectories in a ball to a given equilibrium point, existence of a quadratic Lyapunov function, invariance of a ball, invariance of a quartic semialgebraic set under linear dynamics, local collision avoidance, and existence of a stabilizing control law. We also extend our earlier NP-hardness proof of testing local asymptotic stability for polynomial vector fields to the case of trigonometric differential equations of degree four.
MIT Department
Massachusetts Institute of Technology. Computer Science and Artificial Intelligence Laboratory
Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science
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DOI of Published Version
https://doi.org/10.1109/ACC.2013.6580838
