Analysis of Non-polynomial Systems using the Sum of Squares Decomposition

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Certified Defenses against Adversarial Examples (2018, methodology): “Such methods typically use sum-of-squares veriﬁcation (Papachristodoulou & Prajna, 2002; 2005; Parrilo, 2003) and are restricted to relatively low-dimensional dynamical systems, but could plausibly scale to larger settings.”
Finite-time regional verification of stochastic non-linear systems (2011, methodology): “If we eliminate stochasticity, then we can perform sumof-squares verification on Lyapunov functions (Megretski 2003; Papachristodoulou and Prajna 2005; Prajna et al. 2004c; Tan and Packard 2008; Tobenkin et al. 2011).”
Invariant Funnels around Trajectories using Sum-of-Squares Programming (2010, background): “…great deal of research has been dedicated to region-of-attraction analysis on polynomial vector fields (Parrilo (2003); Topcu et al. (2008); Tan and Packard (2008)) and more general non-polynomial vector fields (Papachristodoulou and Prajna (2005); Chesi (2009)) through Sum-of-Squares programming.”
A tutorial on sum of squares techniques for systems analysis (2005, methodology): “framework is systems with non-polynomial vector fields, which can be treated using a systematic recasting procedure [33].”