The Comparison Principle: Nonlinearity and Nonconvexity

Part of the Systems & Control: Foundations & Applications book series (SCFA, volume 85)


This chapter introduces generalizations and applications of the presented approach prescribed earlier to nonlinear systems, nonconvex reachability sets and systems subjected to non-ellipsoidal constraints. The key element for these issues lies in the Comparison Principle for HJB equations which indicates schemes of approximating their complicated solutions by arrays of simpler procedures. Given along these lines is a deductive derivation of ellipsoidal calculus in contrast with previous inductive derivation.


Nonlinearity Nonconvexity Comparison principle Unicycle  Boxes Zonotopes Ellipsoids 


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© Springer International Publishing Switzerland 2014

Authors and Affiliations

  1. 1.Faculty of Computational Mathematics and CyberneticsMoscow State (Lomonosov) UniversityMoscowRussia
  2. 2.Electrical Engineering and Computer SciencesUniversity of California, BerkeleyBerkeleyUSA

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