This document describes a toolbox of level set methods for solving time-dependent Hamilton-Jacobi partial differential equations (PDEs) in the Matlab programming environment. Level set methods are often used for simulation of dynamic implicit surfaces in graphics, fluid and combustion simulation, image processing, and computer vision. Hamilton-Jacobi and related PDEs arise in fields such as control, robotics, differential games, dynamic programming, mesh generation, stochastic differential equations, financial mathematics, and verification. The algorithms in the toolbox can be used in any number of dimensions, although computational cost and visualization difficulty make dimensions four and higher a challenge. All source code for the toolbox is provided as plain text in the Matlab m-file programming language. The toolbox is designed to allow quick and easy experimentation with level set methods, although it is not by itself a level set tutorial and so should be used in combination with the existing literature.

References in zbMATH (referenced in 22 articles , 1 standard article )

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  1. Mohajerin Esfahani, Peyman; Chatterjee, Debasish; Lygeros, John: The stochastic reach-avoid problem and set characterization for diffusions (2016)
  2. Ghanbarzadeh, Soheil; Hesse, Marc A.; Prodanović, Maša: A level set method for materials with texturally equilibrated pores (2015)
  3. Kurzhanski, Alexander B.; Varaiya, Pravin: Dynamics and control of trajectory tubes. Theory and computation (2014)
  4. Lesser, Kendra; Oishi, Meeko: Reachability for partially observable discrete time stochastic hybrid systems (2014)
  5. Takei, Ryo; Tsai, Richard; Zhou, Zhengyuan: An efficient algorithm for a visibility-based surveillance-evasion game (2014)
  6. Mitchell, Ian M.; Kaynama, Shahab; Chen, Mo; Oishi, Meeko: Safety preserving control synthesis for sampled data systems (2013)
  7. Almeida, Luís; Bagnerini, Patrizia; Habbal, Abderrahmane: Modeling actin cable contraction (2012)
  8. Grepl, Martin A.; Veroy, Karen: A level set reduced basis approach to parameter estimation (2011)
  9. Papadopoulos, Dimitris; Herty, Michael; Rath, Volker; Behr, Marek: Identification of uncertainties in the shape of geophysical objects with level sets and the adjoint method (2011)
  10. Bect, Julien: A unifying formulation of the Fokker-Planck-Kolmogorov equation for general stochastic hybrid systems (2010)
  11. Summers, Sean; Lygeros, John: Verification of discrete time stochastic hybrid systems: a stochastic reach-avoid decision problem (2010)
  12. Clément, Frédérique: Multiscale modelling of endocrine systems: new insight on the gonadotrope axis (2009)
  13. Danzl, Per; Hespanha, João; Moehlis, Jeff: Event-based minimum-time control of oscillatory neuron models (2009)
  14. Feng, Yantao; Anderson, Brian D.O.; Rotkowitz, Michael: A game theoretic algorithm to compute local stabilizing solutions to HJBI equations in nonlinear $H_\infty $ control (2009)
  15. Stefanou, G.; Nouy, A.; Clement, A.: Identification of random shapes from images through polynomial chaos expansion of random level set functions (2009)
  16. Abate, Alessandro; Prandini, Maria; Lygeros, John; Sastry, Shankar: Probabilistic reachability and safety for controlled discrete time stochastic hybrid systems (2008)
  17. Macdonald, Colin B.; Ruuth, Steven J.: Level set equations on surfaces via the closest point method (2008)
  18. Mitchell, Ian M.: The flexible, extensible and efficient toolbox of level set methods (2008)
  19. Asarin, Eugene; Dang, Thao; Girard, Antoine: Hybridization methods for the analysis of nonlinear systems (2007)
  20. Kurzhanski, A.B.; Mitchell, I.M.; Varaiya, P.: Optimization techniques for state-constrained control and obstacle problems (2006)

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