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 49 articles , 1 standard article )

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  1. Alessandri, Angelo; Bagnerini, Patrizia; Gaggero, Mauro; Rossi, Anna: State and observer-based feedback control of normal flow equations (2020)
  2. Brügger, Rahel; Croce, Roberto; Harbrecht, Helmut: Solving a Bernoulli type free boundary problem with random diffusion (2020)
  3. Huang, Yunlong; Krishnaprasad, P. S.: Sub-Riemannian geometry and finite time thermodynamics. I: The stochastic oscillator (2020)
  4. Wilson, Dan: A data-driven phase and isostable reduced modeling framework for oscillatory dynamical systems (2020)
  5. Lebbe, N.; Dapogny, C.; Oudet, E.; Hassan, K.; Gliere, A.: Robust shape and topology optimization of nanophotonic devices using the level set method (2019)
  6. Pettersson, Per; Doostan, Alireza; Nordström, Jan: Level set methods for stochastic discontinuity detection in nonlinear problems (2019)
  7. Botkin, Nikolai; Turova, Varvara; Diepolder, Johannes; Bittner, Matthias; Holzapfel, Florian: Aircraft control during cruise flight in windshear conditions: viability approach (2017)
  8. Xu, Li; Wang, Jin: Quantifying the potential and flux landscapes of multi-locus evolution (2017)
  9. Zanon, Mario; Boccia, Andrea; Palma, Vryan Gil S.; Parenti, Sonja; Xausa, Ilaria: Direct optimal control and model predictive control (2017)
  10. Mohajerin Esfahani, Peyman; Chatterjee, Debasish; Lygeros, John: The stochastic reach-avoid problem and set characterization for diffusions (2016)
  11. Estrela da Silva, Jorge; Borges de Sousa, João; Lobo Pereira, Fernando: Dynamic optimization techniques for the motion coordination of autonomous vehicles (2015)
  12. Ghanbarzadeh, Soheil; Hesse, Marc A.; Prodanović, Maša: A level set method for materials with texturally equilibrated pores (2015)
  13. Lobo Pereira, Fernando; Borges de Sousa, J.; Gomes, R.; Calado, P.: A model predictive control approach to AUVs motion coordination (2015)
  14. Govindarajan, Nithin; de Visser, Cornelis C.; Krishnakumar, Kalmanje: A sparse collocation method for solving time-dependent HJB equations using multivariate (B)-splines (2014)
  15. Kurzhanski, Alexander B.; Varaiya, Pravin: Dynamics and control of trajectory tubes. Theory and computation (2014)
  16. Lesser, Kendra; Oishi, Meeko: Reachability for partially observable discrete time stochastic hybrid systems (2014)
  17. Takei, Ryo; Tsai, Richard; Zhou, Zhengyuan: An efficient algorithm for a visibility-based surveillance-evasion game (2014)
  18. Wilson, Dan; Moehlis, Jeff: A Hamilton-Jacobi-Bellman approach for termination of seizure-like bursting (2014)
  19. Mitchell, Ian M.; Kaynama, Shahab; Chen, Mo; Oishi, Meeko: Safety preserving control synthesis for sampled data systems (2013)
  20. Nabi, Ali; Mirzadeh, Mohammad; Gibou, Frederic; Moehlis, Jeff: Minimum energy desynchronizing control for coupled neurons (2013)

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