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Construction of a global Lyapunov function using radial basis functions with a single operator
1. | Zentrum Mathematik, TU München, Boltzmannstr. 3, D-85747 Garching bei München, Germany |
[1] |
Fabio Camilli, Lars Grüne. Characterizing attraction probabilities via the stochastic Zubov equation. Discrete and Continuous Dynamical Systems - B, 2003, 3 (3) : 457-468. doi: 10.3934/dcdsb.2003.3.457 |
[2] |
Hjörtur Björnsson, Sigurdur Hafstein, Peter Giesl, Enrico Scalas, Skuli Gudmundsson. Computation of the stochastic basin of attraction by rigorous construction of a Lyapunov function. Discrete and Continuous Dynamical Systems - B, 2019, 24 (8) : 4247-4269. doi: 10.3934/dcdsb.2019080 |
[3] |
Najla Mohammed, Peter Giesl. Grid refinement in the construction of Lyapunov functions using radial basis functions. Discrete and Continuous Dynamical Systems - B, 2015, 20 (8) : 2453-2476. doi: 10.3934/dcdsb.2015.20.2453 |
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Martin D. Buhmann, Slawomir Dinew. Limits of radial basis function interpolants. Communications on Pure and Applied Analysis, 2007, 6 (3) : 569-585. doi: 10.3934/cpaa.2007.6.569 |
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Lars Grüne, Hasnaa Zidani. Zubov's equation for state-constrained perturbed nonlinear systems. Mathematical Control and Related Fields, 2015, 5 (1) : 55-71. doi: 10.3934/mcrf.2015.5.55 |
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Oliver Junge, Alex Schreiber. Dynamic programming using radial basis functions. Discrete and Continuous Dynamical Systems, 2015, 35 (9) : 4439-4453. doi: 10.3934/dcds.2015.35.4439 |
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Sohana Jahan, Hou-Duo Qi. Regularized multidimensional scaling with radial basis functions. Journal of Industrial and Management Optimization, 2016, 12 (2) : 543-563. doi: 10.3934/jimo.2016.12.543 |
[8] |
Ezzeddine Zahrouni. On the Lyapunov functions for the solutions of the generalized Burgers equation. Communications on Pure and Applied Analysis, 2003, 2 (3) : 391-410. doi: 10.3934/cpaa.2003.2.391 |
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Daniel G. Alfaro Vigo, Amaury C. Álvarez, Grigori Chapiro, Galina C. García, Carlos G. Moreira. Solving the inverse problem for an ordinary differential equation using conjugation. Journal of Computational Dynamics, 2020, 7 (2) : 183-208. doi: 10.3934/jcd.2020008 |
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Richard A. Norton, G. R. W. Quispel. Discrete gradient methods for preserving a first integral of an ordinary differential equation. Discrete and Continuous Dynamical Systems, 2014, 34 (3) : 1147-1170. doi: 10.3934/dcds.2014.34.1147 |
[11] |
Tomás Caraballo, Renato Colucci, Luca Guerrini. Bifurcation scenarios in an ordinary differential equation with constant and distributed delay: A case study. Discrete and Continuous Dynamical Systems - B, 2019, 24 (6) : 2639-2655. doi: 10.3934/dcdsb.2018268 |
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Lukáš Adam, Jiří Outrata. On optimal control of a sweeping process coupled with an ordinary differential equation. Discrete and Continuous Dynamical Systems - B, 2014, 19 (9) : 2709-2738. doi: 10.3934/dcdsb.2014.19.2709 |
[13] |
Jeremy Levesley, Xinping Sun, Fahd Jarad, Alexander Kushpel. Interpolation of exponential-type functions on a uniform grid by shifts of a basis function. Discrete and Continuous Dynamical Systems - S, 2021, 14 (7) : 2399-2416. doi: 10.3934/dcdss.2020403 |
[14] |
Anne-Sophie de Suzzoni. Consequences of the choice of a particular basis of $L^2(S^3)$ for the cubic wave equation on the sphere and the Euclidean space. Communications on Pure and Applied Analysis, 2014, 13 (3) : 991-1015. doi: 10.3934/cpaa.2014.13.991 |
[15] |
Hiroshi Morishita, Eiji Yanagida, Shoji Yotsutani. Structure of positive radial solutions including singular solutions to Matukuma's equation. Communications on Pure and Applied Analysis, 2005, 4 (4) : 871-888. doi: 10.3934/cpaa.2005.4.871 |
[16] |
Lijuan Wang, Yashan Xu. Admissible controls and controllable sets for a linear time-varying ordinary differential equation. Mathematical Control and Related Fields, 2018, 8 (3&4) : 1001-1019. doi: 10.3934/mcrf.2018043 |
[17] |
Yuriy Golovaty, Anna Marciniak-Czochra, Mariya Ptashnyk. Stability of nonconstant stationary solutions in a reaction-diffusion equation coupled to the system of ordinary differential equations. Communications on Pure and Applied Analysis, 2012, 11 (1) : 229-241. doi: 10.3934/cpaa.2012.11.229 |
[18] |
Qiong Meng, X. H. Tang. Multiple solutions of second-order ordinary differential equation via Morse theory. Communications on Pure and Applied Analysis, 2012, 11 (3) : 945-958. doi: 10.3934/cpaa.2012.11.945 |
[19] |
Jan-Hendrik Webert, Philip E. Gill, Sven-Joachim Kimmerle, Matthias Gerdts. A study of structure-exploiting SQP algorithms for an optimal control problem with coupled hyperbolic and ordinary differential equation constraints. Discrete and Continuous Dynamical Systems - S, 2018, 11 (6) : 1259-1282. doi: 10.3934/dcdss.2018071 |
[20] |
Abdulrazzaq T. Abed, Azzam S. Y. Aladool. Applying particle swarm optimization based on Padé approximant to solve ordinary differential equation. Numerical Algebra, Control and Optimization, 2022, 12 (2) : 321-337. doi: 10.3934/naco.2021008 |
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