114
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22. S. F. Hafstein, “An Algorithm for Constructing Lyapunov Functions,” Electron. J.
Differ. Equ. Monograph, vol. 8, 207.
23. S. Sankaranarayanan, X. Chen, and E. Abraham, “Lyapunov Function Synthesis
using Handelman Representations,” IFAC Proceedings Volumes, vol. 46, no. 23,
pp. 576–581, 2013.
24. J. Kapinski, J. V. Deshmukh, S. Sankaranarayanan, and N. Arechiga, “Simulationguided Lyapunov Analysis for Hybrid Dynamical Systems,” in Proceedings of the
17th international conference on Hybrid systems: computation and control. ACM,
2014, pp. 133–142.
25. S. Gao, S. Kong, and E. M. Clarke, “dReal: An SMT Solver for Nonlinear Theories
over the Reals,” in International Conference on Automated Deduction. Springer,
2013, pp. 208–214.
26. Wolfram Research, Inc., “Mathematica, Version 12.0,” 2019.
27. H. Ravanbakhsh and S. Sankaranarayanan, “Learning Control Lyapunov Functions
from Counterexamples and Demonstrations,” Autonomous Robots, pp. 1–33, 2018.
28. E. M. Clarke, T. A. Henzinger, H. Veith, and R. Bloem, Handbook of model checking. Springer, 2018, vol. 10.
29. Microsoft Research, “The Z3 Theorem Prover,” https://github.com/Z3Prover/z3,
accessed: 2018-07-25.
30. Python Software Foundation, “Python Language Reference, version 2.7,” http:
//www.python.org.
31. J. F. Sturm, “Using SeDuMi 1.02, a MATLAB Toolbox for Optimization over
Symmetric Cones,” Optimization methods and software, vol. 11, no. 1-4, pp. 625–
653, 1999.
32. Y. Chang, N. Roohi, and S. Gao, “Neural Lyapunov Control,” in NeurIPS, 2019,
pp. 3240–3249.
Open Access This chapter is licensed under the terms of the Creative Commons
Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/),
which permits use, sharing, adaptation, distribution and reproduction in any medium
or format, as long as you give appropriate credit to the original author(s) and the
source, provide a link to the Creative Commons license and indicate if changes were
made.
The images or other third party material in this chapter are included in the chapter’s
Creative Commons license, unless indicated otherwise in a credit line to the material. If
material is not included in the chapter’s Creative Commons license and your intended
use is not permitted by statutory regulation or exceeds the permitted use, you will need
to obtain permission directly from the copyright holder.
D. Ahmed et al.
22. S. F. Hafstein, “An Algorithm for Constructing Lyapunov Functions,” Electron. J.
Differ. Equ. Monograph, vol. 8, 207.
23. S. Sankaranarayanan, X. Chen, and E. Abraham, “Lyapunov Function Synthesis
using Handelman Representations,” IFAC Proceedings Volumes, vol. 46, no. 23,
pp. 576–581, 2013.
24. J. Kapinski, J. V. Deshmukh, S. Sankaranarayanan, and N. Arechiga, “Simulationguided Lyapunov Analysis for Hybrid Dynamical Systems,” in Proceedings of the
17th international conference on Hybrid systems: computation and control. ACM,
2014, pp. 133–142.
25. S. Gao, S. Kong, and E. M. Clarke, “dReal: An SMT Solver for Nonlinear Theories
over the Reals,” in International Conference on Automated Deduction. Springer,
2013, pp. 208–214.
26. Wolfram Research, Inc., “Mathematica, Version 12.0,” 2019.
27. H. Ravanbakhsh and S. Sankaranarayanan, “Learning Control Lyapunov Functions
from Counterexamples and Demonstrations,” Autonomous Robots, pp. 1–33, 2018.
28. E. M. Clarke, T. A. Henzinger, H. Veith, and R. Bloem, Handbook of model checking. Springer, 2018, vol. 10.
29. Microsoft Research, “The Z3 Theorem Prover,” https://github.com/Z3Prover/z3,
accessed: 2018-07-25.
30. Python Software Foundation, “Python Language Reference, version 2.7,” http:
//www.python.org.
31. J. F. Sturm, “Using SeDuMi 1.02, a MATLAB Toolbox for Optimization over
Symmetric Cones,” Optimization methods and software, vol. 11, no. 1-4, pp. 625–
653, 1999.
32. Y. Chang, N. Roohi, and S. Gao, “Neural Lyapunov Control,” in NeurIPS, 2019,
pp. 3240–3249.
Open Access This chapter is licensed under the terms of the Creative Commons
Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/),
which permits use, sharing, adaptation, distribution and reproduction in any medium
or format, as long as you give appropriate credit to the original author(s) and the
source, provide a link to the Creative Commons license and indicate if changes were
made.
The images or other third party material in this chapter are included in the chapter’s
Creative Commons license, unless indicated otherwise in a credit line to the material. If
material is not included in the chapter’s Creative Commons license and your intended
use is not permitted by statutory regulation or exceeds the permitted use, you will need
to obtain permission directly from the copyright holder.