Open Access
Issue |
ESAIM: COCV
Volume 30, 2024
|
|
---|---|---|
Article Number | 63 | |
Number of page(s) | 36 | |
DOI | https://doi.org/10.1051/cocv/2024053 | |
Published online | 10 September 2024 |
- P. Chossat and R. Lauterbach, Methods in equivariant bifurcations and dynamical systems. Vol. 15 of Advanced Series in Nonlinear Dynamics. World Scientific Publishing Co., Inc., River Edge, NJ (2000). [CrossRef] [Google Scholar]
- K. Gatermann, Computer algebra methods for equivariant dynamical systems. Vol. 1728 of Lecture Notes in Mathematics. Springer-Verlag, Berlin (2000). [CrossRef] [Google Scholar]
- E. Hubert and G. Labahn, Scaling invariants and symmetry reduction of dynamical systems. Found. Comput. Math. 13 (2013) 479–516. [CrossRef] [MathSciNet] [Google Scholar]
- M.V. Lakshmi, G. Fantuzzi, J.D. Fernandez-Caballero, Y. Hwang and S.I. Chernyshenko, Finding extremal periodic orbits with polynomial optimization, with application to a nine-mode model of shear flow. SIAM J. Appl. Dyn. Syst. 19 (2020) 763–787. [CrossRef] [MathSciNet] [Google Scholar]
- T. Ohsawa, Symmetry reduction of optimal control systems and principal connections. SIAM J. Control Optim. 51 (2013) 96–120. [CrossRef] [MathSciNet] [Google Scholar]
- H.J. Sussmann, Symmetries and integrals of motion in optimal control, in Geometry in nonlinear control and differential inclusions (Warsaw, 1993), Vol. 32 of Banach Center Publ. Polish Acad. Sci. Inst. Math., Warsaw (1995) 379–393. [CrossRef] [Google Scholar]
- C. Riener, T. Theobald, L.J. Andrén and J.B. Lasserre, Exploiting symmetries in SDP-relaxations for polynomial optimization. Math. Oper. Res. 38 (2013) 122–141. [CrossRef] [MathSciNet] [Google Scholar]
- V. Naicker, K. Andriopoulos and P.G. Leach, Symmetry reductions of a Hamilton–Jacobi–Bellman equation arising in financial mathematics. J. Nonlinear Math. Phys. 12 (2005) 268–283. [CrossRef] [MathSciNet] [Google Scholar]
- P.G. Leach, G.J. O’Hara and W. Sinkala, Symmetry-based solution of a model for a combination of a risky investment and a riskless investment. J. Math. Anal. Appl. 334 (2007) 368–381. [CrossRef] [MathSciNet] [Google Scholar]
- L. Rodrigues, D. Henrion and B.J. Cantwell, Symmetries and analytical solutions of the Hamilton–Jacobi–Bellman equation for a class of optimal control problems. Optimal Control Appl. Methods 37 (2016) 749–764. [CrossRef] [MathSciNet] [Google Scholar]
- C. Schlosser and M. Korda, Sparse moment-sum-of-squares relaxations for nonlinear dynamical systems with guaranteed convergence. arXivpreprintarXiv:2012.05572, 2020. [Google Scholar]
- J. Wang, M. Maggio and V. Magron, SparseJSR: a fast algorithm to compute joint spectral radius via sparse sos decompositions, in 2021 American Control Conference (ACC). IEEE (2021) 2254–2259. [CrossRef] [Google Scholar]
- J. Wang, C. Schlosser, M. Korda and V. Magron, Exploiting term sparsity in moment-SOS hierarchy for dynamical systems. IEEE Trans. Automatic Control 68 (2023). [Google Scholar]
- V. Magron and J. Wang, Sparse polynomial optimization: theory and practice. Series on Optimization and Its Applications. World Scientific Press (2023). [CrossRef] [Google Scholar]
- Y. Zheng, G. Fantuzzi and A. Papachristodoulou, Chordal and factor-width decompositions for scalable semidefinite and polynomial optimization. Annu. Rev. Control 52 (2021) 243–279. [CrossRef] [MathSciNet] [Google Scholar]
- R. Vinter, Convex duality and nonlinear optimal control. SIAM J. Control Optim. 31 (1993) 518–538. [CrossRef] [MathSciNet] [Google Scholar]
- J.B. Lasserre, D. Henrion, C. Prieur and E. Trélat, Nonlinear optimal control via occupation measures and LMI- relaxations. SIAM J. Control Optim. 47 (2008) 1643–1666. [CrossRef] [MathSciNet] [Google Scholar]
- S.J. Glaser, U. Boscain, T. Calarco, C.P. Koch, W. Köckenberger, R. Kosloff, I. Kuprov, B. Luy, S. Schirmer, T. Schulte-Herbrüggen, D. Sugny and F.K. Wilhelm, Training schrödinger’s cat: quantum optimal control. Eur. Phys. J. D 69 (2015) 279. [CrossRef] [Google Scholar]
- S. Deffner and S. Campbell, Quantum speed limits: from Heisenberg’s uncertainty principle to optimal quantum control. J. Phys. A: Math. Theor. 50 (2017) 453001. [CrossRef] [Google Scholar]
- M. Golubitsky and I. Stewart, Recent advances in symmetric and network dynamics. Chaos 25 (2015) 097612. [CrossRef] [MathSciNet] [PubMed] [Google Scholar]
- M. Golubitsky and I. Stewart, Rigid patterns of synchrony for equilibria and periodic cycles in network dynamics. Chaos 26 (2016) 094803. [CrossRef] [MathSciNet] [PubMed] [Google Scholar]
- D. Henrion and J.-B. Lasserre, Detecting Global Optimality and Extracting Solutions in GloptiPoly. Springer Berlin Heidelberg, Berlin, Heidelberg (2005) 293–310. [Google Scholar]
- R. Curto and L. Fialkow, The truncated complex k-moment problem. Trans. Am. Math. Soc. 352 (2000) 2825–2855. [CrossRef] [Google Scholar]
- A. Agrachev, D. Barilari and U. Boscain, A Comprehensive Introduction to Sub-Riemannian Geometry. Cambridge University Press, Cambridge (2019). [Google Scholar]
- M. Tacchi, Convergence of Lasserre’s hierarchy: the general case. Optim. Lett. 16 (2022) 1015–1033. [CrossRef] [MathSciNet] [Google Scholar]
- R. Lewis and R. Vinter, Relaxation of optimal control problems to equivalent convex programs. J. Math. Anal. Appl. 74 (1980) 475–493. [CrossRef] [MathSciNet] [Google Scholar]
- J.E. Rubio, Generalized curves and extremal points. SIAM J. Control 13 (1975) 28–47. [CrossRef] [MathSciNet] [Google Scholar]
- J.E. Rubio, Extremal points and optimal control theory. Ann. Mat. Pura Appl. 109 (1976) 165–176. [CrossRef] [MathSciNet] [Google Scholar]
- R.B. Vinter and R.M. Lewis, The equivalence of strong and weak formulations for certain problems in optimal control. SIAM J. Control Optim. 16 (1978) 546–570. [CrossRef] [MathSciNet] [Google Scholar]
- M. Putinar, Positive polynomials on compact semi-algebraic sets. Indiana Univ. Math. J. 42 (1993) 969–984. [CrossRef] [MathSciNet] [Google Scholar]
- J.-P. Serre et al., Linear Representations of Finite Groups, Vol. 42. Springer (1977). [CrossRef] [Google Scholar]
- J. Lofberg, Pre- and post-processing sum-of-squares programs in practice. IEEE Trans. Automatic Control 54 (2009) 1007–1011. [CrossRef] [MathSciNet] [Google Scholar]
- K. Gatermann and F. Guyard, Gröbner bases, invariant theory and equivariant dynamics. J. Symbolic Comput. 28 (1999) 275–302. [CrossRef] [MathSciNet] [Google Scholar]
- S. Marx, E. Pauwels, T. Weisser, D. Henrion and J.B. Lasserre, Semi-algebraic approximation using Christoffel- Darboux kernel. Construct. Approx. 54 (2021) 391–429. [CrossRef] [Google Scholar]
- D. Henrion and J.B. Lasserre, Graph recovery from incomplete moment information. Construct. Approx. 56 (2022) 165–187. [CrossRef] [Google Scholar]
- P. Bernard and G. Contreras, A generic property of families of Lagrangian systems. Ann. Math. 167 (2008) 1099–1108. [CrossRef] [MathSciNet] [Google Scholar]
- A. Barvinok, A Course in Convexity, Vol. 54. American Mathematical Society (2002). [Google Scholar]
- B.J. Schmid, Finite groups and invariant theory, in Topics in Invariant Theory. Springer Berlin Heidelberg, Berlin, Heidelberg (1991) 35–66. [CrossRef] [Google Scholar]
- A. Parusiński and A. Rainer, Lifting differentiable curves from orbit spaces. Transform. Groups 21 (2016) 153–179. [CrossRef] [MathSciNet] [Google Scholar]
- A. Parusiński and A. Rainer, Sobolev lifting over invariants. SIGMA Symmetry Integrability Geom. Methods Appl. 17 (2021) Paper No. 037, 31. [Google Scholar]
- U. Boscain and P. Mason, Time minimal trajectories for a spin 1/2 particle in a magnetic field. J. Math. Phys. 47 (2006) 062101. [CrossRef] [MathSciNet] [Google Scholar]
- D. Henrion, J.-B. Lasserre and J. Löfberg, Gloptipoly 3: moments, optimization and semidefinite programming. Optim. Methods Softw. 24 (2009) 761–779. [CrossRef] [MathSciNet] [Google Scholar]
- J. Lofberg, Yalmip: a toolbox for modeling and optimization in Matlab, in 2004 IEEE International Conference on Robotics and Automation (2004) 284–289. [CrossRef] [Google Scholar]
- J.F. Sturm, Using sedumi 1.02, a matlab toolbox for optimization over symmetric cones. Optim. Methods Softw. 11 (1999) 625–653. [CrossRef] [MathSciNet] [Google Scholar]
- N. Augier, D. Henrion, M. Korda and V. Magron, Matlab code for symmetric optimal control problems (2023). https://github.com/nicolasaugier1/SYMMETRIC_OCP.git. [Google Scholar]
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