Abstract
The switching times optimization problem for switched dynamical systems, with fixed initial state, is considered. A nonnegative cost term for changing dynamics is introduced to induce a sparse switching structure, that is, to reduce the number of switches. To deal with such problems, an inexact Newton-type arc search proximal method, based on a parametric local quadratic model of the cost function, is proposed. Numerical investigations and comparisons on a small-scale benchmark problem are presented and discussed.
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References
Beck, A., Teboulle, M.: A fast iterative shrinkage-thresholding algorithm for linear inverse problems. SIAM J. Imag. Sci. 2(1), 183–202 (2009). https://doi.org/10.1137/080716542
De Marchi, A.: Cardinality, Simplex and Proximal Operator (2019). https://doi.org/10.5281/zenodo.3334538
De Marchi, A.: On the mixed-integer linear-quadratic optimal control with switching cost. IEEE Control Syst. Lett. 3(4), 990–995 (2019). https://doi.org/10.1109/LCSYS.2019.2920425
Gerdts, M.: Optimal Control of ODEs and DAEs. De Gruyter (2011). https://doi.org/10.1515/9783110249996
Lee, J.D., Sun, Y., Saunders, M.A.: Proximal Newton-type methods for minimizing composite functions. SIAM J. Optim. 24(3), 1420–1443 (2014). https://doi.org/10.1137/130921428
Parikh, N., Boyd, S.: Proximal algorithms. Found. Trends® Optim. 1(3), 127–239 (2014). https://doi.org/10.1561/2400000003
Sager, S.: Numerical methods for mixed-integer optimal control problems, Ph.D. thesis. University of Heidelberg, Heidelberg (2005). Interdisciplinary Center for Scientific Computing
Stella, L., Themelis, A., Sopasakis, P., Patrinos, P.: A simple and efficient algorithm for nonlinear model predictive control. In: 56th IEEE Conference on Decision and Control (CDC), pp. 1939–1944. IEEE, New York (2017). https://doi.org/10.1109/CDC.2017.8263933
Stellato, B., Ober-Blöbaum, S., Goulart, P.J.: Second-order switching time optimization for switched dynamical systems. IEEE Trans. Autom. Control 62(10), 5407–5414 (2017). https://doi.org/10.1109/TAC.2017.2697681
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De Marchi, A., Gerdts, M. (2020). Sparse Switching Times Optimization and a Sweeping Hessian Proximal Method. In: Neufeld, J.S., Buscher, U., Lasch, R., Möst, D., Schönberger, J. (eds) Operations Research Proceedings 2019. Operations Research Proceedings. Springer, Cham. https://doi.org/10.1007/978-3-030-48439-2_11
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DOI: https://doi.org/10.1007/978-3-030-48439-2_11
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