×

Control of chaotic systems through reservoir computing. (English) Zbl 07863403

MSC:

34H05 Control problems involving ordinary differential equations
34H10 Chaos control for problems involving ordinary differential equations
65P20 Numerical chaos
37M99 Approximation methods and numerical treatment of dynamical systems
37N35 Dynamical systems in control
Full Text: DOI

References:

[1] Nieto, A. R.; Lilienkamp, T.; Seoane, J. M., Control of escapes in two-degree-of-freedom open Hamiltonian systems, Chaos, 32, 6, 063118 (2022) · Zbl 07874269 · doi:10.1063/5.0090150
[2] Sajan; Dubey, B., Chaos control in a multiple delayed phytoplankton-zooplankton model with group defense and predator’s interference, Chaos, 31, 8, 083101 (2021) · Zbl 07866659 · doi:10.1063/5.0054261
[3] El-Gohary, A., Chaos and optimal control of equilibrium states of tumor system with drug, Chaos Soliton Fractals, 41, 1, 425-435 (2009) · Zbl 1198.37121 · doi:10.1016/j.chaos.2008.02.003
[4] Wang, J.; Gao, Y.; Liu, Y., Intelligent dynamic practical-sliding-mode control for singular Markovian jump systems, Inf. Sci., 607, 153-172 (2022) · Zbl 1533.93100 · doi:10.1016/j.ins.2022.05.059
[5] Shang, D.; Li, X.; Yin, M., Dynamic modeling and control for dual-flexible servo system considering two-dimensional deformation based on neural network compensation, Mech. Mach. Theory, 175, 104954 (2022) · doi:10.1016/j.mechmachtheory.2022.104954
[6] Wang, Y.-L.; Jahanshahi, H.; Bekiros, S., Deep recurrent neural networks with finite-time terminal sliding mode control for a chaotic fractional-order financial system with market confidence, Chaos Soliton Fractals, 146, 110881 (2021) · Zbl 1498.93086 · doi:10.1016/j.chaos.2021.110881
[7] Shakya, A. K.; Bithel, K.; Pillai, G. N., Deep reinforcement learning based super twisting controller for liquid slosh control problem, IFAC-PapersOnLine, 55, 1, 734-739 (2022) · doi:10.1016/j.ifacol.2022.04.120
[8] Canaday, D.; Pomerance, A.; Gauthier, D. J., Model-free control of dynamical systems with deep reservoir computing, J. Phys. Complexity, 2, 3, 035025 (2021) · doi:10.1088/2632-072X/ac24f3
[9] Manjunath, G.; Jaeger, H., Echo state property linked to an input: Exploring a fundamental characteristic of recurrent neural networks, Neural Comput., 25, 3, 671-696 (2013) · Zbl 1269.92006 · doi:10.1162/NECO_a_00411
[10] Fan, H.; Jiang, J.; Zhang, C., Long-term prediction of chaotic systems with machine learning, Phys. Rev. Res., 2, 1, 012080 (2020) · doi:10.1103/PhysRevResearch.2.012080
[11] Sun, J. Q., Stochastic Dynamics and Control[M] (2006), Elsevier · Zbl 1118.74003
[12] Ma, Y.; Zhang, Z.; Yang, L., A resilient optimized dynamic event-triggered mechanism on networked control system with switching behavior under mixed attacks, Appl. Math. Comput., 430, 127300 (2022) · Zbl 1510.93106 · doi:10.1016/j.amc.2022.127300
[13] Gottwald, G. A.; Melbourne, I., On the implementation of the 0-1 test for chaos, SIAM J. Appl. Dyn. Syst., 8, 1, 129-145 (2009) · Zbl 1161.37054 · doi:10.1137/080718851
[14] Gottwald, G. A.; Melbourne, I., Testing for chaos in deterministic systems with noise, Physica D, 212, 1-2, 100-110 (2005) · Zbl 1097.37024 · doi:10.1016/j.physd.2005.09.011
[15] Gottwald, G. A.; Melbourne, I., A new test for chaos in deterministic systems, Proc. R. Soc. London. Ser. A Math. Phys. Eng. Sci., 460, 2042, 603-611 (2004) · Zbl 1042.37060 · doi:10.1098/rspa.2003.1183
[16] Pathak, J.; Wikner, A.; Fussell, R., Hybrid forecasting of chaotic processes: Using machine learning in conjunction with a knowledge-based model, Chaos, 28, 4, 041101 (2018) · doi:10.1063/1.5028373
[17] Carroll, T. L., Using reservoir computers to distinguish chaotic signals, Phys. Rev. E, 98, 5, 052209 (2018) · doi:10.1103/PhysRevE.98.052209
[18] Griffith, A.; Pomerance, A.; Gauthier, D. J., Forecasting chaotic systems with very low connectivity reservoir computers, Chaos, 29, 12, 123108 (2019) · doi:10.1063/1.5120710
[19] Itoh, Y.; Uenohara, S.; Adachi, M., Reconstructing bifurcation diagrams only from time-series data generated by electronic circuits in discrete-time dynamical systems, Chaos, 30, 1, 013128 (2020) · Zbl 1431.37065 · doi:10.1063/1.5119187
[20] Maass, W.; Natschläger, T.; Markram, H., Real-time computing without stable states: A new framework for neural computation based on perturbations, Neural Comput., 14, 11, 2531-2560 (2002) · Zbl 1057.68618 · doi:10.1162/089976602760407955
[21] Patel, D.; Canaday, D.; Girvan, M., Using machine learning to predict statistical properties of non-stationary dynamical processes: System climate, regime transitions, and the effect of stochasticity, Chaos, 31, 3, 033149 (2021) · Zbl 1459.86011 · doi:10.1063/5.0042598
[22] Jin, X.; Shao, J.; Zhang, X., Modeling of nonlinear system based on deep learning framework, Nonlinear Dyn., 84, 1327-1340 (2016) · doi:10.1007/s11071-015-2571-6
[23] Li, Y.; Xu, S.; Duan, J., A machine learning method for computing quasi-potential of stochastic dynamical systems, Nonlinear Dyn., 109, 3, 1877-1886 (2022) · Zbl 1519.37046 · doi:10.1007/s11071-022-07536-x
[24] Shen, M.; Yang, J.; Jiang, W., Stochastic resonance in image denoising as an alternative to traditional methods and deep learning, Nonlinear Dyn., 109, 3, 2163-2183 (2022) · doi:10.1007/s11071-022-07571-8
[25] Sui, Y.; Gao, H., Modified echo state network for prediction of nonlinear chaotic time series, Nonlinear Dyn., 110, 4, 3581-3603 (2022) · doi:10.1007/s11071-022-07788-7
[26] Rodan, A.; Tiňo, P., Simple deterministically constructed cycle reservoirs with regular jumps, Neural Comput., 24, 7, 1822-1852 (2012) · doi:10.1162/NECO_a_00297
[27] Pathak, J.; Lu, Z.; Hunt, B. R., Using machine learning to replicate chaotic attractors and calculate Lyapunov exponents from data, Chaos, 27, 12, 121102 (2017) · Zbl 1390.37138 · doi:10.1063/1.5010300
[28] Lu, Z.; Pathak, J.; Hunt, B., Reservoir observers: Model-free inference of unmeasured variables in chaotic systems, Chaos, 27, 4 (2017) · doi:10.1063/1.4979665
[29] Lin, Z.-F.; Liang, Y.-M.; Zhao, J.-L., Prediction of dynamic systems driven by Lévy noise based on deep learning, Nonlinear Dyn., 111, 2, 1511-1535 (2023) · doi:10.1007/s11071-022-07883-9
[30] Nakai, K.; Saiki, Y., Machine-learning inference of fluid variables from data using reservoir computing, Phys. Rev. E, 98, 2, 023111 (2018) · doi:10.1103/PhysRevE.98.023111
[31] Geurts, B. J.; Holm, D. D.; Luesink, E., Lyapunov exponents of two stochastic Lorenz 63 systems, J. Stat. Phys., 179, 1343-1365 (2020) · Zbl 1459.37066 · doi:10.1007/s10955-019-02457-3
[32] Wang, R.; Kalnay, E.; Balachandran, B., Neural machine-based forecasting of chaotic dynamics, Nonlinear Dyn., 98, 4, 2903-2917 (2019) · Zbl 1430.37043 · doi:10.1007/s11071-019-05127-x
[33] Lin, Z. F.; Zhao, J. L.; Liang, Y. M., RC-FODS algorithm for solving numerical solutions of fractional order dynamical system, AIP Adv., 13, 3 (2023) · doi:10.1063/5.0138585
[34] Lin, Z.-F.; Zhao, J.-L.; Liang, Y.-M., Predicting solutions of the stochastic fractional order dynamical system using machine learning, Theoret. Appl. Mech. Lett., 13, 3, 100433 (2023) · doi:10.1016/j.taml.2023.100433
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.