Abstract
A new iterative spiking adaptive dynamic programming (SADP) algorithm based on the Poisson process for optimal impulsive control problems is investigated with convergence discussion of the iterative process. For a fixed time interval, a 3-tuple can be computed, and then the iterative value functions and control laws can be obtained. Finally, a simulation example verifies the effectiveness of the developed algorithm.
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References
Wang, X., Yu, J., Huang, Y., Wang, H., Miao, Z.: Adaptive dynamic programming for linear impulse systems. J. Zhejiang Univ. Sci. C 15(1), 43–50 (2014). https://doi.org/10.1631/jzus.C1300145
Li, W., Huang, L., Guo, Z., Ji, J.: Global dynamic behavior of a plant disease model with ratio dependent impulsive control strategy. Math. Comput. Simul. 177, 120–139 (2020)
Haddad, W.M., Chellaboina, V., Kablar, N.A.: Non-linear impulsive dynamical systems. Part II: stability of feedback interconnections and optimality. Int. J. Control 74, 1659–1677 (2001)
Chen, W.-H., Luo, S., Zheng, W.X.: Generating globally stable periodic solutions of delayed neural networks with periodic coefficients via impulsive control. IEEE Trans. Cybern. 47, 1590–1603 (2016)
Yao, J., Guan, Z.-H., Chen, G., et al.: Stability, robust stabilization and H? Control of singular-impulsive systems via switching control. Syst. Control Lett. 55, 879–886 (2006)
Zhang, X., Li, C., Huang, T.: Hybrid impulsive and switching Hopfield neural networks with state-dependent impulses. Neural Netw. 93, 176–184 (2017)
Li, X., Song, S.: Stabilization of delay systems: delay-dependent impulsive control. IEEE Trans. Autom. Control 62, 406–411 (2016)
Zhang, Q., Qiao, L., Zhu, B., et al.: Dissipativity analysis and synthesis for a class of T-S fuzzy descriptor systems. IEEE Trans. Syst. Man Cybern. Syst. 47, 1774–1784 (2016)
Woźniak, S., Pantazi, A., Bohnstingl, T., et al.: Deep learning incorporating biologically inspired neural dynamics and in-memory computing. Nat. Mach. Intell. 2, 325–336 (2020)
Kiumarsi, B., Vamvoudakis, K.G., Modares, H., Lewis, F.L.: Optimal and autonomous control using reinforcement learning: a survey. IEEE Trans. Neural Netw. Learn. Syst. 29, 2042–2062 (2017)
Jiang, Y., Jiang, Z.-P.: Robust Adaptive Dynamic Programming. Wiley, Hoboken (2017)
Wen, Y., Si, J., Gao, X., et al.: A new powered lower limb prosthesis control framework based on adaptive dynamic programming. IEEE Trans. Neural Netw. Learn. Syst. 28, 2215–2220 (2016)
Liu, D., Wei, Q., Wang, D., Yang, X., Li, H.: Adaptive Dynamic Programming with Applications in Optimal Control. AIC. Springer, Cham (2017). https://doi.org/10.1007/978-3-319-50815-3
Liu, D., Xu, Y., Wei, Q., et al.: Residential energy scheduling for variable weather solar energy based on adaptive dynamic programming. IEEE/CAA J. Automatica Sinica 5, 36–46 (2017)
Wei, Q., Song, R., Liao, Z., et al.: Discrete-time impulsive adaptive dynamic programming. IEEE Trans. Cybern. 50, 4293–4306 (2019)
Puterman, M.L.: Markov Decision Processes: Discrete Stochastic Dynamic Programming. Wiley, Hoboken (2014)
Kordovan, M., Rotter, S.: Spike train cumulants for linear-nonlinear Poisson cascade models. arXiv preprint arXiv:2001.05057 (2020)
Bux, C.E.R., Pillow, J.W.: Poisson balanced spiking networks. bioRxiv 836601 (2019)
Gerhard, F., Deger, M., Truccolo, W.: On the stability and dynamics of stochastic spiking neuron models: nonlinear Hawkes process and point process GLMs. PLoS Comput. Biol. 13, e1005390 (2017)
Newman, J.P., Fong, M.-f., Millard, D.C., et al.: Optogenetic feedback control of neural activity. Elife 4, e07192 (2015)
Fong, M.-F., Newman, J.P., Potter, S.M., et al.: Upward synaptic scaling is dependent on neurotransmission rather than spiking. Nat. Commun. 6, 1–11 (2015)
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Wei, Q., Han, L., Zhang, T. (2021). Spiking Adaptive Dynamic Programming with Poisson Process. In: Tan, Y., Shi, Y. (eds) Advances in Swarm Intelligence. ICSI 2021. Lecture Notes in Computer Science(), vol 12690. Springer, Cham. https://doi.org/10.1007/978-3-030-78811-7_49
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DOI: https://doi.org/10.1007/978-3-030-78811-7_49
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