Skip to main content

Spiking Adaptive Dynamic Programming with Poisson Process

  • Conference paper
  • First Online:
Advances in Swarm Intelligence (ICSI 2021)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 12690))

Included in the following conference series:

  • 1192 Accesses

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.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. 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

    Article  Google Scholar 

  2. 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)

    Article  MathSciNet  Google Scholar 

  3. 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)

    Article  Google Scholar 

  4. 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)

    Article  Google Scholar 

  5. 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)

    Article  MathSciNet  Google Scholar 

  6. Zhang, X., Li, C., Huang, T.: Hybrid impulsive and switching Hopfield neural networks with state-dependent impulses. Neural Netw. 93, 176–184 (2017)

    Article  Google Scholar 

  7. Li, X., Song, S.: Stabilization of delay systems: delay-dependent impulsive control. IEEE Trans. Autom. Control 62, 406–411 (2016)

    Article  MathSciNet  Google Scholar 

  8. 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)

    Article  Google Scholar 

  9. 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)

    Article  Google Scholar 

  10. 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)

    Article  MathSciNet  Google Scholar 

  11. Jiang, Y., Jiang, Z.-P.: Robust Adaptive Dynamic Programming. Wiley, Hoboken (2017)

    Book  Google Scholar 

  12. 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)

    Google Scholar 

  13. 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

    Book  MATH  Google Scholar 

  14. 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)

    Article  Google Scholar 

  15. Wei, Q., Song, R., Liao, Z., et al.: Discrete-time impulsive adaptive dynamic programming. IEEE Trans. Cybern. 50, 4293–4306 (2019)

    Article  Google Scholar 

  16. Puterman, M.L.: Markov Decision Processes: Discrete Stochastic Dynamic Programming. Wiley, Hoboken (2014)

    MATH  Google Scholar 

  17. Kordovan, M., Rotter, S.: Spike train cumulants for linear-nonlinear Poisson cascade models. arXiv preprint arXiv:2001.05057 (2020)

  18. Bux, C.E.R., Pillow, J.W.: Poisson balanced spiking networks. bioRxiv 836601 (2019)

    Google Scholar 

  19. 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)

    Article  Google Scholar 

  20. Newman, J.P., Fong, M.-f., Millard, D.C., et al.: Optogenetic feedback control of neural activity. Elife 4, e07192 (2015)

    Google Scholar 

  21. 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)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Qinglai Wei .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2021 Springer Nature Switzerland AG

About this paper

Check for updates. Verify currency and authenticity via CrossMark

Cite this paper

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

Download citation

  • DOI: https://doi.org/10.1007/978-3-030-78811-7_49

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-78810-0

  • Online ISBN: 978-3-030-78811-7

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics