Papers
Topics
Authors
Recent
Assistant
AI Research Assistant
Well-researched responses based on relevant abstracts and paper content.
Custom Instructions Pro
Preferences or requirements that you'd like Emergent Mind to consider when generating responses.
Gemini 2.5 Flash
Gemini 2.5 Flash 168 tok/s
Gemini 2.5 Pro 49 tok/s Pro
GPT-5 Medium 37 tok/s Pro
GPT-5 High 34 tok/s Pro
GPT-4o 99 tok/s Pro
Kimi K2 214 tok/s Pro
GPT OSS 120B 466 tok/s Pro
Claude Sonnet 4.5 37 tok/s Pro
2000 character limit reached

The optimizing mode classification stabilization of sampled stochastic jump systems via an improved hill-climbing algorithm based on Q-learning (2402.17539v2)

Published 27 Feb 2024 in math.OC, cs.SY, eess.SY, math.ST, and stat.TH

Abstract: This paper addresses the stabilization problem of stochastic jump systems (SJSs) closed by a generally sampled controller. Because of the controller's switching and state both sampled, it is challenging to study its stabilization. A new stabilizing method deeply depending on the mode classifications is proposed to deal with the above sampling situation, whose quantity is equal to a Stirling number of the second kind. For the sake of finding the best stabilization effect among all the classifications, a convex optimization problem is developed, whose globally solution is proved to be existent and can be computed by an augmented Lagrangian function. More importantly, in order to further reduce the computation complexity but retaining a better performance as much as possible, a novelly improved hill-climbing algorithm is established by applying the Q-learning technique to provide an optimal attenuation coefficient. A numerical example is offered so as to verify the effectiveness and superiority of the methods proposed in this study.

Definition Search Book Streamline Icon: https://streamlinehq.com
References (28)
  1. H. Zhang, J. Wang, Z. Wang and H. Liang, “Mode-dependent stochastic synchronization for Markovian coupled neural networks with time-varying mode-delays,” IEEE Transactions on Neural Networks and Learning Systems, vol. 26, no. 11, pp. 2621-2634, 2015.
  2. G. Zhuang, Q. Ma, B. Zhang, S. Xu and J. Xia, “Admissibility and stabilization of stochastic singular Markovian jump systems with time delays,” Systems and Control Letters, vol. 114, pp.1-10, 2018.
  3. B. Cai, L. Zhang and Y. Shi, “Observed-mode-dependent state estimation of hidden semi-Markov jump linear systems,” IEEE Transactions on Automatic Control, vol. 65, no. 1, pp. 442-449, 2019.
  4. K. Ding and Q. Zhu, “Extended dissipative anti-disturbance control for delayed switched singular semi-Markovian jump systems with multi-disturbance via disturbance observer,” Automatica, vol. 128, pp. 109556, 2021.
  5. W. Qi, Y. Zhou, L. Zhang, J. Cao and J. Cheng, “Non-fragile H∞subscript𝐻H_{\infty}italic_H start_POSTSUBSCRIPT ∞ end_POSTSUBSCRIPT SMC for Markovian jump systems in a finite-time,” Journal of the Franklin Institute, vol. 358, no. 9, pp. 4721-4740, 2021.
  6. R. Zhang, H. Wang, J. H. Park, K. Shi and P. He, “Mode-dependent adaptive event-triggered control for stabilization of Markovian memristor-based reaction-diffusion neural networks,” IEEE Transactions on Neural Networks and Learning Systems, vol. 34, no. 8, pp. 3939-3951, 2023.
  7. C. E. de. Souza, A. Trofino and K. A. Barbosa, “Mode-independent H∞subscript𝐻H_{\infty}italic_H start_POSTSUBSCRIPT ∞ end_POSTSUBSCRIPT filters for Markovian jump linear systems,” IEEE Transactions on Automatic Control, vol. 51, no. 11, pp. 1837-1841, 2006.
  8. H. N. Wu, and K. Y. Cai, “Mode-independent robust stabilization for uncertain Markovian jump nonlinear systems via fuzzy control,” IEEE Transactions on Systems Man and Cybernetics Part B-Cybernetics, vol. 36, no. 3, pp. 509-519, 2005.
  9. P. H. Liu, D. W. C. Ho and F. C. Sun, “Design of H∞subscript𝐻H_{\infty}italic_H start_POSTSUBSCRIPT ∞ end_POSTSUBSCRIPT filter for Markov jumping linear systems with non-accessible mode information,” Automatica, vol. 44, no, 10, pp. 2655-2660, 2008.
  10. X. Li, W. Zhang and D. Lu, “Robust asynchronous output-feedback controller design for Markovian jump systems with output quantization,” IEEE Transactions on Systems, Man, and Cybernetics: Systems, vol. 52, no. 2, pp. 1214-1223, 2022.
  11. G. L. Wang, B. Y. Li, Q. L. Zhang and C. Y. Yang, “A partially delay-dependent and disordered controller design for discrete-time delayed systems,” Interational Journal of Robust Nonlinear Control, vol. 27, no. 16, pp. 2646-2668, 2017.
  12. O. L. V. Costa, M. D. Fragoso and M. G. Todorov, “A detector-based approach for the H2subscript𝐻2H_{2}italic_H start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT control of Markov jump linear systems with partial information,” IEEE Transactions on Automatic Control, vol. 60, no. 5, pp. 1219-1234, 2014.
  13. G. L. Wang, Q. L. Zhang and C. Y. Yang, “Fault-tolerant control of Markovian jump systems via a partially mode-available but unmatched controller,” Journal of the Franklin Institute, vol. 354, no. 17, pp. 7717-7731, 2017.
  14. G. L. Wang and L. Xu, “Almost sure stability and stabilization of Markovian jump systems with stochastic switching,” IEEE Transactions on Automatic Control, vol. 67, no. 3, pp. 1529-1536, 2022.
  15. G. L. Wang and Y. Y. Sun, “Almost sure stabilization of continuous-time jump linear systems via a stochastic scheduled controller,” IEEE Transactions on Cybernetics, vol. 52, no. 5, pp. 2712-2724, 2022.
  16. G. L. Wang, Y. S. Ren and Z. Q. Li, “Almost Sure Stabilization of Continuous-Time Semi-Markov Jump Systems via an Earliest Deadline First Scheduling Controller,” IEEE Transactions on Systems, Man, and Cybernetics: Systems, vol. 54, no. 1, pp. 656-667, 2024.
  17. G. L. Wang, “Stabilization of semi-Markovian jump systems via a quantity limited controller,” Nonlinear Analysis: Hybrid Systems, vol. 42, Artical: 101085, 2021.
  18. X. Mao, “Stabilization of continuous-time hybrid stochastic differential equations by discrete-time feedback control,” Automatica, vol. 49, no. 12, pp. 3677-3681, 2013.
  19. X. Mao, “Almost sure exponential stabilization by discrete-time stochastic feedback control,” IEEE Transactions on Automatic Control, vol. 61, pp. 1619-1624, 2015.
  20. G. F. Song, Z. Y. Lu, B. C. Zheng and et al, “Almost sure stabilization of hybrid systems by feedback control based on discrete-time observations of mode and state,” Science China Information Sciences, vol. 61, pp. 70213, 2018.
  21. G. L. Wang, Y. S. Ren and C. Huang, “Stabilizing control of Markovian jump systems with sampled switching and state signals and applications,” Interational Journal of Robust Nonlinear Control, vol. 33, no. 10, pp. 5198-5228, 2023.
  22. G. L. Wang, “Mode-independent control of singular Markovian jump systems: A stochastic optimization viewpoint,” Applied Mathematics and Computation, vol. 286, pp. 155-170, 2016.
  23. B. C. Rennie and A. J. Dobson, “On stirling numbers of the second kind,” Journal of Combinatorial Theory, vol. 7, no. 2, pp. 116-121, 1969.
  24. K. N. Boyadzhiev, “Close encounters with the Stirling numbers of the second kind,” Mathematics Magazine, vol. 85, no. 4, pp. 252-266, 2012.
  25. S. H. Jacobson and E. Yu¨¨u\rm\ddot{u}over¨ start_ARG roman_u end_ARGcesan, “Analyzing the performance of generalized hill climbing algorithms,” Journal of Heuristics, vol. 10, pp. 387-405, 2004.
  26. X. T. Wu, Y. Tang, J. D. Cao and X. R. Mao, “Stability analysis for continuous-time switched systems with stochastic switching signals,” IEEE Transactions on Automatic Control, vol. 63, no. 9, pp. 3083-3090, 2017.
  27. C. J. C. H. Watkins and P. Dayan, “Q-learning,” Machine learning, vol. 8, pp. 279-292, 1992.
  28. G. L. Wang and Y. S. Ren, “Stability analysis of delayed Markovian jump systems with delay switching and state signals and applications,” Interational Journal of Robust Nonlinear Control, vol. 32, no. 9, pp. 5141-5163, 2022.

Summary

We haven't generated a summary for this paper yet.

Ai Sparkles Streamline Icon: https://streamlinehq.com Summarize Now
Lightbulb Streamline Icon: https://streamlinehq.com

Continue Learning

We haven't generated follow-up questions for this paper yet.

Ai Sparkles Streamline Icon: https://streamlinehq.com Generate Now

Authors (1)

  1. Guoliang Wang
List To Do Tasks Checklist Streamline Icon: https://streamlinehq.com

Collections

Sign up for free to add this paper to one or more collections.

User Circle Single Streamline Icon: https://streamlinehq.com Sign Up