iBet uBet web content aggregator. Adding the entire web to your favor.
iBet uBet web content aggregator. Adding the entire web to your favor.



Link to original content: https://unpaywall.org/10.1007/S00521-021-05909-8
Reinforcement learning-based nonlinear tracking control system design via LDI approach with application to trolley system | Neural Computing and Applications Skip to main content
Springer Nature Link
Log in

Reinforcement learning-based nonlinear tracking control system design via LDI approach with application to trolley system

  • Special Issue on Computational Intelligence-based Control and Estimation in Mechatronic Systems
  • Published:
Neural Computing and Applications Aims and scope Submit manuscript

Abstract

In this paper, a novel scheme for the tracking problem of nonlinear systems is proposed. First, as a new technology of neural network in control field, linear differential inclusion is used to approximate the nonlinear term for the entire system. Based on the equivalent linear system, tracking reference signal is given and a new augmented system is built. According to the mentioned value function, two reinforcement learning algorithms are proposed to design the optimal control law. Notice that the online algorithm does not involve the system dynamics and tracking dynamics. In the simulation section, the model of trolley system is given to prove the effectiveness and accuracy of the scheme proposed in this paper.

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

Access this article

Log in via an institution

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9

Similar content being viewed by others

Explore related subjects

Discover the latest articles, news and stories from top researchers in related subjects.

References

  1. Bai W, Li T, Tong S (2020) NN reinforcement learning adaptive control for a class of nonstrict-feedback discrete-time systems. IEEE Trans Cybern. https://doi.org/10.1109/TCYB.2020.2963849

    Article  Google Scholar 

  2. Song Z, Yang J, Mei X et al (2020) Deep reinforcement learning for permanent magnet synchronous motor speed control systems. Neural Comput Appl. https://doi.org/10.1007/s00521-020-05352-1

    Article  Google Scholar 

  3. Khater A, El-Nagar A, El-Bardini M et al (2020) Online learning based on adaptive learning rate for a class of recurrent fuzzy neural network. Neural Comput Appl 32(12):8691–8710. https://doi.org/10.1007/s00521-019-04372-w

    Article  Google Scholar 

  4. Li H, Wu Y, Chen M (2020) Adaptive fault-tolerant tracking control for discrete-time multiagent systems via reinforcement learning algorithm. IEEE Trans Cybern. https://doi.org/10.1109/TCYB.2020.2982168

    Article  Google Scholar 

  5. Vrabie D, Pastravanu O, Abu-Khalaf M et al (2009) Adaptive optimal control for continuous-time linear systems based on policy iteration. Automatica 45(2):477–484. https://doi.org/10.1016/j.automatica.2008.08.017

    Article  MathSciNet  MATH  Google Scholar 

  6. Li H, Liu D, Wang D (2014) Integral reinforcement learning for linear continuous-time zero-sum games with completely unknown dynamics. IEEE Trans Autom Sci Eng 11(3):706–714. https://doi.org/10.1109/TASE.2014.2300532

    Article  Google Scholar 

  7. He S, Zhang M, Fang H et al (2019) Reinforcement learning and adaptive optimization of a class of Markov jump systems with completely unknown dynamic information. Neural Comput Appl. https://doi.org/10.1007/s00521-019-04180-2

    Article  Google Scholar 

  8. Wu H, Song S, You K et al (2018) Depth control of model-free auvs via reinforcement learning. IEEE Trans Syst Man Cybern Syst 49(12):2499–2510. https://doi.org/10.1109/TSMC.2017.2785794

    Article  Google Scholar 

  9. Liang Y, Zhang H, Xiao G et al (2018) Reinforcement learning-based online adaptive controller design for a class of unknown nonlinear discrete-time systems with time delays. Neural Comput Appl 30(6):1733–1745. https://doi.org/10.1007/s00521-018-3537-7

    Article  Google Scholar 

  10. Modares H, Nageshrao SP, Lopes GAD et al (2016) Optimal model-free output synchronization of heterogeneous systems using off-policy reinforcement learning. Automatica 71:334–341. https://doi.org/10.1016/j.automatica.2016.05.017

    Article  MathSciNet  MATH  Google Scholar 

  11. Hu Y, Wang H, He S, Zheng J, Ping Z, Ke S, Cao Z, Man Z (2021) Adaptive tracking control of an electronic throttle valve based on recursive terminal sliding mode. IEEE Trans Veh Technol. https://doi.org/10.1109/TVT.2020.3045778

    Article  Google Scholar 

  12. Zhang J, Wang H, Zheng J, Cao Z, Man Z, Yu M, Chen L (2020) Adaptive sliding mode-based lateral stability control of Steer-by-Wire vehicles with experimental validations. IEEE Trans Veh Technol 69(9):9589–9600. https://doi.org/10.1109/TVT.2020.3003326

    Article  Google Scholar 

  13. Hu Y, Wang H, Cao Z, Zheng J, Ping Z, Chen L, Jin X (2019) Extreme-learning-machine-based FNTSM control strategy for electronic throttle. Neural Comput Appl 32:14507–14518. https://doi.org/10.1007/s00521-019-04446-9

    Article  Google Scholar 

  14. Yang Y, Wan Y, Zhu J et al (2020) \(H_\infty\) tracking control for linear discrete-time systems: model-free Q-Learning designs. IEEE Control Syst Lett 5(1):175–180. https://doi.org/10.1109/LCSYS.2020.3001241

    Article  Google Scholar 

  15. Qin C, Zhang H, Luo Y (2014) Online optimal tracking control of continuous-time linear systems with unknown dynamics by using adaptive dynamic programming. Int J Control 87(5):1000–1009. https://doi.org/10.1080/00207179.2013.863432

    Article  MathSciNet  MATH  Google Scholar 

  16. Xiao G, Zhang H, Luo Y et al (2016) Data-driven optimal tracking control for a class of affine non-linear continuous-time systems with completely unknown dynamics. IET Control Theory Appl 10(6):700–710. https://doi.org/10.1049/iet-cta.2015.0590

    Article  MathSciNet  Google Scholar 

  17. Yang X, He H, Liu D et al (2017) Adaptive dynamic programming for robust neural control of unknown continuous-time non-linear systems. IET Control Theory Appl 11(14):2307–2316. https://doi.org/10.1049/iet-cta.2017.0154

    Article  MathSciNet  Google Scholar 

  18. Yang X, Liu D, Wei Q et al (2016) Guaranteed cost neural tracking control for a class of uncertain nonlinear systems using adaptive dynamic programming. Neurocomputing 198:80–90. https://doi.org/10.1016/j.neucom.2015.08.119

    Article  Google Scholar 

  19. Zhang J, Wang H, Cao Z, Zheng J, Yu M, Yazdani A, Shahnia F (2019) Fast nonsingular terminal sliding mode control for permanent magnet linear motor via ELM. Neural Comput Appl 32:14447–14457. https://doi.org/10.1007/s00521-019-04502-4

    Article  Google Scholar 

  20. Ye M, Wang H (2020) Robust adaptive integral terminal sliding mode control for steer-by-wire systems based on extreme learning machine. Comput Electr Eng. https://doi.org/10.1016/j.compeleceng.2020.106756

    Article  Google Scholar 

  21. He S, Fang H, Zhang M et al (2019) Adaptive optimal control for a class of nonlinear systems: the online policy iteration approach. IEEE Trans Neural Netw Learn Syst 31(2):549–558. https://doi.org/10.1109/TNNLS.2019.2905715

    Article  MathSciNet  Google Scholar 

  22. Fang H, Zhu G, Stojanovic V, Nie R, He S, Luan X, Liu F (2020) Adaptive optimization algorithm for nonlinear Markov jump systems with parrtial unknown dynamics. Int J Robust Nonlinear Control. https://doi.org/10.1002/rnc.5350

    Article  Google Scholar 

  23. Wang C, Fang H, He S (2020) Adaptive optimal controller design for a class of LDI-based neural network systems with input time-delays. Neurocomputing 385:292–299. https://doi.org/10.1016/j.neucom.2019.12.084

    Article  Google Scholar 

  24. Chen L, Wang H, Huang Y, Ping Z, Yu M, Ye M, Hu Y (2020) Robust hierarchical terminal sliding mode control of two-wheeled self-balancing vehicle using perturbation estimation. Mech Syst Signal Process. https://doi.org/10.1016/j.ymssp.2019.106584

    Article  Google Scholar 

  25. Ye M, Wang H (2019) A robust adaptive chattering-free sliding mode control strategy for automotive electronic throttle system via genetic algorithm. IEEE Access 8(99):68–80. https://doi.org/10.1109/ACCESS.2019.2934232

    Article  Google Scholar 

  26. Suykens JAK, De Moor B, Vandewalle J (2000) Robust local stability of multilayer recurrent neural networks. IEEE Trans Neural Netw 11(1):222–229. https://doi.org/10.1109/72.822525

    Article  Google Scholar 

  27. Modares H, Lewis FL (2014) Linear quadratic tracking control of partially-unknown continuous-time systems using reinforcement learning. IEEE Trans Autom Control 59(11):3051–3056. https://doi.org/10.1109/TAC.2014.2317301

    Article  MathSciNet  MATH  Google Scholar 

  28. Kleinman D (1968) On an iterative technique for Riccati equation computations. IEEE Trans Autom Control 13(1):114–115. https://doi.org/10.1109/TAC.1968.1098829

    Article  Google Scholar 

  29. Jiang Y, Jiang Z (2012) Computational adaptive optimal control for continuous-time linear systems with completely unknown dynamic. Automatica 48(10):2699–2704. https://doi.org/10.1016/j.automatica.2012.06.096

    Article  MathSciNet  MATH  Google Scholar 

Download references

Acknowledgements

This work was supported in part by National Natural Science Foundation of China (Nos. 62073001, 61673001), Foundation for Distinguished Young Scholars of Anhui Province (No. 1608085J05) and Key Support Program of University Outstanding Youth Talent of Anhui Province (No.gxydZD2017001).

Author information

Authors and Affiliations

  1. Key Laboratory of Intelligent Computing and Signal Processing (Ministry of Education), School of Electrical Engineering and Automation, Anhui University, Hefei, 230601, China

    Yidong Tu, Haiyang Fang & Shuping He

  2. School of Electrical Engineering, Computing and Mathematical Sciences, Curtin University, Perth, WA, 6102, Australia

    Yanyan Yin

  3. School of Electronic Information and Electrical Engineering, Chengdu University, Chengdu, 610106, China

    Shuping He

Authors
  1. Yidong Tu
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Haiyang Fang
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Yanyan Yin
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Shuping He
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Shuping He.

Ethics declarations

Conflict of interest

The authors declare that there is no conflict of interest regarding the publication of this paper.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Appendix

Appendix

Equation (7) can be obtained as follows:

Proof

$$\begin{aligned}&NN(x,W_1,W_2,\ldots ,W_L) \\&\quad =\digamma _L(W_L\cdots \digamma _2(W_2\digamma (W_1x))\cdots ) \\&\quad =\digamma _L(W_L\cdots \digamma _2(W_2[\sum _{i=0}^{1}h_{11}(i)\theta (i,\phi _{11})(W_1x)_1,\sum _{i=0}^{1}h_{12}(i)\\&\theta (i,\phi _{12})(W_1x)_2\cdots \sum _{i=0}^{1}h_{1n_1}(i)\theta (i,\phi _{1n_1})(W_1x)_{n1}])\cdots ) \\&\quad =\digamma _L(W_L\cdots \digamma _2(W_2[\sum _{i_{11}=0}^{1}\sum _{i_{12}=0}^{1}\cdots \sum _{i_{1n}=0}^{1}[h_{11}(i_{11})\;h_{12}(i_{12})\\&\quad \cdots h_{1n_1}(i_{1n_1})]{diag}[\theta (i_{11},\phi _{11}),\theta (i_{12},\phi _{12})\cdots \theta (i_{1n_1},\phi _{1n_1})]\\&(W_1x)])\cdots ) \\&\quad =\digamma _L(W_L\cdots [\sum _{i_{21}=0}^{1}\sum _{i_{22}=0}^{1}\cdots \sum _{i_{2n}=0}^{1}[h_{21}(i_{21})\;h_{22}(i_{22})\cdots h_{2n_2}\\&(i_{2n_2})]{diag}[\theta (i_{21},\phi _{21}), \theta (i_{22},\phi _{22})\cdots \theta (i_{2n_2},\phi _{2n_2})]W_2[\sum _{i_{11}=0}^{1}\\&\sum _{i_{12}=0}^{1}\cdots \sum _{i_{1n}=0}^{1}[h_{11}(i_{11})\;h_{12}(i_{12})\cdots h_{1n_1}(i_{1n_1})]{diag} [\theta (i_{11},\phi _{11}),\\&\theta (i_{12},\phi _{12})\cdots \theta (i_{1n_1},\phi _{1n_1})](W_1x)])\cdots )\\&\quad =\digamma _L(W_L\cdots [\sum _{i_{21}=0}^{1}\cdots \sum _{i_{2n_2}=0}^{1}\sum _{i_{11}=0}^{1}\cdots \sum _{i_{1n_1}=0}^{1}])[h_{11}(i_{11})\;h_{12}(i_{12})\\&\quad \cdots h_{1n_1}(i_{1n_1})\;h_{21}(i_{21})\; h_{22}(i_{22})\cdots h_{2n_1}(i_{2n_1})]{diag}[\theta (i_{21},\phi _{21}),\\&\theta (i_{22},\phi _{22})\cdots \theta (i_{2n_2},\phi _{2n_2})]W_2{diag}[\theta (i_{11},\phi _{11}),\theta (i_{12},\phi _{12})\\&\quad \cdots \theta (i_{1n_1},\phi _{1n_1})](W_1x)])\cdots ). \end{aligned}$$

Taking into account the characteristics of the activation function mentioned in Eq. (4), \(\sum _{i=0}^{1}h(i)=0\). Then, for the whole neural network, it can obtain Eq. (7), and the proof is completed. \(\square\)

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Tu, Y., Fang, H., Yin, Y. et al. Reinforcement learning-based nonlinear tracking control system design via LDI approach with application to trolley system. Neural Comput & Applic 34, 5055–5062 (2022). https://doi.org/10.1007/s00521-021-05909-8

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00521-021-05909-8

Keywords

Search

Navigation