Skip to main content
SpringerLink
Log in

Optimal tracking control of a class of nonlinear discrete-time switched systems using adaptive dynamic programming

  • Original Article
  • Published:
Neural Computing and Applications Aims and scope Submit manuscript

Abstract

In this paper, an infinite-horizon optimal tracking control scheme is proposed for a class of nonlinear discrete-time switched systems. First, via system transformation, the optimal tracking problem is converted into designing an optimal regulator for the tracking error dynamics. And then, with convergence analysis in terms of value function and control policy, the iterative adaptive dynamic programming (ADP) algorithm is introduced to obtain the infinite-horizon optimal tracking controller which makes the value function close to its optimal value function. Next, two neural networks are used as parametric structures to implement the ADP algorithm, which aim at approximating the value function and the control policy, respectively. Finally, a simulation example is included to complement the theoretical discussions.

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

Access this article

Log in via an institution

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

Similar content being viewed by others

References

  1. Liberzon D (2003) Switching in systems and control. Birkhauser, Boston

    Book  MATH  Google Scholar 

  2. Borrelli F, Baotić M, Bemporad A, Morari M (2005) Dynamic programming for constrained optimal control of discrete-time linear hybrid systems. Automatica 41:1709–1721

    Article  MATH  Google Scholar 

  3. Chai T, Geng Z, Yue H, Wang H, Su C (2009) A hybrid intelligent optimal control method for complex flotation process. Int J Syst Sci 40:945–960

    Article  Google Scholar 

  4. Gao H, Lam J, Wang C (2006) Model simplification for switched hybrid systems. Syst Control Lett 55:1015–1021

    Article  MATH  MathSciNet  Google Scholar 

  5. Jiang B, Yang H, Shi P (2010) Switching fault tolerant control design via global dissipativity. Int J Syst Sci 41:1003–1012

    Article  MATH  MathSciNet  Google Scholar 

  6. Ni W, Cheng D (2010) Control of switched linear systems with input saturation. Int J Syst Sci 41:1057–1065

    Article  MATH  MathSciNet  Google Scholar 

  7. Seatzu C, Corona D, Giua A, Bempoard A (2006) Optimal control of continuous time switched affine systems. IEEE Trans Autom Control 51:726–741

    Article  Google Scholar 

  8. Du D, Jiang B, Shi P, Zhou S (2007) H\(\infty\) Filtering of discrete-time switched systems with state delays via switched lyapunov function approach. IEEE Trans Autom Control 52:1520–1525

    Article  MathSciNet  Google Scholar 

  9. Zhang L, Gao H (2010) Asynchronously switched control of switched linear systems with average dwell time. Automatica 46:953–958

    Article  MATH  Google Scholar 

  10. Niu B, Zhao J Tracking control for output-constrained nonlinear switched systems with a barrier Lyapunov function. Int J Syst Sci. doi:10.1080/00207721.2011.652222

  11. Yu L, Fei S, Li X (2010) Robust adaptive neural tracking control for a class of switched affine nonlinear systems. Neurocomputing 73:2274–2279

    Article  Google Scholar 

  12. Li Q, Zhao J, Dimirovski G (2009) Tracking control for switched time-varying delays systems with stabilizable and unstabilizable subsystems. Nonlinear Anal Hybrid Syst 3:133–142

    Article  MATH  MathSciNet  Google Scholar 

  13. Wang M, Zhao J, Dimirovski G (2010) Output tracking control of nonlinear switched cascade systems using a variable structure control method. Int J Control 83(2):394–403

    Article  MATH  MathSciNet  Google Scholar 

  14. Lin D, Wang X, Nian F, Zhang Y (2010) Dynamic fuzzy neural networks modeling and adaptive backstepping tracking control of uncertain chaotic systems. Neurocomputing 73:2873–2881

    Article  Google Scholar 

  15. Lin D, Wang X, Yao Y (2012) Fuzzy neural adaptive tracking control of unknown chaotic systems with input saturation. Nonlinear Dyn 67(4):2889–2897

    Article  MATH  MathSciNet  Google Scholar 

  16. Bellman RE (1957) Dynamic programming. Princeton University Press, Princeton

    MATH  Google Scholar 

  17. Xu X-P, Antsaklis P-J (2003) Results and perspectives on computational methods for optimal control of switched systems. In: Maler O, Pnueli A (eds) Hybrid systems: computation and control (HSCC). Springer, Berlin, pp 540–555

  18. Lincoln B, Rantzer A (2006) Relaxing dynamic programming. IEEE Trans Autom Control 51:1249–1260

    Article  MathSciNet  Google Scholar 

  19. Murray JJ, Cox CJ, Lendaris GG, Saeks R (2002) Adaptive dynamic programming. IEEE Trans Syst Man Cybern Part C Appl Rev 32:140–153

    Article  Google Scholar 

  20. Wang FY, Zhang H, Liu D (2009) Adaptive dynamic programming: an introduction. IEEE Comput Intell Mag 43:9–47

    Google Scholar 

  21. Si J, Wang YT (2001) On-line learning control by association and reinforcement. IEEE Trans Neural Netw 12:264–276

    Article  Google Scholar 

  22. Al-Tamimi A, Lewis FL, Abu-Khalaf M (2008) Discrete-time nonlinear HJB solution using approximate dynamic programming: convergence proof. IEEE Trans Syst Man Cybern Part B Cybern 38:943–949

    Article  Google Scholar 

  23. Bertsekas DP, Tsitsiklis JN (1996) Neuro-dynamic programming. Athena Scientific, Belmont

    MATH  Google Scholar 

  24. Prokhorov DV, Wunsch DC (1997) Adaptive critic designs. IEEE Trans Neural Netw 8:997–1007

    Article  Google Scholar 

  25. Sutton RS, Barto AG (1998) Reinforcement learning: an introduction. The MIT Press, Cambridge

    Google Scholar 

  26. Zhang H, Luo Y, Liu D (2009) Neural-network-based near-optimal control for a class of discrete-time affine nonlinear systems with control constraints. IEEE Trans Neural Netw 20:1490–1503

    Article  Google Scholar 

  27. Zhang H, Cui L, Zhang X, Luo Y (2011) Data-driven robust approximate optimal tracking control for unknown general nonlinear systems using adaptive dynamic programming method. IEEE Trans Neural Netw 22:2226–2236

    Article  Google Scholar 

  28. Cao N, Zhang H, Luo Y, Feng D (2011) Infinite horizon optimal control of affine nonlinear discrete switched systems using two-stage approximate dynamic programming. Int J Syst Sci. doi:10.1080/00207721.2010.549590

  29. Zhang H, Wei Q, Luo Y (2008) A novel infinite-time optimal tracking control scheme for a class of discrete-time nonlinear system based on greedy HDP iteration algorithm. IEEE Trans Syst Man Cybern Part B Cybern 38:937–942

    Article  Google Scholar 

  30. Dierks T, Jagannathan S (2009) Optimal tracking control of affine nonlinear discrete-time systems with unknown internal dynamics. In: Proceedings of joint 48th IEEE conference on decision and control and 28th Chinese control conference. Shanghai, PR China, pp 6750–6755

  31. Wang D, Liu D, Wei Q (2012) Finite-horizon neuro-optimal tracking control for a class of discrete-time nonlinear systems using adaptive dynamic programming approach. Neurocomputing 78:14–22

    Article  Google Scholar 

  32. Park Y, Choi M, Lee K (1996) An optimal tracking neuro-controller for nonlinear dynamic systems. IEEE Trans Neural Netw 7:1099–1110

    Article  Google Scholar 

  33. Lin D, Wang X (2010) Observer-based decentralized fuzzy neural sliding mode control for interconnected unknown chaotic systems via network structure adaptation. Fuzzy Sets Syst 161(15):2066–2080

    Article  MATH  Google Scholar 

  34. Wang X, Zhao J (2010) Cryptanalysis on a parallel keyed hash function based on chaotic neural network. Neurocomputing 73:3224–3228

    Article  Google Scholar 

  35. Lin D, Wang X (2011) Self-organizing adaptive fuzzy neural control for the synchronization of uncertain chaotic systems with random-varying parameters. Neurocomputing 74:2241–2249

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. College of Information Science and Engineering, Northeastern University, Box 134, Shenyang, 110819, Liaoning, People’s Republic of China

    Chunbin Qin, Huaguang Zhang & Yanhong Luo

  2. Basic Experiment Teaching Center, Henan University, Kaifeng, 475004, Henan, People’s Republic of China

    Chunbin Qin

Authors
  1. Chunbin Qin
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Huaguang Zhang
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Yanhong Luo
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Huaguang Zhang.

Additional information

This work was supported by the National Natural Science Foundation of China (50977008, 60821063, 61034005, 61104010 ).

Rights and permissions

Reprints and permissions

About this article

Cite this article

Qin, C., Zhang, H. & Luo, Y. Optimal tracking control of a class of nonlinear discrete-time switched systems using adaptive dynamic programming. Neural Comput & Applic 24, 531–538 (2014). https://doi.org/10.1007/s00521-012-1238-1

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00521-012-1238-1

Keywords

Search

Navigation