Multi-objective Optimal Control for Time-Delay Systems

  • Ruizhuo SongEmail author
  • Qinglai Wei
  • Qing Li
Part of the Studies in Systems, Decision and Control book series (SSDC, volume 166)


A novel multi-objective ADP method is constructed to obtain the optimal controller of a class of nonlinear time-delay systems in this chapter. Using the weighted sum technology, the original multi-objective optimal control problem is transformed to the single one. An ADP method is established for nonlinear time-delay systems to solve the optimal control problem. To demonstrate the presented iterative performance index function sequence is convergent and the closed-loop system is asymptotically stable, the convergence analysis is also given. The neural networks are used to get the approximative control policy and the approximative performance index function, respectively. Two simulation examples are presented to illustrate the performance of the presented optimal control method.


  1. 1.
    Wei, Q., Zhang, H., Dai, J.: Model-free multiobjective approximate dynamic programming for discrete-time nonlinear systems with general performance index functions. Neurocomputing 72(7–9), 1839–1848 (2009)CrossRefGoogle Scholar
  2. 2.
    Wang, D., Liu, D., Wei, Q., Zhao, D., Jin, N.: Optimal control of unknown nonaffine nonlinear discrete-time systems based on adaptive dynamic programming. Automatica 48(8), 1825–1832 (2012)MathSciNetCrossRefGoogle Scholar
  3. 3.
    Song, R., Xiao, W., Zhang, H.: Multi-objective optimal control for a class of unknown nonlinear systems based on finite-approximation-error ADP algorithm. Neurocomputing 119(7), 212–221 (2013)CrossRefGoogle Scholar
  4. 4.
    Zhang, H., Song, R., wei, Q., Zhang, T.: Optimal tracking control for a class of nonlinear discrete-time systems with time delays based on heuristic dynamic programming. IEEE Trans. Neural Netw. 22(12), 1851–1862 (2011)CrossRefGoogle Scholar
  5. 5.
    Gyurkovics, É., Takács, T.: Quadratic stabilisation with \(\text{ H }_\infty \)-norm bound of non-linear discrete-time uncertain systems with bounded control. Syst. Control Lett. 50, 277–289 (2003)MathSciNetCrossRefGoogle Scholar

Copyright information

© Science Press, Beijing and Springer Nature Singapore Pte Ltd. 2019

Authors and Affiliations

  1. 1.University of Science and Technology BeijingBeijingChina
  2. 2.Institute of AutomationChinese Academy of SciencesBeijingChina

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