Zeroing Neural Dynamics for Control Design: Comprehensive Analysis on Stability, Robustness, and Convergence Speed

Lin Xiao, Shuai Li, Faa Jeng Lin, Zhiguo Tan, Ameer Hamza Khan

Research output: Contribution to journalArticlepeer-review

57 Scopus citations

Abstract

Zeroing neural dynamics (ZND) can be seen as an effective controller to solve various challenging scientific and engineering problems. Computing Lyapunov equation is a kind of important issue in nonlinear systems for stability analysis in control. This paper presents a systematic and constructive procedure on using ZND to design control laws based on the efficient solution of dynamic Lyapunov equation. We particularly address three important aspects in the design: 1) the global stability of ZND, to guarantee the effectiveness of the solution; 2) the robustness against additive noises, to ensure the capability of ZND for using in harsh environments; and 3) the finite-time convergence of ZND, to endow ZND for real-time solution of dynamical problems. To do so, a novel formula is first designed in a unified manner of ZND. Differing from the conventional formula appearing in ZND, the proposed formula simultaneously has finite-time convergence and noise robustness property. According to this novel formula, a novel control law (termed nonlinear neural dynamics, NND) is established to compute dynamic Lyapunov equation in the presence of various additive noises. Both theoretical and simulative results ensure the finite-time convergence and noise robustness property of the NND model for computing dynamic Lyapunov equation in front of various additive noises. As compared to the conventional ZND model for computing dynamic Lyapunov, the superior property of the NND model is further demonstrated.

Original languageEnglish
Article number8445623
Pages (from-to)2605-2616
Number of pages12
JournalIEEE Transactions on Industrial Informatics
Volume15
Issue number5
DOIs
StatePublished - May 2019

Keywords

  • Design formula
  • dynamic Lyapunov equation
  • finite-time convergence
  • noise suppression
  • zeroing neural network (ZNN)

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