Time-scale expansion-based approximated optimal control for underactuated systems using projection neural networks

Yinyan Zhang, Shuai Li

Research output: Journal article publicationJournal articleAcademic researchpeer-review

27 Citations (Scopus)


In this paper, a time-scale expansion-based scheme is proposed for approximately solving the optimal control problem of continuous-time underactuated nonlinear systems subject to input constraints and system dynamics. By time-scale Taylor approximation of the original performance index, the optimal control problem is relaxed into an approximated optimal control problem. Based on the system dynamics, the problem is further reformulated as a quadratic programming problem, which is solved by a projection neural network. Theoretical analysis on the closed-loop system synthesized by the controlled system and the projection neural network is conducted, which reveals that, under certain conditions, the closed-loop system possesses exponential stability and the original performance index converges to zero as time tends to infinity. In addition, two illustrative examples, which are based on a flexible joint manipulator and an underactuacted ship, are provided to validate the theoretical results and demonstrate the efficacy and superiority of the proposed control scheme.

Original languageEnglish
Article number7932185
Pages (from-to)1957-1967
Number of pages11
JournalIEEE Transactions on Systems, Man, and Cybernetics: Systems
Issue number11
Publication statusPublished - 1 Nov 2018


  • Input constraint
  • optimal control
  • projection neural network
  • stability analysis
  • time-scale expansion
  • underactuated system

ASJC Scopus subject areas

  • Software
  • Control and Systems Engineering
  • Human-Computer Interaction
  • Computer Science Applications
  • Electrical and Electronic Engineering

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