Approximation-based adaptive tracking control of pure-feedback nonlinear systems with multiple unknown time-varying delays

  • Authors:
  • Min Wang;Shuzhi Sam Ge;Keum-Shik Hong

  • Affiliations:
  • College of Automation and the Center for Control and Optimization, South China University of Technology, Guangzhou, China;Social Robotics Lab., Interactive Digital Media Institute and Dept. of Electrical and Computer Eng., National Univ. of Singapore, Singapore and Institute of Int. Systems and Inf. Techn., Univ. of ...;Department of Cogno-Mechatronics Engineering, Pusan National University, Busan, Korea

  • Venue:
  • IEEE Transactions on Neural Networks
  • Year:
  • 2010

Quantified Score

Hi-index 0.00

Visualization

Abstract

This paper presents adaptive neural tracking control for a class of non-affine pure-feedback systems with multiple unknown state time-varying delays. To overcome the design difficulty from non-affine structure of pure-feedback system, mean value theorem is exploited to deduce affine appearance of state variables xi as virtual controls αi, and of the actual control u. The separation technique is introduced to decompose unknown functions of all time-varying delayed states into a series of continuous functions of each delayed state. The novel Lyapunov-Krasovskii functionals are employed to compensate for the unknown functions of current delayed state, which is effectively free from any restriction on unknown time-delay functions and overcomes the circular construction of controller caused by the neural approximation of a function of u and u. Novel continuous functions are introduced to overcome the design difficulty deduced from the use of one adaptive parameter. To achieve uniformly ultimate boundedness of all the signals in the closed-loop system and tracking performance, control gains are effectively modified as a dynamic form with a class of even function, which makes stability analysis be carried out at the present of multiple time-varying delays. Simulation studies are provided to demonstrate the effectiveness of the proposed scheme.