Backstepping design for cascade systems with relaxed assumption on Lyapunov functions

H. Ye, W. Gui, Zhong-Ping Jiang

Research output: Contribution to journalArticle

Abstract

This study proposes a novel backstepping technique for non-linear cascade systems whose driven subsystems have a feedforward structure and include higher order terms. A small control is first assigned to stabilise the driven subsystem, and a simple backstepping procedure is then followed. When dealing with the driven subsystem, we adopt an approach of using a small control to attenuate the higher order term, rather than the usual method in which the higher order term is tackled under the guidance of a single Lyapunov function. The stability analysis is carried out using some boundedness information to explicitly compute the higher order term, and the global asymptotical stability of the whole closed-loop system is obtained using the 'converging-input bounded-state' criterion. This is in sharp contrast with previous designs where (involved) Lyapunov functions are utilised in both the control design and stability analysis. As applications, global stabilisation designs are presented for several classical mechanical systems including the inertia wheel pendulum, the translational oscillator with rotating actuator and the cart-pole system.

Original languageEnglish (US)
Pages (from-to)700-712
Number of pages13
JournalIET Control Theory and Applications
Volume5
Issue number5
DOIs
StatePublished - Mar 17 2011

Fingerprint

Backstepping Design
Backstepping
Lyapunov functions
Lyapunov Function
Cascade
Higher Order
Subsystem
Term
Stability Analysis
Global Asymptotical Stability
Pendulums
Closed loop systems
Poles
Wheels
Actuators
Pendulum
Stabilization
Feedforward
Control Design
Mechanical Systems

ASJC Scopus subject areas

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

Cite this

Backstepping design for cascade systems with relaxed assumption on Lyapunov functions. / Ye, H.; Gui, W.; Jiang, Zhong-Ping.

In: IET Control Theory and Applications, Vol. 5, No. 5, 17.03.2011, p. 700-712.

Research output: Contribution to journalArticle

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