Uniting local and global controllers for uncertain nonlinear systems: Beyond global inverse optimality

Hiroshi Ito*, Randy A. Freeman

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

6 Scopus citations


This paper provides a solution to a new problem of global robust control for uncertain nonlinear systems. A new recursive design of stabilizing feedback control is proposed in which inverse optimality is achieved globally through the selection of generalized state-dependent scaling. The inverse optimal control law can always be designed such that its linearization is identical to linear optimal control, i.e. H optimal control, for the linearized system with respect to a prescribed quadratic cost functional. Like other backstepping methods, this design is always successful for systems in strict-feedback form. The significance of the result stems from the fact that our controllers achieve desired level of 'global' robustness which is prescribed a priori. By uniting locally optimal robust control and global robust control with global inverse optimality, one can obtain global control laws with reasonable robustness without solving Hamilton-Jacobi equations directly.

Original languageEnglish (US)
Pages (from-to)59-79
Number of pages21
JournalSystems and Control Letters
Issue number1
StatePublished - Jan 15 2002


  • Generalized state-dependent scaling
  • Global robust stability
  • Inverse optimal control
  • Nonlinear control
  • Robust control Lyapunov function
  • Uncertain systems

ASJC Scopus subject areas

  • Control and Systems Engineering
  • General Computer Science
  • Mechanical Engineering
  • Electrical and Electronic Engineering


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