Abstract
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 language | English (US) |
|---|---|
| Pages (from-to) | 59-79 |
| Number of pages | 21 |
| Journal | Systems and Control Letters |
| Volume | 45 |
| Issue number | 1 |
| DOIs | |
| State | Published - Jan 15 2002 |
Funding
This present work was motivated by discussions Randy A. Freeman had with Kenan Ezal, Zigang Pan, and Petar Kokotović concerning their results in [3] , and we are grateful to them for sharing their contributions with us. This work was supported in part by the National Science Foundation under grant ECS-9703294.
Keywords
- 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