Mathematical Problems in Engineering
Volume 5 (2000), Issue 6, Pages 499-542

Nonlinear robust hierarchical control for nonlinear uncertain systems

Alexander Leonessa, Wassim M. Haddad, and Vijaysekhar Chellaboina

School of Aerospace Engineering, Georgia Institute of Technology, Atlanta 30332-0150, GA, USA

Received 24 September 1999; Revised 11 October 1999

Copyright © 2000 Alexander Leonessa et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


A nonlinear robust control-system design framework predicated on a hierarchical switching controller architecture parameterized over a set of moving nominal system equilibria is developed. Specifically, using equilibria-dependent Lyapunov functions, a hierarchical nonlinear robust control strategy is developed that robustly stabilizes a given nonlinear system over a prescribed range of system uncertainty by robustly stabilizing a collection of nonlinear controlled uncertain subsystems. The robust switching nonlinear controller architecture is designed based on a generalized (lower semicontinuous) Lyapunov function obtained by minimizing a potential function over a given switching set induced by the parameterized nominal system equilibria. The proposed framework robustly stabilizes a compact positively invariant set of a given nonlinear uncertain dynamical system with structured parametric uncertainty. Finally, the efficacy of the proposed approach is demonstrated on a jet engine propulsion control problem with uncertain pressure-flow map data.