Nonlinear robust hierarchical control for nonlinear uncertain systems. (English) Zbl 0958.93084

Leonessa, Alexander; Haddad, Wassim M.; Chellaboina, Vijaysekhar

Math. Probl. Eng. 5, No. 6, 499-542 (2000).

The paper studies a nonlinear robust control system with a set of moving nominal system equilibria, i.e., the equilibrium points which exist under admissible constant controls. The authors generalize the Barbashin-Krasovskij-LaSalle results on a Lyapunov function to the case where it is noncontinuous and lower semicontinuous. A theorem for global asymptotic robust stability of a compact positively invariant set is given. A hierarchical robust switching control strategy is constructed to stabilize a given nonlinear system. The goal of the strategy is a stabilization of subsystems generated by the parameterized equilibria. The hierarchical robust strategy is applied to a jet engine propulsion control problem with uncertain compressor pressure-flow maps.

Reviewer: Georgy Osipenko (St.Peterburg)

MSC:

93D21	Adaptive or robust stabilization
93C10	Nonlinear systems in control theory
93A13	Hierarchical systems
93B12	Variable structure systems

Keywords:

Lyapunov function; nonliner robust control; domain of attraction; hierarchical switching control; moving equilibria; stability of invariant set; stabilization; jet engine propulsion