Aggressive Nonlinear Regulators for Nominally Linear Systems with Uncertainties and Nonlinearities

This article is concerned with a robust control design framework with various degrees of aggressiveness for a certain class of uncertain nonlinear systems which are nominally linear, but suffer from matched disturbances and system uncertainties and both matched and unmatched nonlinearities. The LMI–based design of the linear part of the composite controller is based on the nominal linear system and is formulated as a multi–objective H-infinity minimization problem for disturbance rejection, performance (with various degrees of control aggressiveness) and minimization of the 2-norm of the state feedback gains. The design of the nonlinear part is based on Lyapunov redesign (the “unit vector” variant of Sliding Mode Control), which is a continuous nonlinear state feedback guaranteeing Uniform Ultimate Boundedness (UUB) of the closed–loop system. Explicit formulae are derived for the size of the UUB region and the Radius of the Attracting Ball (RAB), indicating a tradeoff between aggressiveness and chattering. The numerical example of a single input system demonstrates the efficacy of the proposed methodology.