Control of linear systems with nonlinear disturbance dynamics

Globally asymptotic tracking and disturbance rejection is a desirable performance in many applications. Linear feedback control based on internal model principle achieves asymptotic tracking performance for linear systems with linear exogenous signal dynamics. This paper investigates the case of tracking or rejecting unknown exogenous signals with known nonlinear generating dynamics particularly chaotic signals for linear systems in the continuous time domain. Two different control structures are investigated: nonlinear internal model principle control and predictive internal model control. It is shown that globally asymptotic tracking or disturbance rejection can be achieved when perfect model matching for the linear system is possible. The closed loop robust stability and performance rely on the relative size of the model matching errors to the exogenous signal's local growth rate.