Global uniform output regulation of nonlinear systems

Abstract

The output regulation problem is a control problem that encompasses tracking, disturbance rejection, synchronization and observer design problems. The goal in output regulation is for a given system to achieve asymptotic tracking of a reference signal. In this thesis the output regulation problem is considered for nonlinear systems. We give sufficient conditions for solvability of both the local and global output regulation problem. This requires considering the solvability of the so called regulator equations and proving the existence of a stabilizing controller such that the system is made uniformly convergent.

We first focus on presenting and discussing sufficient conditions for uniform convergence of systems with inputs. We discuss the Demidovich condition and extend it using contractivity to form a more general result guaranteeing exponential convergence. We consider two stabilizing controllers, one for quadratically stabilizable systems corresponding to the Demidovich condition and one for systems stabilizable using contractivity. Then we solve the regulator equations for a standard harmonic oscillator, a harmonic oscillator with nonlinear damping and some other simple systems. Also we present a known algorithm for solving the regulator equations for control affine systems and apply it to the Hopfield neural network model. Finally we apply the discussed control design methods to the harmonic oscillators and the Hopfield model to solve the uniform output regulation problem.