Short Course on Output Regulation
CeSOS - NTNU Trondheim, Norway

Prof. Andrea Serrani
Department of Electrical and Computer Engineering
The Ohio State University
Columbus, OHUSA


Goal: To provide a general, up-to-date coverage of fundamental issues and recent research developments in output regulation of nonlinear systems.

Synopsis: The problem of controlling the output of a system so as to achieve asymptotic tracking of prescribed trajectories and/or asymptotic rejection of disturbances is one of the most fundamental problems in control theory. In its typical formulation, the class of signals to be tracked and of disturbances to be rejected is restricted to be the trajectories generated by a given autonomous stable LTI system, referred to as the exosystem. These include constant and sinusoidal signals of known frequency, but unknown amplitude and phase. A peculiar feature of the servomechanism problem, which makes it a difficult problem to solve, is the requirement that the controller has access to the regulation error only, without direct measurements either of the state of the plant, or the exogenous signals. In linear system theory, a powerful approach to the solution of this problem is the design of a controller incorporating an internal model of all exogenous inputs.
The extension of this approach to nonlinear systems has been thoroughly investigated in the past ten years. The purpose of this short course is to review the major achievements in this area and to present the directions on which the research is presently progressing. In particular, the course provide a self-contained treatment of the theory of nonlinear output regulation, ranging from its geometric foundations to the latest results on robust regulation in the large, and regulation in presence of uncertainties on the exogenous systems. Latest techniques and tools from nonlinear stabilization, adaptive control, passivity theory are employed throughout the presentation. Application of nonlinear regulation theory to robust autonomous guidance of aerospace systems are presented and discussed in detail.

Slides (pdf)

  1. The linear output regulation problem. The internal model principle.
  2. Nonlinear regulation: geometric conditions. Structurally stable regulation.
  3. Robust nonlinear regulation in the large: the case of systems in feedback form. Adaptive regulation.
  4. Applications: autonomous guidance of helicopters.