Lecturers
Jaime A. Moreno
Engineering Institute
Universidad Nacional Autónoma de México (UNAM), Mexico
JMorenoP@ii.unam.mx
Schedule and place
This course will take place on April 16, 18, 20, 23, 25, 27, 2012 (9:15-12:15) at UCL, Bâtiment Euler, 4 av. Georges Lemaître, 1348 Louvain-la-Neuve (room A002, ground floor).
Travel instructions are available here.
Description
Observing a dynamical system consists in estimating unmeasured (internal) variables from the information obtained from the measurements and the knowledge of the model. Observation is one of the basic problems in control, and it has been studied during the last half century. It finds application in Output Feedback Control, Fault Detection and Isolation, Supervision, Fault Tolerant Control, Adaptive Control, Software Sensors,... Understanding the basic features of observers, such as convergence velocity, noise sensitivity, and robustness against model unertainty and perturbations, is crucial for a successful application. Although for linear systems their characteristics are well understood and there are powerful design algorithms, they offer very challenging problems for nonlinear and other classes of systems.
The objective of this course, divided in 6 lectures, is to give an overview of this vast topic, ranging from the basic linear theory, passing through the ubiquitous Extended Kalman Filter and culminating with a description of several methods of observer design for nonlinear systems. The mathematical developments are complemented by examples taken from different fields. Their behavior in closed loop, under sensor noise and their robustness under model uncertainties and perturbations is also discussed.
Overview
The topics of the lectures are:
- Observers and the Observability Property of Dynamical Systems: The basic task of an observer of estimating not measured variables from the measurements and the knowledge of the model is feasible only if sufficient information is available, i.e. if the system is observable (or detectable). In this lecture these concepts are introduced and characterized for linear and nonlinear systems.
- Observers for Linear Systems: We discuss the different methods to design observers for linear time invariant and time-varying systems. In particular we consider the Luenberger and the Kalman observers. Their behaviour in closed loop, the separation principle, and their robustness and noise sensitivity will be studied.
- Linearization Methods to design observers for Nonlinear Systems: The standard method to design an observer for a nonlinear system consists in linearizing the system at an operating point or along a trajectory, and then to design an observer for the obtained linear system. In the latter case we obtain an Extended Kalman Filter that has found very wide application in process control and many other fields. We discuss these designs in this lecture and the properties of these algorithms in closed loop. We will also discuss exact linearization methods for the design of nonlinear observers. They differ from the previous approximate linearization methods since they aim at obtaining an estimation error dynamics that is exactly linear in some coordinate system. The properties of these algorithms will be also discussed.
- High-Gain Observers for nonlinear systems: For nonlinear systems that are uniformly observable, that is, they are observable for every input signal, it is possible to design high-gain observers. In this lecture we develop the theory of these observers, how they behave in closed loop, and their noise and robustness properties.
- Other observer design methods for nonlinear systems: there are several methods proposed in the literature for observer design in the case of nonlinear systems. We will present in this lecture some of them in a unified way. For this we use a general framework for observer design, based on the dissipativity theory, developed in recent years by the lecturer. This methodology extends and generalizes several design methods proposed in the literature.
- Unknown Input Observers: Unknown input observers are a special class of estimators that are able to reconstruct the state of a system, despite uncertain inputs. The basic problem and the classical existence results will be reviewed. A design approach using dissipativity will then be presented. This kind of observers have found wide application for (bio)process control, under the name of asymptotic observers, due to their capability of estimating the state variables despite of large uncertainties in the reaction rates. They are also a basic tool for Fault Detection and Isolation tasks.
