An investigation of techniques for nonlinear state observation
Date
2016
Authors
McBride, Dean Christian Tait
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Abstract
An investigation and analysis of a collection of different techniques, for estimating the states of
nonlinear systems, was undertaken. It was found that most of the existing literature on the topic
could be organized into several groups of nonlinear observer design techniques, of which each
group follows a specific concept and slight variations thereof.
From out of this investigation it was discovered that a variation of the adaptive observer could be
successfully applied to numerous nonlinear systems, given only limited output information. This
particular technique formed the foundation on which a design procedure was developed in order to
asymptotically estimate the states of nonlinear systems of a certain form, using only partial state
information available. Lyapunov stability theory was used to prove the validity of this technique,
given that certain conditions and assumptions are satisfied. A heuristic procedure was then
developed to get a linearized model of the error transient behaviour that could form the upper
bounds of the transient times of the observer.
The technique above, characterized by a design algorithm, was then applied to three well-known
nonlinear systems; namely the Lorenz attractor, the Rössler attractor, and the Van Der Pol
oscillator. The results, illustrated through numerical simulation, clearly indicate that the technique
developed is successful, provided all assumptions and conditions are satisfied.
Description
A dissertation submitted to the Faculty of Engineering and the Built Environment,
University of the Witwatersrand, in fulfilment of the requirements for the degree of
Master of Science in Engineering.
Johannesburg, 2016
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Citation
McBride, Dean Christiaan Tait (2016) An investigation of techniques for nonlinear state observation, University of the Witwatersrand, Johannesburg, <http://hdl.handle.net/10539/22656>