This thesis introduces, develops and applies methods for analysing nonlinear systems with the multiple challenges of time-varying, non-polynomial, uncertain or large-scale proper- ties. Both computational and analytic methods using Lyapunov functions are developed and the methods are applied to a range of examples. Generalised Absolute stability is introduced, which is a method of treating polynomial systems with non polynomial, uncertain or time-varying feedback. Analysis is completed with Sum of Squares programming, and this method extends both the applicability of sum of squares as well as existing absolute stability theory. Perturbation methods for invariant Sum of Squares and Semidefinite programs are introduced, which significantly improves scalability of computations and al- lows sum of squares programming to be used for large scale systems. Finally, invariance principles are introduced for nonlinear, time-varying systems. The concept of trajectories leaving sets uniformly in time is introduced, which allows a non-autonomous version of Barbashin-Krasovskii theorem.

This dissertation introduces the Explicit Reference Governor: a simple and systematic add-on control unit that provides constraint handling capabilities to any pre-stabilized nonlinear system by suitably manipulating its applied reference. The main innovation of the proposed framework is that constraint satisfaction is ensured without having to solve implicit equations. As a result, the Explicit Reference Governor is particularly well suited for applications with limited computational capabilities. The basic idea behind the scheme consists in manipulating the derivative of the applied reference so that, at any given time instant, the currently applied reference will not cause a violation of constraints anytime in the future. The theory behind the proposed framework is presented in general terms and is then detailed to provide specific design strategies. Possible extensions to ensure robustness are also proposed. In addition to introducing the general theory of the Explicit Reference Governor, the dissertation illustrates its step-by-step implementation on Unmanned Aerial Vehicles. / Doctorat en Sciences de l'ingénieur et technologie / info:eu-repo/semantics/nonPublished

No description available.

The non-local stabilization of nonlinear systems by output feedback is a challenging problem that remains the subject of continuing investigation in control theory. In this thesis we develop two globally asymptotically stabilizing output feedback algorithms for multivariable nonlinear systems. Our first result is an extension a well-known output feedback method to a class of nonlinear systems whose dynamics can be written as a collection of subsystems that are dynamically coupled through output-dependent nonlinear terms. We show that this method must be modified to accommodate the dynamic coupling by introducing additional nonlinear damping terms into each control input. Our second contribution involves the application of observer backstepping to systems in a restricted block-triangular observer form. In this form, the nonlinearities entering each subsystem are allowed to depend on the output associated with the subsystem, and all upper subsystem states, including unmeasured ones. The proposed algorithm is demonstrated on a magnetically levitated ball. / Controls

Thesis (M. S.)--Mechanical Engineering, Georgia Institute of Technology, 2009. / Committee Chair: Sadegh, Nader; Committee Member: Chen, Xu-Yan; Committee Member: Chen, Ye-Hwa. Part of the SMARTech Electronic Thesis and Dissertation Collection.

Thesis (Ph. D.)--Ohio State University, 2007. / Title from first page of PDF file. Includes bibliographical references (p. 145-153).

Thesis (Ph. D.)--University of Missouri-Columbia, 1997. / Typescript. Vita. Includes bibliographical references (leaves [256]-267). Also available on the Internet.

Thesis (Ph. D.)--University of Missouri-Columbia, 1997. / Typescript. Vita. Includes bibliographical references (leaves [256]-267). Also available on the Internet.