In this dissertation, four nonlinear controllers are proposed for different class of multi-input multi-output (MIMO) systems with matched and mismatched perturbations. All the plants to be controlled contains input uncertainty. The technique of the adaptive sliding mode control (ASMC) scheme is first introduced in order to solve the regulation or tracking problems. By applying adaptive techniques to the design of a novel sliding surface as well as to the design of sliding mode controller, one can not only enable the fulfillment of reaching mode in fi- nite time, but also suppress the mismatched perturbations when system is in the sliding mode. Secondly, the design methodology of block backstepping is proposed to solve the regulation problem in chapter 5. Some adaptive mechanisms are employed in the virtual input controller, so that the mismatched perturbations can be tackled and the proposed robust controller can guarantee stability of the controlled systems. All these control schemes are designed by means of Lyapunov stability theorem. Each robust controller contains two parts. The first part is for eliminating measurable feedback signals of the plant, and the second part is an adaptive control mechanism, which is capable of adapting some unknown constants embedded in the least upper bounds of perturbations, so that the knowledge of the least upper bounds of matched and mismatched perturbations is not required and can achieve asymptotic stability. Several numerical examples and industrial applications are demonstrated for showing the feasibility of the proposed control schemes.

In 2 ¡Ñ2 case,we discuss the uniqueness of the u-invariant measure on projective space.Under the condition that |detM|=1 for any M in Gu and Gu is not compact,we have the followings: (1) For any x in P(R^2),if #{M¡Dx|M belongs Gu}>2, then the u-invariant measure is unique. (2) For some x in P(R^2),there exists x1,x2 such that {M¡Dx|M belongs Gu} is contained in {x1,x2},if x1 and x2 are both fixed,then the u-invariant measure v is not unique;otherwise,if u has mass only on x1 and x2,then the u-invariant measure is unique.

Voltage flicker limitation of electric utilities has been discussed in the past three decades. Arc furnace is one of the most disturbing loads that cause flicker problems in the power network. If displeasing flicker levels are predictable, then corrective solution such as static var compensation or furnace controls could be developed in cooperation between the utility and the customer. In the past, the electric fluctuations in the arc furnace voltage have been proven to be chaotic in nature. This thesis proposes a phase space approach based on nonlinearity chaotic techniques to analyze and predict voltage flicker. The determination of the phase space dimension and the application of Lyapunov exponent for flicker prediction are described. Test results have shown that accurate prediction results are obtainable for short term flicker prediction based on chaos theory.

Die Charakterisierung hochdimensionaler Systeme mit Lyapunov-Instabilität wird durch das Lyapunov-Spektrum und die zugehörigen Lyapunov-Vektoren ermöglicht. Für eine Vielzahl von derartigen Systemen (Coupled-Map-Lattices, Hartkugel-Systeme, Systeme mit ausgedehnten Potentialen ...) konnte durch die Untersuchung der Lyapunov-Vektoren die Existenz von hydrodynamischen Lyapunov-Moden nachgewiesen werden. Diese kollektiven Anregungen zeigen sich in Lyapunov-Vektoren, deren Lyapunov-Exponenten dem Betrage nach am kleinsten sind. Da Lyapunov-Exponenten charakteristische Zeitskalen innerhalb der Systeme repräsentieren, ist durch die Lyapunov-Moden eine Untersuchung des Langzeitverhaltens möglich. In dieser Arbeit werden die hydrodynamischen Lyapunov-Moden durch Molekulardynamiksimulationen von mehrkomponentigen Lennard-Jones-Flüssigkeiten untersucht. Die Charakterisierung der Lyapunov-Moden zeigt im weiteren eine Ähnlichkeit zu Dispersionsrelationen von Phononen.

Thesis (M. Ed.)--University of Hong Kong, 2001. / Includes bibliographical references (leaves 27-31).

Thèse de doctorat : SCIENCES APPLIQUEES : Metz : 1997. / 1997METZ040S. 58 REF.

This thesis presents a comparison of controller designs and a system software design for a general Guidance, Navigation and Control (GNC) system. The first part of the thesis investigates four control algorithms based on Lyapunov Direct Method in conjunction with sliding mode and adaptive control. These algorithms address three practical issues in controller design: maximum actuation limitation, external disturbances, and imperfect dynamic models. Each of the algorithms is proven to be globally asymptotically stable within its constraints. A simulation is then used to model a cube-satellite attitude maneuver using each of the controllers to evaluate its performance. The second part of this thesis discusses the development of a high-level flight software architecture capable of handling common tasks, including ground station communication and attitude maneuvers, as well as power or device failures. / text

This thesis first addresses an important topic concerning space structure control systems, namely, attitude stabilization and control, which is followed by a study on subsystem interactions of general Multi Input Multi Output (MIMO) systems for better performance and actuator fault tolerance. A novel and simple output feedback stabilization approach is proposed for a space structure system characterized with kinematics and dynamics. The approach globally, asymptotically stabilizes the plant and the closed-loop stability is proved using Lyapunov analysis. The simplicity and robustness of the designed controller are demonstrated by investigating the closed-loop response after reducing the degree of freedom in control structure. The stability of the closed-loop system is further analyzed and the performance is compared with two other robust control approaches. The study carries on to another space plant, a Large Space Telescope (LST). Its dynamic model which is fitted with reaction wheels initially developed by NASA is analyzed and the fully coupled dynamics are derived by taking into account the nonlinear coupling phenomena and other terms neglected in their original (NASA) form. The dynamics are combined with Quaternion based kinematics to form an intricate yet realistic LST attitude model. The attitude of the nonlinear LST model is stabilized using a state feedback controller and the LST model is shown to track a time varying attitude reference. Structure configuration is an imperative task in the design of MIMO control systems. In order to make use of interactions between multiple channels so that the system can deal with vulnerability due to actuator degradation, a novel interaction measure is proposed. It is defined as Relative Dependency Index (RDI) and is based on H∞ norms. Such a measurement is effective in understanding the influence of the jth input on the ith output of a system. RDI based guidelines are outlined for configuring a system towards coupling/decoupling. RDI is further extended to the Input Impact Index (i.i.i.) which helps in determining how much an actuator degradation would affect the output of a system. The validity of RDI and i.i.i. is illustrated by simulation results and tested on the linearized spacecraft attitude model presented in the former part of the thesis.

published_or_final_version / Mathematics / Master / Master of Philosophy

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