This dissertation considers the problem of approximate dissipative potentials construction and their use in smooth feedback stabilization of nonlinear control systems. For mechanical systems, dissipative potentials, usually a generalized Hamiltonian function, can be derived from physical intuition. When a dissipative Hamiltonian is not available, one can rely on dissipative Hamiltonian realization techniques, as proposed recently by Cheng and coworkers. Extensive results are available in the literature for (robust) stabilization based on the obtained potential. For systems of interest in chemical engineering, especially systems with mass action kinetics, energy is often ill-defined. Moreover, realization techniques are difficult to apply, due to the nonlinearities associated with the reaction terms. Approximate dissipative realization techniques have been considered by many researchers for analysis and feedback design of controllers in the context of chemical processes. The objective of this thesis is to study the construction of local dissipative potentials and their application to solve stabilization problems. The present work employs the geometric stabilization approach proposed by Jurdjevic and Quinn, refined by Faubourg and Pomet, and by Malisoff and Mazenc, for the design of stabilizing feedback laws. This thesis seeks to extend and apply the Jurdjevic--Quinn stabilization method to nonlinear stabilization problems, assuming no a priori knowledge of a Lyapunov function. A homotopy-based local decomposition method is first employed to study the dissipative Hamiltonian realization problem, leading to the construction of locally defined dissipative potentials. If the obtained potential satisfies locally the weak Jurdjevic--Quinn conditions, it is then shown how to construct feedback controllers using that potential, and under what conditions a Lyapunov function can be constructed locally for time-independent control affine systems. The proposed technique is then used for the construction of state feedback regulators and for the stabilization of periodic orbits based on a construction proposed by Bacciotti and Mazzi. In the last chapter of the thesis, stabilization of time-dependent control affine systems is considered, and the main result is used for the stabilization of periodic solutions using asymptotic feedback tracking. Low-dimensional examples are used throughout the thesis to illustrate the proposed techniques and results. / Thesis (Ph.D, Chemical Engineering) -- Queen's University, 2010-06-17 10:13:42.201

A theory is presented which describes the global reflection and transmission characteristics of a self-focused channel propagating at an oblique angle of incidence to an interface separating two or more self-focusing nonlinear dielectric media. A complete characterization of the different behavior of the channel is given in the proper parameter space. In the dominant region, the nonlinear wavepacket representing the self-focused channel is represented as an equivalent particle moving in an equivalent potential. The dynamics of the particle is described by Newton's equations of motion, with the asymptotic propagation paths of the channel being read off from the associated phase planes of the equivalent potential. This theory provides therefore, the nonlinear Snell's Laws of refleciton or transmission since the particle dynamics gives the critical angle of total reflection and in the case of transmission, the corresponding angle of transmission. This theory also gives the stability characteristics of nonlinear surface waves, which had only been partially established in the past through numerical simulations. Finally, some applications of the theory are presented such as the design of an all-optical power adjustable spatial scanning element and an all optical switch. Extensions of the theory to waveguides with multiple interfaces are also given and possible new directions are also suggested.

Thesis (Ph.D.)--Hong Kong University of Science and Technology, 2005. / Includes bibliographical references. Also available in electronic version.

Digitized by Kansas Correctional Industries

The signal integrity, power integrity, and timing analysis of todays high-speed digital systems are computationally exhaustive, both in terms of CPU memory required and simulation time consumed. One way to reduce this complexity is to use macromodels of the subcircuits comprising these high-speed digital systems. Since digital driver/receiver circuits have a major share in this computational load, modeling digital driver/receiver circuits accurately to capture their nonlinearity becomes a big challenge. The contribution of this thesis is to generate black-box macromodels of driver/receiver circuits that result in huge computational speed-up compared to actual transistor-level driver/receiver circuits and at the same time maintain high accuracy. It is always useful to have a black-box modeling approach as the modeling technique is independent of the knowledge of the internal logic of the circuit being modeled. This would make the modeling approach more robust and more applicable to a wide variety of circuits. Driver/receiver macromodels have been extended to multiple ports to take into account the effect of non-ideal power and ground nodes in this thesis.

Thesis (Ph. D.)--Lehigh University, 2000. / Includes vita. Includes bibliographical references (leaf 82).

Periodic steady-state analysis plays an important role in both theoretical topics and numerical simulations. It has been applied to numerous fields such as electronics, economics, biology, chemistry and so on. Particularly in electronics it is the basis of microwave and radio frequency (RF) circuit simulation. Although the topic has been studied for decades, periodic steady-state analysis still remains a difficulty in certain aspects including the analysis of the exact analytical formulas of limit cycles, as well as fast and accurate approximation of periodic steady states with unknown frequencies. In this thesis, two innovative methods are proposed in order to overcome two difficulties in the field of periodic steady-state analysis accordingly: on the one hand, a limit cycle identification method is developed to provide a robust method for computation of the exact analytical formulas of limit cycles. The method can be further extended to a wide range of nonlinear systems by the technique called state immersion. On the other hand, a method for highly accurate periodic steady-state approximation based on harmonic balancing is proposed. It combines the robustness of Macaulay matrix approach for small size polynomial root(s) finding, and the efficiency of a guided global optimization for higher order approximations. Thus, it is capable of computing approximations of periodic steady states with a high accuracy. Together, the two methods establish a reliable framework where highly accurate periodic steady-state analysis for a wide range of nonlinear systems can be performed. / published_or_final_version / Electrical and Electronic Engineering / Master / Master of Philosophy

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