Although cardinality constraints naturally arise in many applications, e.g., in portfolio selection problems of choosing small number of assets from a large pool of stocks or dynamic portfolio selection problems with limited trading dates within a given time horizon and in subset selection of the regression analysis, the state-of-the-art in cardinality constrained optimization has been stagnant up to this stage, largely due to the inherent combinatorial nature of such hard problems. We focus in this research on developing efficient and implementable solution algorithms for cardinality constrained optimization by investigating prominent structures and hidden properties of such problems. More specifically, we develop solution algorithms for four specific cardinality constrained optimization problems, including (i) the cardinality constrained linear-quadratic control problem, (ii) the optimal control problem of linear switched system with limited number of switching, (iii) the time cardinality constrained dynamic mean- variance portfolio selection problem, and (iv) cardinality constrained quadratic optimization problem. Taking advantages of a linear-quadratic structure of cardinality constrained optimization problems, we strive for analytical solutions when possible. More specifically, we derive an analytical solution for problem (iii) and obtain for both problems (i) and (ii) semi-analytical expressions of the solution governed by a family of Ricatti-like equations, which still suffer an exponentially growing complexity. To achieve high-performance of the solution algorithm, we devise algorithms of a branch and bound (BnB) type with various tight and computationally-cheap lower bounds achieved by identifying suitable SDP formulations and by exploiting geometric properties of the problem. We demonstrate efficiency of our proposed solution schemes evidenced from numerical experiments and present a firm step-forward in tackling this long-standing challenge of cardinality constrained optimization. / Gao, Jianjun. / Adviser: Duan Li. / Source: Dissertation Abstracts International, Volume: 72-11, Section: B, page: . / Thesis (Ph.D.)--Chinese University of Hong Kong, 2009. / Includes bibliographical references (leaves 134-142). / Electronic reproduction. Hong Kong : Chinese University of Hong Kong, [2012] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Electronic reproduction. [Ann Arbor, MI] : ProQuest Information and Learning, [201-] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Abstract also in Chinese.

Hu San-qing. / "December 2001." / Thesis (Ph.D.)--Chinese University of Hong Kong, 2001. / Includes bibliographical references (p. 181-192). / Electronic reproduction. Hong Kong : Chinese University of Hong Kong, [2012] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Mode of access: World Wide Web. / Abstracts in English and Chinese.

A digital adaptive slope control (DASC) technique is presented to improve the dynamic response and efficiency of a current programmed mode (CPM) buck converter employing a low-cost auxiliary phase. Compared to the existing nonlinear control techniques, the advantages of the proposed control scheme include superior voltage droop and settling time, and on-line calibration to compensate for tolerance in the inductance. The proposed technique is experimentally verified on a 500 kHz, 10 V to 2.5 V CPM buck converter prototype. Charge balancing and optimal transient response are achieved for a range of positive and negative load steps. In addition, compared to a representative single phase converter, the proposed system not only has better dynamic response but also achieves 2 % heavy-load and 10 % light-load steady-state efficiency improvement. The impact of the auxiliary phase operation on the converter’s dynamic efficiency is also evaluated at different load step amplitudes and frequencies.

A digital adaptive slope control (DASC) technique is presented to improve the dynamic response and efficiency of a current programmed mode (CPM) buck converter employing a low-cost auxiliary phase. Compared to the existing nonlinear control techniques, the advantages of the proposed control scheme include superior voltage droop and settling time, and on-line calibration to compensate for tolerance in the inductance. The proposed technique is experimentally verified on a 500 kHz, 10 V to 2.5 V CPM buck converter prototype. Charge balancing and optimal transient response are achieved for a range of positive and negative load steps. In addition, compared to a representative single phase converter, the proposed system not only has better dynamic response but also achieves 2 % heavy-load and 10 % light-load steady-state efficiency improvement. The impact of the auxiliary phase operation on the converter’s dynamic efficiency is also evaluated at different load step amplitudes and frequencies.

The first loudspeaker was invented almost 150 years ago and even though much has changed regarding the manufacturing, the main idea is still the same. To produce clean sound, modern loudspeaker consist of expensive materials that often need advanced manufacturing equipment. The relatively newly established company Actiwave AB uses digital signal processing to enhance the audio for loudspeakers with poor acoustic properties. Their algorithms concentrate on attenuating the linear distortion but there is no compensation for the loudspeakers' non-linear distortion, such as harmonic distortion. To attenuate the harmonic distortion, this thesis presents controllers based on exact input-output linearisation. This type of controller needs an accurate model of the system. A loudspeaker model has been derived based on the LR-2 model, an extension of the more common Thiele-Small model. A controller based on exact input-output linearisation also needs full state feedback, but since feedback risk being expensive, state estimators were used. The state estimators were based on feed-forward or observers using the extended Kalman filter or the unscented Kalman filter. A combination of feed-forward state estimation and a PID controller were designed as well. In simulations, the total harmonic distortion was attenuated for all controllers up to 180 Hz. The simulations also showed that the controllers are sensitive to inaccurate parameter values in the loudspeaker model. During real-life experiments, the controllers needed to be extended with a model of the used amplifier to function properly. The controllers that were able to attenuate the harmonic distortion were the two methods using feed-forward state estimation. Both controllers showed improvement compared to the uncontrolled case for frequencies up to 40 Hz.

Includes bibliographical references (p. 121-124).

As the speed and power demands on Buck converters continue to increase, it has become time to replace the linearly-controlled conventional Buck converter. Digital circuits, such as microprocessors, are requiring higher dynamic currents, at lower voltages, than ever before. Traditionally, such Buck converters have been controlled by linear voltage-mode or current-mode control methods. While these controllers offer such advantages as fixed switching frequencies and zero steady-state error, their reaction speed is inherently limited by their bandwidth which is a fraction of the converter switching frequency. Therefore, to improve the transient response of a Buck converter in a practical manner, four novel ideas are presented in this thesis. The first contribution is an analog “charge balance controller”. The control method utilizes the concept of capacitor charge balance to achieve a near-optimal transient response for Buck converters undergoing a rapid load change. Unlike previous work, the proposed controller does not require expensive and/or slow analog multipliers/dividers. In addition, the nominal inductance value is not required by the proposed controller. Simulation and experimental results demonstrate a significant improvement in transient performance over that of a linear voltage-mode controller. For low duty cycle applications, the unloading transient performance of a Buck converter tends to be poor when compared to the corresponding loading transient performance. Therefore, the second contribution is an auxiliary circuit and an analog auxiliary controller which drastically improves the performance of a Buck converter undergoing an unloading transient. Significant overshoot reduction was observed over that of a linearly-controlled conventional Buck converter. The third contribution is a digital implementation of the aforementioned “charge balance control” concept. Through digital implementation the control law is extended to include load-line regulation. Unlike previous work, large lookup tables are not required to perform complex mathematical functions, thus the number of required gates is significantly reduced. The final contribution is a digital implementation of the “charge balance controller” capable of operating with the previously-mentioned auxiliary circuit. This complete solution is capable of improving the voltage deviation caused by loading and unloading transients. In addition, the combined auxiliary circuit and control law is extended to load-line regulation applications. / Thesis (Ph.D, Electrical & Computer Engineering) -- Queen's University, 2010-01-31 23:01:24.606

Thesis (Ph. D.)--Ohio University, November, 1995. / Title from PDF t.p.

Thesis (M.S.)--Oregon State University, 2009. / Printout. Includes bibliographical references (leaves 39-40). Also available on the World Wide Web.

Thesis (Ph.D.)--University of Wollongong, 2008. / Typescript. Includes bibliographical references: p. 227-238.