This thesis is concerned with the analysis and synthesis of positive systems under ℓ1 and L1 performance. Two classes of systems are considered: positive linear systems and positive Takagi-Sugeno (T-S) fuzzy systems. For positive linear systems, the controller, state-bounding observer and filter design problems are considered. Due to the special structures and unique features of positive systems, some previous approach used for general systems, such as similarity transformation, are no longer applicable to positive systems. First, the stabilization problem for positive linear systems is studied. In detail, analytical formulae to compute the exact values of ℓ1-induced and L1-induced norms are presented. Moreover, it is shown how the necessary and sufficient conditions can be constructed such that the closed-loop system is stable and satisfies a prescribed L1-induced performance. For single-input multiple-output (SIMO) positive systems, analytical solutions are established to show how the optimal ℓ1-induced and L1-induced controllers are designed. In addition, the L1-induced sparse state-feedback controller is investigated for continuous-time interval positive systems. Then, to estimate the state of positive systems at all times, the problem of positive state-bounding observers for interval positive systems is studied under the L1-induced performance. Necessary and sufficient conditions are presented to design a pair of state-bounding positive observers. Finally, the positive filtering problem is addressed for positive systems under the L1-induced performance. A pair of positive filters with error-bounding feature is designed to estimate the output of positive systems and the obtained results are expressed in terms of linear programming problems. For positive T-S fuzzy systems, the controller and filter design problems are investigated under the ℓ1-induced performance. First, novel performance characterization of positive fuzzy systems is established. Sufficient conditions are further established for the existence of state-feedback controller. An iterative convex optimization algorithm is developed to solve the design conditions. Furthermore, a pair of error-bounding positive filters are constructed to estimate the output of positive T-S fuzzy systems. A new performance characterization is first established to guarantee the asymptotic stability of the filtering error system with the ℓ1-induced performance. Then, sufficient conditions expressed by linear programming problems are derived to design the required filters. / published_or_final_version / Mechanical Engineering / Doctoral / Doctor of Philosophy

The Best PhD Thesis in the Faculties of Dentistry, Engineering, Medicine and Science (University of Hong Kong), Li Ka Shing Prize,2010-11 / published_or_final_version / Mechanical Engineering / Doctoral / Doctor of Philosophy

This capstone project was part of a group project completed by five school and district administrators in Hillsborough County, Florida. The project began because of our passion for teachers who are able to establish a culture of care in their classrooms that support students academically but transform their learning through experiences that enable them to be more highly engaged and productive students, regardless of ethnicity, socioeconomic status, perceived academic abilities, and backgrounds. My focus in this group project looked at school climate, culture and student behavior in high needs schools. I asked, what steps can be taken by a school leader to improve school climate and culture in turnaround schools? What happens with student behavior as school climate and culture improve? Selected literature was reviewed that concentrated on current issues with school discipline, multi-tiered approaches for support, and the role of school-based leadership in student success (mediated by the size of student enrollment). I applied what I learned to developing a collaborative working environment for teachers, implementing school uniforms, developing discipline procedures for managing student behavior, and looking for ways to encourage positive student behaviors. Key findings in my area of focus included development of a common understanding of discipline infractions and procedures, decrease in discipline referrals, increase in teacher satisfaction with discipline processes, and improved school grade.

Thesis (PhD (Physics))--University of Stellenbosch, 2006. / Carbon monoxide (CO) is a diatomic molecule of particular interest in astrophysics, due to its high abundance in interstellar space. The Fourth Positive System A1Π−X1Σ+ of CO is an important feature in the vacuum ultraviolet (VUV) region of the electromagnetic spectrum in astronomical observations, especially in high-resolution spectra recorded by satellite-based spectrographs. The interpretation of these astronomically detected spectra requires accurate laboratory wavelengths to serve as rest wavelengths and to resolve possible Doppler-shifts. Such rest wavelengths are known for the 12C16O, 13C16O and 12C18O isotopomers for all astronomically observed spectral lines of the Fourth Positive System. The only laboratory wavelengths currently available for the Fourth Positive System of the 12C17O isotopomer have been determined in a previous work carried out in our laboratory for the vibronic band A1Π(v0 = 3)−X1Σ+(v00 = 0). The present study continues this work for the other vibronic bands which have been detected astronomically, namely A1Π(v0 = 2 − 5)−X1Σ+(v00 = 0). The A1Π(v0 = 0− 1)−X1Σ+(v00 = 0) vibronic bands have also been investigated due to their probability for future astronomical detection. Rotationally-resolved spectra of these six vibronic bands were obtained by selective rovibronic laser excitation, and subsequent detection of the undispersed fluorescence, observed as a function of the excitation wavelength in the VUV. A tunable narrow-bandwidth VUV laser source is used for excitation, and the CO gas sample is introduced by supersonic expansion. Flow-cooling in the supersonic expansion to rotational temperatures roughly corresponding to temperatures in the interstellar medium simplifies and aids the spectral analysis of the spectral lines of interest. The cold conditions in the supersonic expansion facilitates a high sensitivity for detection of the low-J lines, and allows the detection of rare isotopomers of CO in natural abundance. The experimental setup has been improved in the present study by the addition of a vacuum monochromator, facilitating an improved characterisation of the VUV source. Furthermore, a number of experimental conditions have been optimised for the detection of rare CO isotopomers, significantly increasing the signals of these lines in the spectra. The combination of this increase in sensitivity and the addition of the vacuum monochromator to the experimental setup, allowed the simultaneous detection of absorption spectra with the fluorescence spectra as an additional source of information in spectral analysis. The increased sensitivity also contributed to the detection of a large number of spectral lines of interest, with some additional lines identified in the previously studied vibronic band. Spectral lines of 12C16O, 13C16O, 12C18O and 12C17O were detected in each vibronic band, allowing accurate calibration of the spectra. A total of 29 new lines of 12C17O were recorded in the six vibronic bands investigated. Additionally, 10 new singlet-triplet lines of 12C16O were recorded in the wavelength regions investigated. The new wavelengths of 12C17O have been applied to calculate consistent heliocentric velocities of a gas cloud toward the star X Persei, obtained from spectra of the different CO isotopomers taken by the Hubble space telescope.

<p>The contributions of this thesis are in the area of control of systems with nonlinear dynamics. The thesis is divided into three parts. The two first parts are similar in the sense that they both consider output feedback of rather general classes of nonlinear systems, and both approaches are based on mathematical programming (although in quite different ways). The third part contains a state feedback approach for a specific system class, and is more application oriented.</p><p>The first part treats control of systems described by nonlinear difference equations, possibly with uncertain terms. The system dynamics are represented by piecewise affine difference inclusions, and for this system class, piecewise affine controller structures are suggested. Controller synthesis inequalities for such controller structures are given in the form of Bilinear Matrix Inequalities (BMIs). A solver for the BMIs is developed. The main contribution is to the output feedback case, where an observer-based controller structure is proposed. The theory is exemplified through two examples.</p><p>In the second part the output feedback problem is examined in the setting of Nonlinear Model Predictive Control (NMPC). The state space formulation of NMPC is inherently a state feedback approach, since the state is needed as initial condition for the prediction in the controller. Consequently, for output feedback it is natural to use observers to obtain estimates of the state. A high gain observer is applied for this purpose. It is shown that for several existing NMPC schemes, the state feedback stability properties ``semiglobally'' hold in the output feedback case. The theory is illuminated with a simple example.</p><p>Finally, a state feedback controller for a class of positive systems is proposed. Convergence of the state to a certain subset of the first orthant, corresponding to a constant ``total mass'' (interpreting states as masses) is obtained. Conditions are given under which convergence to this set implies asymptotic stability of an equilibrium. Simple examples illustrate some properties of the controller. Furthermore, the control strategy is applied to the stabilization of a gas-lifted oil well, and simulations on a rigorous multi-phase dynamic simulator of such a well demonstrate the controller performance.</p>

The contributions of this thesis are in the area of control of systems with nonlinear dynamics. The thesis is divided into three parts. The two first parts are similar in the sense that they both consider output feedback of rather general classes of nonlinear systems, and both approaches are based on mathematical programming (although in quite different ways). The third part contains a state feedback approach for a specific system class, and is more application oriented. The first part treats control of systems described by nonlinear difference equations, possibly with uncertain terms. The system dynamics are represented by piecewise affine difference inclusions, and for this system class, piecewise affine controller structures are suggested. Controller synthesis inequalities for such controller structures are given in the form of Bilinear Matrix Inequalities (BMIs). A solver for the BMIs is developed. The main contribution is to the output feedback case, where an observer-based controller structure is proposed. The theory is exemplified through two examples. In the second part the output feedback problem is examined in the setting of Nonlinear Model Predictive Control (NMPC). The state space formulation of NMPC is inherently a state feedback approach, since the state is needed as initial condition for the prediction in the controller. Consequently, for output feedback it is natural to use observers to obtain estimates of the state. A high gain observer is applied for this purpose. It is shown that for several existing NMPC schemes, the state feedback stability properties ``semiglobally'' hold in the output feedback case. The theory is illuminated with a simple example. Finally, a state feedback controller for a class of positive systems is proposed. Convergence of the state to a certain subset of the first orthant, corresponding to a constant ``total mass'' (interpreting states as masses) is obtained. Conditions are given under which convergence to this set implies asymptotic stability of an equilibrium. Simple examples illustrate some properties of the controller. Furthermore, the control strategy is applied to the stabilization of a gas-lifted oil well, and simulations on a rigorous multi-phase dynamic simulator of such a well demonstrate the controller performance.

Dissertation (PhD)--University of Stellenbosch, 2006. / Bibliography. Also available via the Internet.

Thesis (Ph.D.)--Baylor University, 2009. / Includes bibliographical references (p. 77-79).

Positive systems, which carry the well known property of confining the state, output, and/or input variables to the nonnegative orphant, are of great practical importance, as the nonnegative property occurs quite frequently in numerous applications and in nature. These type of systems frequently occur in hydrology where they are used to model natural and artificial networks of reservoirs; in biology where they are used to describe the transportation, accumulation, and drainage processes of elements and compounds like hormones, glucose, insulin, and metals; and in stocking, industrial, and engineering systems where chemical reactions, heat exchanges, and distillation processes take place. The interest of this dissertation is in two key problems: positive stabilization and the positive servomechanism problem. In particular, this thesis outlines the necessary and sufficient conditions for the stabilization of positive linear time-invariant (LTI) systems using state feedback control, along with providing an algorithm for constructing such a stabilizing regulator. Moreover, the results on stabilization also encompass the two problems of the positive separation principle and stabilization via observer design. The second, and most emphasized, problem of this dissertation considers the positive servomechanism problem for both single-input single-output (SISO) and multi-input multi-output (MIMO) stable positive LTI systems. The study of the positive servomechanism problem focuses on the tracking problem of nonnegative constant reference signals for unknown/known stable SISO/MIMO positive LTI systems with nonnegative unmeasurable/measurable constant disturbances via switching tuning clamping regulators (TcR), linear quadratic clamping regulators (LTQcR), and ending with MPC control. Finally, all theoretical results on the positive servomechanism problem are justified via numerous experimental results on a waterworks system.

Positive systems, which carry the well known property of confining the state, output, and/or input variables to the nonnegative orphant, are of great practical importance, as the nonnegative property occurs quite frequently in numerous applications and in nature. These type of systems frequently occur in hydrology where they are used to model natural and artificial networks of reservoirs; in biology where they are used to describe the transportation, accumulation, and drainage processes of elements and compounds like hormones, glucose, insulin, and metals; and in stocking, industrial, and engineering systems where chemical reactions, heat exchanges, and distillation processes take place. The interest of this dissertation is in two key problems: positive stabilization and the positive servomechanism problem. In particular, this thesis outlines the necessary and sufficient conditions for the stabilization of positive linear time-invariant (LTI) systems using state feedback control, along with providing an algorithm for constructing such a stabilizing regulator. Moreover, the results on stabilization also encompass the two problems of the positive separation principle and stabilization via observer design. The second, and most emphasized, problem of this dissertation considers the positive servomechanism problem for both single-input single-output (SISO) and multi-input multi-output (MIMO) stable positive LTI systems. The study of the positive servomechanism problem focuses on the tracking problem of nonnegative constant reference signals for unknown/known stable SISO/MIMO positive LTI systems with nonnegative unmeasurable/measurable constant disturbances via switching tuning clamping regulators (TcR), linear quadratic clamping regulators (LTQcR), and ending with MPC control. Finally, all theoretical results on the positive servomechanism problem are justified via numerous experimental results on a waterworks system.