Linear Control Theory with an ℋ∞ Optimality Criterion

This expository paper sets out the principal results in ℋ∞ control theory in the context of continuous-time linear systems. The focus is on the mathematical theory rather than computational methods

Direct and Inverse Computational Methods for Electromagnetic Scattering in Biological Diagnostics

Scattering theory has had a major roll in twentieth century mathematical physics. Mathematical modeling and algorithms of direct,- and inverse electromagnetic scattering formulation due to biological tissues are investigated. The algorithms are used for a model based illustration technique within the microwave range. A number of methods is given to solve the inverse electromagnetic scattering problem in which the nonlinear and ill-posed nature of the problem are acknowledged.Comment: 61 pages, 5 figure

協方差型隨機子空間識別法之應用

In this research the application of output-only system identification technique known as Stochastic Subspace Identification (SSI) algorithms in civil structures is carried out. With the aim of finding accurate modal parameters of the structure in off-line analysis, a stabilization diagram is constructed by plotting the identified poles of the system with increasing the size of data matrix. A sensitivity study of the implementation of SSI through stabilization diagram is firstly carried out, different scenarios such as noise effect, nonlinearity, time-varying systems and closely-spaced frequencies are considered. Comparison between different SSI approaches was also discussed. In the following, the identification task of a real large scale structure: Canton Tower, a benchmark problem for structural health monitoring of high-rise slender structures is carried out, for which the capacity of Covariance-driven SSI algorithm (SSI-COV) will be demonstrated. The introduction of a subspace preprocessing algorithm known as Singular Spectrum Analysis (SSA) can greatly enhance the identification capacity, which in conjunction with SSI-COV is called the SSA-SSI-COV method, it also allows the determination of the best system order. The objective of the second part of this research is to develop on-line system parameter estimation and damage detection technique through Recursive Covariance-driven Stochastic Subspace identification (RSSI-COV) approach. The Extended Instrumental Variable version of Projection Approximation Subspace Tracking algorithm (EIV-PAST) is taking charge of the system-related subspace updating task. To further reduce the noise corruption in field experiments, the data pre-processing technique called recursive Singular Spectrum Analysis technique (rSSA) is developed to remove the noise contaminant measurements, so as to enhance the stability of data analysis. Through simulation study as well as the experimental research, both RSSI-COV and rSSA-SSI-COV method are applied to identify the dynamic behavior of systems with time-varying characteristics, the reliable control parameters for the model are examined. Finally, these algorithms are applied to track the evolution of modal parameters for: (1) shaking table test of a 3-story steel frame with instantaneous stiffness reduction. (2) Shaking table test of a 1-story 2-bay reinforced concrete frame, both under earthquake excitation, and at last, (3) damage detection and early warning of an experimental steel bridge under continuous scour.UCR::Vicerrectoría de Docencia::Ingeniería::Facultad de Ingeniería::Escuela de Ingeniería Civi

Computation of H∞ controllers for infinite dimensional plants using numerical linear algebra

The mixed sensitivity minimization problem is revisited for a class of single-input-single-output unstable infinite dimensional plants with low order weights. It is shown that H∞ controllers can be computed from the singularity conditions of a parameterized matrix whose dimension is the same as the order of the sensitivity weight. The result is applied to the design of H∞ controllers with integral action. Connections with the so-called Hamiltonian approach are also established. © 2012 John Wiley & Sons, Ltd