Magnetic resonance (MR) brain section images are segmented and then synthetically colored to give visual representations of the original data with three approaches: the literal and approximate fuzzy c-means unsupervised clustering algorithms, and a supervised computational neural network. Initial clinical results are presented on normal volunteers and selected patients with brain tumors surrounded by edema. Supervised and unsupervised segmentation techniques provide broadly similar results. Unsupervised fuzzy algorithms were visually observed to show better segmentation when compared with raw image data for volunteer studies. For a more complex segmentation problem with tumor/edema or cerebrospinal fluid boundary, where the tissues have similar MR relaxation behavior, inconsistency in rating among experts was observed, with fuzz-c-means approaches being slightly preferred over feedforward cascade correlation results. Various facets of both approaches, such as supervised versus unsupervised learning, time complexity, and utility for the diagnostic process, are compared. >

A comparison of neural network and fuzzy clustering techniques in segmenting magnetic resonance images of the brain

Brief Guaranteed state estimation by zonotopes

A new method of approximating the transfer function of a high-order linear system by one of lower order is proposed. Called the "Routh approximation method" because it is based on an expansion that uses the Routh table of the original transfer function, the method has a number of useful properties: if the original transfer function is stable, then all approximants are stable; the sequence of approximants converge monotonically to the original in terms of "impulse response" energy; the approximants are partial Pade approximants in the sense that the first k coefficients of the power series expansions of the k th-order approximant and of the original are equal; the poles and zeros of the approximants move toward the poles and zeros of the original as the order of the approximation is increased. A numerical example is given for the calculation of the Routh approximants of a fourth-order transfer function and for illustration of some of the properties.

Routh approximations for reducing order of linear, time-invariant systems

https://www3.ntu.edu.sg/home/ecywen/IEEE/2010_12.pdf

Brief paper: Adaptive actuator failure compensation control of uncertain nonlinear systems with guaranteed transient performance

Lecture notes in control and information sciences

New techniques for the model simplification problem are presented. If the given system is expressed by a high-order transfer function, the technique is to expand the function into a continued fraction and then ignore some quotients. If the system is in the state equations form, the method is realized by partitioning the matrix and discarding some parts. The new approach not only offers a simple procedure and a good approximation but also gives a unified viewpoint of the general analysis of linear systems.

A novel approach to linear model simplification

A computational method is presented for finding the linear quadratic regulator such that the optimal closed-loop system has eigenvalues lying within a vertical strip in the complex plane. The proposed method is suitable for the two-stage optimal design of two-time scale systems.

Linear quadratic regulators with eigenvalue placement in a vertical strip

Fuzzy Kalman filtering

A recursive algorithm is developed for the piecewise-constant solution of dynamic equations via block-pulse functions φj(t),where j=1,2,...,m. For 1≤j≤m (where j and m are integers) and final timeT, each block-pulse function φj(t) is defined by φj(t)=1 for (j−1)T/m≤t<j T/m and φj(t)=1otherwise. Compared with Walsh function approaches, the proposed method is simpler to compute, is more suitable for computer programming, and provides the same accuracy. Also, a discrete-time solution is derived for a zero-input state equation.

Solution of state-space equations via block-pulse functions

This note summarizes some existing stability and instability conditions of the second-order matrix polynomial which arises in the formulation of classical mechanics, aerodynamics, and robotic systems. Also, some sufficient conditions for stability or instability of the second-order matrix polynomial are newly developed via the relevant linear matrix equation obtained from the Lyapunov theory.

Leang S. Shieh

Papers

A novel approach to linear model simplification

Linear quadratic regulators with eigenvalue placement in a vertical strip

Fuzzy Kalman filtering

Solution of state-space equations via block-pulse functions

Stability of the second-order matrix polynomial