다중혈관 관상동맥 환자에서 y-문합을 이용하여 양쪽 내흉동맥만을 사용한 우회술의 조기 성적

/pdf/convex-analysisnoer-san-nojin-zhan-nituite-5dl2rbmoyr.pdf

Convex Analysisの二,三の進展について

Introduction to linear and nonlinear programming

Initial-value ordinary differential equation solution via variable order Adams method (SIVA/DIVA) package is collection of subroutines for solution of nonstiff ordinary differential equations. There are versions for single-precision and double-precision arithmetic. Requires fewer evaluations of derivatives than other variable-order Adams predictor/ corrector methods. Option for direct integration of second-order equations makes integration of trajectory problems significantly more efficient. Written in FORTRAN 77.

Solving Ordinary Differential Equations

Most of the signal processing that we will study in this course involves local operations on a signal, namely transforming the signal by applying linear combinations of values in the neighborhood of each sample point. You are familiar with such operations from Calculus, namely, taking derivatives and you are also familiar with this from optics namely blurring a signal. We will be looking at sampled signals only. Let's start with a few basic examples. Local difference Suppose we have a 1D image and we take the local difference of intensities, DI(x) = 1 2 (I(x + 1) − I(x − 1)) which give a discrete approximation to a partial derivative. (We compute this for each x in the image.) What is the effect of such a transformation? One key idea is that such a derivative would be useful for marking positions where the intensity changes. Such a change is called an edge. It is important to detect edges in images because they often mark locations at which object properties change. These can include changes in illumination along a surface due to a shadow boundary, or a material (pigment) change, or a change in depth as when one object ends and another begins. The computational problem of finding intensity edges in images is called edge detection. We could look for positions at which DI(x) has a large negative or positive value. Large positive values indicate an edge that goes from low to high intensity, and large negative values indicate an edge that goes from high to low intensity. Example Suppose the image consists of a single (slightly sloped) edge:

http://ieeexplore.ieee.org/iel5/5/31307/01456462.pdf

Linear systems

Transition probability bounds for the stochastic stability robustness of continuous- and discrete-time Markovian jump linear systems

A new control method, the switching time computation (STC) method (Kaya, C Y and J L Noakes, Proc 33rd IEEE Conf on Decision and Control, Orlando, FL, 1994, pp 3823-3824), is described in detail for single-input non-linear systems, and the mathematical reasoning behind it is explained A concatenation of constant-input arcs is used to get from an initial point to the target, and an optimization procedure is employed to find the necessary time lengths of the arcs General difficulties of the STC method in finding the necessary arc time lengths are emphasized and exemplified The STC method is incorporated in a time-optimal bang-bang control (TOBC) algorithm The results of the application of the TOBC algorithm to the van der Pol equation, a third-order non-linear system and a non-linear dynamical model of the F-8 aircraft are presented The STC method is shown to be fast by making comparisons with a general optimal control software package

Computations and time-optimal controls

A numerical method is proposed for constructing an approximation of the Pareto front of nonconvex multi-objective optimal control problems. First, a suitable scalarization technique is employed for the multi-objective optimal control problem. Then by using a grid of scalarization parameter values, i.e., a grid of weights, a sequence of single-objective optimal control problems are solved to obtain points which are spread over the Pareto front. The technique is illustrated on problems involving tumor anti-angiogenesis and a fed-batch bioreactor, which exhibit bang---bang, singular and boundary types of optimal control. We illustrate that the Bolza form, the traditional scalarization in optimal control, fails to represent all the compromise, i.e., Pareto optimal, solutions.

A numerical method for nonconvex multi-objective optimal control problems

We study convergence properties of a modified subgradient algorithm, applied to the dual problem defined by the sharp augmented Lagrangian. The primal problem we consider is nonconvex and nondifferentiable, with equality constraints. We obtain primal and dual convergence results, as well as a condition for existence of a dual solution. Using a practical selection of the step-size parameters, we demonstrate the algorithm and its advantages on test problems, including an integer programming and an optimal control problem.

On a Modified Subgradient Algorithm for Dual Problems via Sharp Augmented Lagrangian

This paper considers the problems of stability and filtering for a class of linear hybrid systems with nonlinear uncertainties and Markovian jump parameters. The hybrid system under study involves a continuous-valued system state vector and a discretevalued system mode. The unknown nonlinearities in the system are time varying and norm bounded. The Markovian jump parameters are modeled by a Markov process with a finite number of states. First, we show the equivalence of the sets of norm-bounded linear and nonlinear uncertainties. Then, instead of the original hybrid linear system with nonlinear uncertainties, we consider the same system with linear uncertainties. By using a Riccati equation approach for this new system, a robust filter is designed using two sets of coupled Riccati-like equations such that the estimation error is guaranteed to have an upper bound.

C. Yalçın Kaya

Papers

Transition probability bounds for the stochastic stability robustness of continuous- and discrete-time Markovian jump linear systems

Computations and time-optimal controls

A numerical method for nonconvex multi-objective optimal control problems

On a Modified Subgradient Algorithm for Dual Problems via Sharp Augmented Lagrangian

Robust Kalman Filter Design for Markovian Jump Linear Systems with Norm-Bounded Unknown Nonlinearities