The design of variable-structure control (VSC) systems for a class of multivariable, nonlinear, time-varying systems is presented. Using the Utkin-Drazenovic method of equivalent control and generalized Lyapunov stability concepts, the VSC design is described in a unified manner. Complications that arise due to multiple inputs are examined, and several approaches useful in overcoming them are developed. Recent developments are investigated, as is the kinship of VSC and the deterministic approach to the control of uncertain systems. All points are illustrated by numerical examples. The recent literature on VSC applications is surveyed. >

Variable structure control of nonlinear multivariable systems: a tutorial

In this paper, we develop an online sequential learning algorithm for single hidden layer feedforward networks (SLFNs) with additive or radial basis function (RBF) hidden nodes in a unified framework. The algorithm is referred to as online sequential extreme learning machine (OS-ELM) and can learn data one-by-one or chunk-by-chunk (a block of data) with fixed or varying chunk size. The activation functions for additive nodes in OS-ELM can be any bounded nonconstant piecewise continuous functions and the activation functions for RBF nodes can be any integrable piecewise continuous functions. In OS-ELM, the parameters of hidden nodes (the input weights and biases of additive nodes or the centers and impact factors of RBF nodes) are randomly selected and the output weights are analytically determined based on the sequentially arriving data. The algorithm uses the ideas of ELM of Huang developed for batch learning which has been shown to be extremely fast with generalization performance better than other batch training methods. Apart from selecting the number of hidden nodes, no other control parameters have to be manually chosen. Detailed performance comparison of OS-ELM is done with other popular sequential learning algorithms on benchmark problems drawn from the regression, classification and time series prediction areas. The results show that the OS-ELM is faster than the other sequential algorithms and produces better generalization performance

A Fast and Accurate Online Sequential Learning Algorithm for Feedforward Networks

Computational intelligence techniques have been used in wide applications. Out of numerous computational intelligence techniques, neural networks and support vector machines (SVMs) have been playing the dominant roles. However, it is known that both neural networks and SVMs face some challenging issues such as: (1) slow learning speed, (2) trivial human intervene, and/or (3) poor computational scalability. Extreme learning machine (ELM) as emergent technology which overcomes some challenges faced by other techniques has recently attracted the attention from more and more researchers. ELM works for generalized single-hidden layer feedforward networks (SLFNs). The essence of ELM is that the hidden layer of SLFNs need not be tuned. Compared with those traditional computational intelligence techniques, ELM provides better generalization performance at a much faster learning speed and with least human intervene. This paper gives a survey on ELM and its variants, especially on (1) batch learning mode of ELM, (2) fully complex ELM, (3) online sequential ELM, (4) incremental ELM, and (5) ensemble of ELM.

Extreme learning machines: a survey

Sliding mode observers for fault detection and isolation

Nonlinear Programming: A Unified Approach

A modern, up-to-date introduction to optimization theory and methods This authoritative book serves as an introductory text to optimization at the senior undergraduate and beginning graduate levels. With consistently accessible and elementary treatment of all topics, An Introduction to Optimization, Second Edition helps students build a solid working knowledge of the field, including unconstrained optimization, linear programming, and constrained optimization. Supplemented with more than one hundred tables and illustrations, an extensive bibliography, and numerous worked examples to illustrate both theory and algorithms, this book also provides: * A review of the required mathematical background material * A mathematical discussion at a level accessible to MBA and business students * A treatment of both linear and nonlinear programming * An introduction to recent developments, including neural networks, genetic algorithms, and interior-point methods * A chapter on the use of descent algorithms for the training of feedforward neural networks * Exercise problems after every chapter, many new to this edition * MATLAB(r) exercises and examples * Accompanying Instructor's Solutions Manual available on request An Introduction to Optimization, Second Edition helps students prepare for the advanced topics and technological developments that lie ahead. It is also a useful book for researchers and professionals in mathematics, electrical engineering, economics, statistics, and business.

An introduction to optimization

This paper contains a comparative study of four techniques for observing the slates of non-linear systems. The first technique examined is inspired by Bestle and Zeitz, and ICrener and Respondek, In this method a non-linear transformation is found that brings the system into a canonical form, from where observer design is facilitated. The second technique is attributable to Thau. In this method, the error between the system's true state and the output of the observer is shown to be asymptotically convergent to zero provided that an additional assumption is valid. The third technique is due to Baumann and Rugh. In this method, extended or pseudolinearization of the error differential equation about a family of equilibrium points results in an observer design such that the eigenvalues of the linearized error equation are locally invariant. Finally, techniques from variable-structure systems are utilized to design an observer that yields an exponentially decaying error like Thau's observer, but, unl...

Comparative study of non-linear state-observation techniques

Design procedures are proposed for two different classes of observers for systems withunknown inputs In thefirst approach, the state of the observed system is decomposed into known and unknown components The unknown component is a projection, not necessarily orthogonal, of the whole state along the subspace in which the available state component resides Then, a dynamical system to estimate the unknown component is constructed Combining the output of the dynamical system, which estimates the unknown state component, with the available state information results in an observer that estimates the whole state It is shown that some previously proposed observer architectures can be obtained using the projection operator approach presented in this paper The second approach combines sliding modes and the second method of Lyapunov resulting in a nonlinear observer The nonlinear component of the sliding mode observer forces the observation error into the sliding mode along a manifold in the observation error space Design algorithms are given for both types of observers

/pdf/observer-design-for-systems-with-unknown-inputs-2xlwagy5ts.pdf

Observer design for systems with unknown inputs

An Introduction to Optimization: Chong/An Introduction

https://engineering.purdue.edu/~zak/Automatica_UIO.pdf

Stanislaw H. Żak

Papers

An introduction to optimization

Comparative study of non-linear state-observation techniques

Observer design for systems with unknown inputs

An Introduction to Optimization: Chong/An Introduction

Brief paper: Sliding-mode observers for systems with unknown inputs: A high-gain approach