We will review some of the major results in random graphs and some of the more challenging open problems. We will cover algorithmic and structural questions. We will touch on newer models, including those related to the WWW.

Random graphs

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

This book, written by two major figures in adaptive control, provides a wealth of material for researchers, practitioners, and students. While some researchers in adaptive control may note the absence of a particular topic, the book‘s scope represents a high-gain instrument. It can be used by designers of control systems to enhance their work through the information on many new theoretical developments, and can be used by mathematical control theory specialists to adapt their research to practical needs. The book is strongly recommended to anyone interested in adaptive control.

Adaptive Control

This paper studies the tracking control problem for an uncertain ${n}$ -link robot with full-state constraints The rigid robotic manipulator is described as a multiinput and multioutput system Adaptive neural network (NN) control for the robotic system with full-state constraints is designed In the control design, the adaptive NNs are adopted to handle system uncertainties and disturbances The Moore–Penrose inverse term is employed in order to prevent the violation of the full-state constraints A barrier Lyapunov function is used to guarantee the uniform ultimate boundedness of the closed-loop system The control performance of the closed-loop system is guaranteed by appropriately choosing the design parameters Simulation studies are performed to illustrate the effectiveness of the proposed control

Adaptive Neural Network Control of an Uncertain Robot With Full-State Constraints

Chapter 8 establishes the relationship between the input and output power spectral densities of a linear system. Limitations on results are carefully detailed and the case of oscillator noise is considered. The theory is extended to multiple input-multiple output systems.

Linear System Theory

A two-hop neighborhood information-based routing protocol is proposed for real-time wireless sensor networks. The approach of mapping packet deadline to a velocity is adopted as that in SPEED; however, our routing decision is made based on the novel two-hop velocity integrated with energy balancing mechanism. Initiative drop control is embedded to enhance energy utilization efficiency, while reducing packet deadline miss ratio. Simulation and comparison show that the new protocol has led to lower packet deadline miss ratio and higher energy efficiency than two existing popular schemes. The result has also indicated a promising direction in supporting real-time quality-of-service for wireless sensor networks.

/pdf/enhancing-real-time-delivery-in-wireless-sensor-networks-4jghehuh22.pdf

Enhancing Real-Time Delivery in Wireless Sensor Networks With Two-Hop Information

In this paper, we present a novel tracking controller for a class of uncertain nonaffine systems with time-varying asymmetric output constraints. Firstly, the original nonaffine constrained (in the sense of the output signal) control system is transformed into a output-feedback control problem of an unconstrained affine system in normal form. As a result, stabilization of the transformed system is sufficient to ensure constraint satisfaction. It is subsequently shown that the output tracking is achieved without violation of the predefined asymmetric time-varying output constraints. Therefore, we are capable of quantifying the system performance bounds as functions of time on both transient and steady-state stages. Furthermore, the transformed system is linear with respect to a new input signal and the traditional backstepping scheme is avoided, which makes the synthesis extremely simplified. All the signals in the closed-loop system are proved to be semi-globally, uniformly, and ultimately bounded via Lyapunov synthesis. Finally, the simulation results are presented to illustrate the performance of the proposed controller.

Adaptive Neural Control of a Class of Output-Constrained Nonaffine Systems

In this paper, adaptive neural control is investigated for a class of unknown multiple-input multiple-output nonlinear systems with time-varying asymmetric output constraints. To ensure constraint satisfaction, we employ a system transformation technique to transform the original constrained (in the sense of the output restrictions) system into an equivalent unconstrained one, whose stability is sufficient to solve the output constraint problem. It is shown that output tracking is achieved without violation of the output constraint. More specifically, we can shape the system performance arbitrarily on transient and steady-state stages with the output evolving in predefined time-varying boundaries all the time. A single neural network, whose weights are tuned online, is used in our design to approximate the unknown functions in the system dynamics, while the singularity problem of the control coefficient matrix is avoided without assumption on the prior knowledge of control input’s bound. All the signals in the closed-loop system are proved to be semiglobally uniformly ultimately bounded via Lyapunov synthesis. Finally, the merits of the proposed controller are verified in the simulation environment.

Youxian Sun

Papers

Enhancing Real-Time Delivery in Wireless Sensor Networks With Two-Hop Information

Adaptive Neural Control of a Class of Output-Constrained Nonaffine Systems

Adaptive Neural Control of Nonlinear MIMO Systems With Time-Varying Output Constraints

Adaptive actuator fault tolerant control for uncertain nonlinear systems with multiple actuators

Adaptive neural control of high-order uncertain nonaffine systems: A transformation to affine systems approach