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 paper studies a number of quantized feedback design problems for linear systems. We consider the case where quantizers are static (memoryless). The common aim of these design problems is to stabilize the given system or to achieve certain performance with the coarsest quantization density. Our main discovery is that the classical sector bound approach is nonconservative for studying these design problems. Consequently, we are able to convert many quantized feedback design problems to well-known robust control problems with sector bound uncertainties. In particular, we derive the coarsest quantization densities for stabilization for multiple-input-multiple-output systems in both state feedback and output feedback cases; and we also derive conditions for quantized feedback control for quadratic cost and H/sub /spl infin// performances.

The sector bound approach to quantized feedback control | NOVA. The University of Newcastle's Digital Repository

http://www.ece.ualberta.ca/~tchen/papers/Gao_auto08n1.pdf

A new delay system approach to network-based control

Event-triggered consensus of multiagent systems (MASs) has attracted tremendous attention from both theoretical and practical perspectives due to the fact that it enables all agents eventually to reach an agreement upon a common quantity of interest while significantly alleviating utilization of communication and computation resources. This paper aims to provide an overview of recent advances in event-triggered consensus of MASs. First, a basic framework of multiagent event-triggered operational mechanisms is established. Second, representative results and methodologies reported in the literature are reviewed and some in-depth analysis is made on several event-triggered schemes, including event-based sampling schemes, model-based event-triggered schemes, sampled-data-based event-triggered schemes, and self-triggered sampling schemes. Third, two examples are outlined to show applicability of event-triggered consensus in power sharing of microgrids and formation control of multirobot systems, respectively. Finally, some challenging issues on event-triggered consensus are proposed for future research.

/pdf/an-overview-of-recent-advances-in-event-triggered-consensus-3rmvpx3qkr.pdf

An Overview of Recent Advances in Event-Triggered Consensus of Multiagent Systems

A novel method is proposed in this note for stability analysis of systems with a time-varying delay. Appropriate Lyapunov functional and augmented Lyapunov functional are introduced to establish some improved delay-dependent stability criteria. Less conservative results are obtained by considering the additional useful terms (which are ignored in previous methods) when estimating the upper bound of the derivative of Lyapunov functionals and introducing the new free-weighting matrices. The resulting criteria are extended to the stability analysis for uncertain systems with time-varying structured uncertainties and polytopic-type uncertainties. Numerical examples are given to demonstrate the effectiveness and the benefits of the proposed method

Further Improvement of Free-Weighting Matrices Technique for Systems With Time-Varying Delay

This paper is concerned with global asymptotic stability for a class of generalized neural networks (NNs) with interval time-varying delays, which include two classes of fun- damental NNs, i.e., static neural networks (SNNs) and local field neural networks (LFNNs), as their special cases. Some novel delay-independent and delay-dependent stability criteria are derived. These stability criteria are applicable not only to SNNs but also to LFNNs. It is theoretically proven that these stability criteria are more effective than some existing ones either for SNNs or for LFNNs, which is confirmed by some numerical examples.

Global Asymptotic Stability for a Class of Generalized Neural Networks with Interval

The network-based modeling and active control for an offshore steel jacket platform with an active tuned mass damper mechanism is investigated in this chapter. A network-based state feedback control scheme is developed. Under this scheme, the corresponding closed-loop system is modeled by a system with an artificial interval time-varying delay. Then, a delay-dependent stability criterion for the corresponding closed-loop system is derived. Based on this stability criterion, a sufficient condition on the existence of the network-based controller is obtained. It is found through simulation results that (i) both the oscillation amplitudes of the offshore platform and the required control force under the network-based state feedback controller are smaller than those under the nonlinear controller [65] and the dynamic output feedback controller [100]; (ii) the oscillation amplitudes of the offshore steel jacket platform under the network-based feedback controller are almost the same as the ones under the integral sliding mode controller [99], while the required control force by the former is smaller than the one by the latter.

Network-Based Modeling and Active Control

In this chapter, sliding mode H∞ control for an offshore steel jacket platform subject to nonlinear self-excited wave force and external disturbance is developed. A sliding mode H∞ controller is designed to reduce oscillation amplitudes of the offshore platform. In the case that the dynamic model of the offshore platform is subject to parameter perturbations, a robust sliding mode H∞ control scheme is proposed. It is found through simulation results that compared with an H∞ controller and a sliding mode controller, the sliding mode H∞ controller requires much less control force; and the oscillation amplitudes of the offshore platform under the sliding mode H∞ controller are less than those under the sliding mode controller.

Integral Sliding Mode H ∞ Control

Protocol-based performance analysis of artificial neural networks and their applications

This paper is concerned with active packet dropouts-based anti-disturbance performance optimization for a continuous-time networked control system (NCS) under consideration of time-varying network-induced delays. By proposing the active packet dropouts method, a new model for an NCS is established. Based on the established model, stabilizing controller design criteria are derived to optimize the anti-disturbance performance of the considered NCS. When transferring nonlinear matrix inequalities into linear matrix inequalities, a parameter searching algorithm and new bounding inequalities are proposed to introduce less conservatism. The mutually exclusive distribution characteristic of the interval time-varying delays is made full use to deal with integral inequalities for products of vectors. A numerical example is given to illustrate the effectiveness of the proposed active packet dropouts-based anti-disturbance performance optimization.

Xian-Ming Zhang

Papers

Global Asymptotic Stability for a Class of Generalized Neural Networks with Interval

Network-Based Modeling and Active Control

Integral Sliding Mode H ∞ Control

Protocol-based performance analysis of artificial neural networks and their applications

Active packet dropouts-based networked control system performance optimization