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

Feedback systems: Input-output properties

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L2 Gain And Passivity Techniques In Nonlinear Control

In this paper, restorations for both voltage and frequency in the droop-controlled inverter-based islanded microgrid (MG) are addressed. A distributed finite-time control approach is used in the voltage restoration which enables the voltages at all the distributed generations (DGs) to converge to the reference value in finite time, and thus, the voltage and frequency control design can be separated. Then, a consensus-based distributed frequency control is proposed for frequency restoration, subject to certain control input constraints. Our control strategies are implemented on the local DGs, and thus, no central controller is required in contrast to existing control schemes proposed so far. By allowing these controllers to communicate with their neighboring controllers, the proposed control strategy can restore both voltage and frequency to their respective reference values while having accurate real power sharing, under a sufficient local stability condition established. An islanded MG test system consisting of four DGs is built in MATLAB to illustrate our design approach, and the results validate our proposed control strategy.

Distributed Secondary Voltage and Frequency Restoration Control of Droop-Controlled Inverter-Based Microgrids

https://www3.nd.edu/~vgupta2/research/publications/kmxgaaut14.pdf

On relationships among passivity, positive realness, and dissipativity in linear systems

Control of cyberphysical systems using passivity and dissipativity based methods

We consider state estimation for multiple plants across a shared communication network. Each linear time-invariant plant transmits information through the common network according to either a time-triggered or an event-triggered rule. For an event-triggered algorithm with carrier sense multiple access (CSMA), each plant is assumed to access the network based on a priority mechanism. For a time-triggered algorithm combined with time division multiple access (TDMA), each plant uses the network according to a schedule that is decided a priori . Performance in terms of the communication frequency and the estimation error covariance is analytically characterized for event-triggered schemes. Using these characterizations, we show that event-triggered schemes may perform worse than time-triggered schemes when the effect of the communication network is explicitly considered.

Networked State Estimation Over a Shared Communication Medium

In this paper, we introduce a passivity-based design framework for event-triggered networked control systems. We consider the effects of network-induced time delays, signal quantization, and data loss in communication links between the plant and controller and show $L_2$ -stability and robustness for the control design. We introduce simple asynchronous triggering conditions that do not rely on the exact knowledge of the systems’ dynamics and are located on both sides of the communication network. This leads to a great decrease in the communication rate between systems. Additionally, we show lower bounds on interevent time intervals for the triggering conditions and characterize the design's robustness against external disturbances. We illustrate the relationship among stability, robustness, and passivity levels of the plant and controller. Moreover, we analyze our design's robustness against packet dropouts. Finally, we calculate the passivity levels for the entire event-triggered networked control system. This is beneficial in design of compositional networked control systems. Our results are design-oriented. By following our proposed framework, the designer can characterize clear tradeoffs among passivity levels, design parameters, time delays, effects of signal quantization and triggering conditions, stability, robustness, and performance, and make design decisions accordingly.

Passivity-Based Design for Event-Triggered Networked Control Systems

In this paper, we consider the following problem: what passivity properties can be inferred for a system by studying only an approximate mathematical model for it. Our results show that an excess of passivity (whether in the form of input strictly passive, output strictly passive or very strictly passive) in the approximate model guarantees a certain passivity index for the system, provided that the norm of the error between the approximate and the true models is sufficiently small in a suitably defined sense. Further, we consider (Q, S, R)-dissipative systems and show that (Q, S, R)-dissipativity has a similar robustness property, even though the supply rates for the system and its approximation may be different. These results may be particularly useful if either the approximate model is much easier to analyze, or if the precise system model is unknown. We illustrate the results by considering particular approximation methods, e.g., model reduction, discretization, quantization, and linearization around an equilibrium point.

Meng Xia

Papers

On relationships among passivity, positive realness, and dissipativity in linear systems

Control of cyberphysical systems using passivity and dissipativity based methods

Networked State Estimation Over a Shared Communication Medium

Passivity-Based Design for Event-Triggered Networked Control Systems

Passivity and Dissipativity Analysis of a System and its Approximation