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

Convex Analysisの二,三の進展について

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

Numerical Initial Value Problems in Ordinary Differential Equations

Model Predictive Control (MPC), the dominant advanced control approach in industry over the past twenty-five years, is presented comprehensively in this unique book. With a simple, unified approach, and with attention to real-time implementation, it covers predictive control theory including the stability, feasibility, and robustness of MPC controllers. The theory of explicit MPC, where the nonlinear optimal feedback controller can be calculated efficiently, is presented in the context of linear systems with linear constraints, switched linear systems, and, more generally, linear hybrid systems. Drawing upon years of practical experience and using numerous examples and illustrative applications, the authors discuss the techniques required to design predictive control laws, including algorithms for polyhedral manipulations, mathematical and multiparametric programming and how to validate the theoretical properties and to implement predictive control policies. The most important algorithms feature in an accompanying free online MATLAB toolbox, which allows easy access to sample solutions. Predictive Control for Linear and Hybrid Systems is an ideal reference for graduate, postgraduate and advanced control practitioners interested in theory and/or implementation aspects of predictive control.

Predictive Control for Linear and Hybrid Systems

“Multivalued Analysis” is the theory of set-valued maps (called multifonctions) and has important applications in many different areas. Multivalued analysis is a remarkable mixture of many different parts of mathematics such as point-set topology, measure theory and nonlinear functional analysis. It is also closely related to “Nonsmooth Analysis” (Chapter 5) and in fact one of the main motivations behind the development of the theory, was in order to provide necessary analytical tools for the study of problems in nonsmooth analysis. It is not a coincidence that the development of the two fields coincide chronologically and follow parallel paths. Today multivalued analysis is a mature mathematical field with its own methods, techniques and applications that range from social and economic sciences to biological sciences and engineering. There is no doubt that a modern treatise on “Nonlinear Functional Analysis” can not afford the luxury of ignoring multivalued analysis. The omission of the theory of multifunctions will drastically limit the possible applications.

SET-Valued Analysis

On linear passive complementarity systems

Lately, with the increasing use of automated manual transmissions (AMT) the engagement control of the dry clutch becomes more important. The engagement control plays a crucial role, since different and conflicting objectives have to be satisfied: preservation of driver comfort, fast engagement and small friction losses. In this paper two optimal control strategies for clutch engagement, based on hybrid control principles, are compared. For developing a useful clutch control scheme, the driveline is modelled as a piecewise linear system. The first control strategy is widely known as explicit MPC. However, it seems that it is not suitable (yet) for this type of problem. The second strategy is a piecewise LQ controller, based on piecewise quadratic Lyapunov functions. Simulation results obtained with both strategies are presented and discussed.

/pdf/hybrid-optimal-control-of-dry-clutch-engagement-2e1wax9j9b.pdf

Hybrid optimal control of dry clutch engagement

Piecewise-linear (PL) modeling is often used to approximate the behavior of nonlinear circuits. One of the possible PL modeling methodologies is based on the linear complementarity problem, and this approach has already been used extensively in the circuits and systems community for static networks. In this paper, the object of study is dynamic electrical circuits that can be recast as linear complementarity systems, i.e. as interconnections of linear time-invariant differential equations and complementarity conditions (ideal diode characteristics). A mathematically precise framework is developed that formalizes the mixed discrete and continuous behavior of these switched networks. Within this framework, the fundamental question of well-posedness (existence and uniqueness of solution trajectories given an initial condition) is studied and additional properties of the behavior are derived. For instance, a full characterization is presented of the inconsistent states.

/pdf/on-the-dynamic-analysis-of-piecewise-linear-networks-450d2uifk3.pdf

On the dynamic analysis of piecewise-linear networks

The problem of checking certain controllability properties of even very simple piecewise linear systems is known to be undecidable. This paper focuses on conewise linear systems, i.e., systems for which the state space is partitioned into conical regions and a linear dynamics is active on each of these regions. For this class of systems, we present algebraic necessary and sufficient conditions for controllability. We also show that the classical results of controllability of linear systems and input-constrained linear systems can be recovered from our main result. Our treatment employs tools both from geometric control theory and mathematical programming.

/pdf/algebraic-necessary-and-sufficient-conditions-for-the-4wyvuy0g0r.pdf

Algebraic Necessary and Sufficient Conditions for the Controllability of Conewise Linear Systems

The switching behavior of power converters with ldquoidealrdquo electronic devices (EDs) makes it difficult to define a switched model that describes the dynamics of the converter in all possible operating conditions, i.e., a ldquocompleterdquo model. Indeed, simplifying assumptions on the sequences of modes are usually adopted, also in order to obtain averaged models and discrete-time maps. In this paper, we show how the complementarity framework can be used to represent complete switched models of a wide class of power converters, with EDs having characteristics represented by piecewise-affine (even complicated) relations. The model equations can be written in an easy and compact way without the enumeration of all converter modes, eventually formalizing the procedure to an algorithm. The complementarity model can be used to perform transient simulations and time-domain analysis. Mathematical tools coming from nonlinear programming allow to simulate numerically the transient behavior of even complex power converters. Also rigorous time-domain analysis is possible without excluding pathological situations like, for instance, inconsistent initial conditions and simultaneous switchings. Basic converter topologies are used as examples to show the construction procedure for the complementarity models and their usefulness for simulating the dynamic evolution also for nontrivial operating conditions.

/pdf/a-new-perspective-for-modeling-power-electronics-converters-uue15jyuin.pdf

M.K. Camlibel

Papers

On linear passive complementarity systems

Hybrid optimal control of dry clutch engagement

On the dynamic analysis of piecewise-linear networks

Algebraic Necessary and Sufficient Conditions for the Controllability of Conewise Linear Systems

A New Perspective for Modeling Power Electronics Converters: Complementarity Framework