There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.

Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

I and i

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

Convex Analysisの二,三の進展について

This paper recalls a few past achievements in Model Predictive Control, gives an overview of some current developments and suggests a few avenues for future research.

Model Predictive Control

Robust stability and control for systems that combine continuous-time and discrete-time dynamics. This article is a tutorial on modeling the dynamics of hybrid systems, on the elements of stability theory for hybrid systems, and on the basics of hybrid control. The presentation and selection of material is oriented toward the analysis of asymptotic stability in hybrid systems and the design of stabilizing hybrid controllers. Our emphasis on the robustness of asymptotic stability to data perturbation, external disturbances, and measurement error distinguishes the approach taken here from other approaches to hybrid systems. While we make some connections to alternative approaches, this article does not aspire to be a survey of the hybrid system literature, which is vast and multifaceted.

Hybrid dynamical systems

The issue of cyber-security has become ever more prevalent in the analysis and design of networked systems. In this paper, we analyze networked control systems in the presence of denial-of-service (DoS) attacks, namely attacks that prevent transmissions over the network. We characterize frequency and duration of the DoS attacks under which input-to-state stability (ISS) of the closed-loop system can be preserved. To achieve ISS, a suitable scheduling of the transmission times is determined. It is shown that the considered framework is flexible enough so as to allow the designer to choose from several implementation options that can be used for trading-off performance versus communication resources. Examples are given to substantiate the analysis.

Input-to-State Stabilizing Control Under Denial-of-Service

The anti-windup problem for discrete-time linear systems is formalized in terms of the l2 norm of the deviation of the actual response of the system with saturation and anti-windup compensation from the (ideal) unconstrained response. We show that, paralleling continuous-time re- sults (27), the problem is globally solvable if and only if the plant is non exponentially unstable and it is robustly globally solvable if and only if the plant is exponentially stable. We provide a constructive solution whenever the problem is solvable. Also offered is a high-performance global solution for exponentially stable plants based on receding horizon control. Illustrative simulations are in- cluded.

http://ieeexplore.ieee.org/iel5/8775/27842/01242575.pdf

systems: definition and solutions

Discussion on: ‘A Performance Criterion for Anti-windup Compensators’ by A. Rantzer

Extreme shape controller

We propose a redesign strategy to avoid an arbitrary value of the input signal. With a hybrid architecture based on a switching logic with two modes we obtain robust global asymptotic stability and ensure that the input never takes the unwanted value, while preserving the nominal closed-loop behaviour in a neighbourhood of the origin. In the case where the minimization problem is too computationally expensive, we provide a simpler, albeit more conservative, way to determine the scaling factor. We then present a nonlinear generalization to a fairly general class of input-affine nonlinear systems. Numerical examples are used to illustrate the theoretical results.

https://ieeexplore.ieee.org/ielx7/7782633/7912304/10158333.pdf

A Hybrid Redesign for Robust Stabilization Without Unit Input

We analyze the stability properties of Lur'e systems with piecewise continuous nonlinearities by exploiting the notion of set-valued Lie derivative for Lur'e-Postnikov Lyapunov functions. We first extend an existing result of the literature to establish the global asymptotic stability of the origin under a more general sector condition. We then present the main results of this work, namely additional conditions under which output and state finite-time stability properties also hold for the considered class of systems. We highlight the relevance of these results by certifying the stability properties of two engineering systems of known interest: mechanical systems affected by friction and cellular neural networks.

pdf/finite-time-stability-properties-of-lur-e-systems-with-224c0ny8.pdf

Finite-time stability properties of Lur'e systems with piecewise continuous nonlinearities

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