Time-delays are fundamental to understand phenomena in control applications as networked systems, traffic management, control of vibrations, and supply chains. The need for a performance and reliability on these systems has to overcome challenges related to the constraints in the controlled systems. These constraints can be physical, such as input magnitude saturation on actuators, or technological, such as the limited bandwidth in a networked system or the fixed structure in a control architecture, where only a few parameters can be set. This volume provides a wide-ranging collection of methods for the analysis and design of control laws for delay systems with constraints. These methods cover fundamental analytical aspects as, for instance, the stability analysis of Positive Delay systems or the achievable performance of PID controls for delay systems. The book gives valuable material for researchers and graduate students in Automatic Control.
Author(s): Giorgio Valmorbida, Wim Michiels, Pierdomenico Pepe
Series: Advances in Delays and Dynamics, 12
Publisher: Springer
Year: 2022
Language: English
Pages: 260
City: Cham
Preface
Contents
Acronyms
*-20pt Analytical Methods for Analysis and Design
Stabilizing Systems with Uncertain Time Delay via PID Control: How Good Is It?
1 Introduction
2 Preliminaries and Problem Formulation
3 First-Order Unstable Systems
4 Second-Order Unstable Plants
4.1 Real Poles
4.2 Complex Conjugate Poles
4.3 Oscillatory Poles
5 Examples
6 Conclusion
References
Stability Analysis of Linear Delay Systems via Internally Positive Representations: An Overview
1 Introduction
2 Positive Linear Delay Systems
2.1 Delay Differential Systems
2.2 Delay Difference Systems
2.3 Coupled Delay Differential-Difference Systems
3 Internally Positive Representation of Delay Systems
3.1 Positive Representation of Vectors and Matrices
3.2 IPR of Delay Differential Systems
3.3 IPR of Delay Difference Systems
3.4 IPR of Coupled Delay Differential-Difference Systems
4 Stability Analysis
4.1 Delay Differential Systems
4.2 Delay Difference Systems
4.3 Coupled Delay Differential-Difference Systems
5 Examples
6 Conclusions and Future Work
References
Control by Set Invariance of a Class of Convolution Systems
1 Introduction
2 Background Concepts
2.1 Polytopes
2.2 Controlled Invariance and mathcalD-invariance of Polytopes
2.3 Bounds for Input-Output Convolution Systems
3 Control of Time Delay System by Set Invariance
3.1 Problem Formulation
3.2 Artstein's Reduction
3.3 mathcalD-invariance of the Time Delay System
4 Application on a Supply Chain with Two Elements
5 Conclusion
References
Sub-platooning via Agent Separation for Improved Traffic Flow Metrics in a Car-Following Model
1 Introduction
2 A Self-Regulation Mechanism via Agent Separation
3 A Car Following Model and Linear Stability
4 Case Study
4.1 Distance Threshold Condition on Car 7 and Platoon Separation
4.2 Threshold Condition on Car 6 and Sub-platooning
4.3 Threshold Condition Modification Based on Linear Analysis
4.4 Metrics
5 Conclusions
References
On the Ore Extension Ring of Differential Time-Varying Delay Operators
1 Introduction
2 Skew Polynomial Rings and Ore Extensions
3 An Ore Extension Construction
4 Algebraic Properties of the Ore Extension D
4.1 Algebraic Analysis Framework
4.2 Some Properties of the Ring of DTVD Operators
5 Algebraic Analysis Approach
6 Conclusion
References
Practical Stability Preservation Under Sampling, Actuation Disturbance and Measurement Noise, for Globally Lipschitz Time-Delay Systems
1 Introduction
2 Preliminaries
3 Main Results
4 Example
5 Conclusion
References
*-20pt Numerical Methods for Analysis and Design
15 Years or So of Pseudospectral Collocation Methods for Stability and Bifurcation of Delay Equations
1 Introduction
1.1 Pseudospectral Collocation
2 Equilibria and Characteristic Roots
2.1 Infinitesimal Generator Approach
3 Periodic Solutions and Floquet Multipliers
3.1 Solution Operator Approach
4 Continuation and Bifurcation Analysis
4.1 Nonlinear Approach
5 Extensions
5.1 Infinite Delay
5.2 Lyapunov Exponents
5.3 Uncertain Parameters
5.4 Other Classes of Equations
6 Overview and Future
References
Sensitivity Analysis for Stability of Uncertain Delay Differential Equations Using Polynomial Chaos Expansions
1 Introduction
2 Polynomial Chaos Expansions
2.1 Computation of the Chaos Coefficients
2.2 Sobol Indices and PCEs
3 Uncertain Delay Differential Equations
4 The Stochastic IG Approach
5 Numerical Results
5.1 Oscillator with Feedback Delay
5.2 Thermal Circulation System with Control
5.3 A Model for Bacteriophage Infection
6 Conclusions and Future Works
References
Lyapunov Stability of a Coupled Ordinary Differential System and a String Equation with Polytopic Uncertainties
1 Introduction
2 Problem Statement
3 Preliminaries
3.1 Legendre Polynomials and Bessel-Legendre Inequality
3.2 Convexity Lemma
4 From Stability to Robust Stability Analysis
4.1 First Result
4.2 An Equivalent Formulation
4.3 Robustness Analysis
5 Examples
6 Conclusion
References
Regional Stability of Nonlinear Sampled-Data Controlled Systems Under Actuator Saturation: A Quasi-LPV Approach
1 Introduction
2 Problem Formulation
3 Preliminaries
3.1 Local Polytopic Modeling
3.2 Saturation Handling
3.3 Looped-Functional Approach
4 Stability Assessment
5 Optimization Problems
5.1 Maximization of the Estimate of the Region of Attraction
5.2 Maximization of the Sampling Interval
6 Numerical Example
7 Conclusion
References
A Method for Computation and Analysis of Partial Synchronization Manifolds of Delay Coupled Systems
1 Introduction
2 Characterization and Computation of Partial Synchronization Manifolds
2.1 Characterization
2.2 Computation
3 Dynamics Decomposition of Partially Synchronized Network
3.1 Synchronization Error Dynamics
3.2 Dynamics on the Synchronization Manifolds
3.3 Software
4 Example
5 Conclusion
References
Analysis of Linear Partial Differential Equations Using Convex Optimization
1 Introduction
1.1 Notation
2 Problem Statement
3 Integral Inequalities on Hilbert Spaces
4 Slack Integrals
5 Main Result
5.1 Numerical Example
6 Conclusions and Future Work
References
Index
