Stability and Control of Dynamical Systems with Applications : A Tribute to Anthony N. Michel

It is with great pleasure that I offer my reflections on Professor Anthony N. Michel's retirement from the University of Notre Dame. I have known Tony since 1984 when he joined the University of Notre Dame's faculty as Chair of the Depart­ ment of Electrical Engineering. Tony has had a long and outstanding career. As a researcher, he has made im­ portant contributions in several areas of systems theory and control theory, espe­ cially stability analysis of large-scale dynamical systems. The numerous awards he received from the professional societies, particularly the Institute of Electrical and Electronics Engineers (IEEE), are a testament to his accomplishments in research. He received the IEEE Control Systems Society's Best Transactions Paper Award (1978), and the IEEE Circuits and Systems Society's Guillemin-Cauer Prize Paper Award (1984) and Myril B. Reed Outstanding Paper Award (1993), among others. In addition, he was a Fulbright Scholar (1992) and received the Alexander von Hum­ boldt Forschungspreis (Alexander von Humboldt Research Award for Senior U.S. Scientists) from the German government (1997). To date, he has written eight books and published over 150 archival journal papers. Tony is also an effective administrator who inspires high academic standards.

I: Issues in Stability Analysis.- 1 Wave-Digital Concepts and Relativity Theory.- 1.1 Introduction.- 1.2 Nonlinear Passive Kirchhoff Circuits and the Wave-Digital Method.- 1.3 Nonlinear Relativistic Mass.- 1.4 Direct Derivation of the Alternative Results.- 1.5 Some Applications.- 1.6 Conclusions.- 2 Time, Systems, and Control: Qualitative Properties and Methods.- 2.1 Introduction.- 2.2 Physical Variables, Time, and Continuity.- 2.3 Complete Transfer Function Matrix.- 2.4 Consistent Lyapunov Methodology for Nonlinear Systems.- 2.5 Vector Lyapunov Function Concept and Complex Systems.- 2.6 Conclusions.- 2.7 Appendix.- 3 Asymptotic Stability of Multibody Attitude Systems.- 3.1 Introduction.- 3.2 Equations of Motion.- 3.3 Conservation of Energy and Lyapunov Stability.- 3.4 Asymptotic Stability Analysis.- 3.5 Examples.- 3.6 Conclusions.- 4 Robust Regulation of Polytopic Uncertain Linear Hybrid Systems with Networked Control System Applications.- 4.1 Introduction.- 4.2 Problem Formulation.- 4.3 Robust One-Step Predecessor Set.- 4.4 Safety, Reachability, and Attainability.- 4.5 Hybrid Regulation.- 4.6 Networked Control Systems (NCS).- 4.7 Conclusions.- 5 Stability Analysis of Swarms in a Noisy Environment.- 5.1 Introduction.- 5.2 Swarm and Environment Models.- 5.3 Stability Analysis of Swarm Cohesion Properties.- 5.4 Cohesion Characteristics and Swarm Dynamics.- 5.5 Conclusions.- 6 Stability of Discrete Time-Varying Linear Delay Systems and Applications to Network Control.- 6.1 Introduction.- 6.2 The Stability Test.- 6.3 The Algorithm.- 6.4 Applications in Communication Network Control.- 6.5 Conclusions.- 6.6 Appendix: Pseudocode for the Stability Testing Algorithm.- 7 Stability and L2 Gain Analysis of Switched Symmetric Systems.- 7.1 Introduction and Problem Formulation.- 7.2 Stability Analysis.- 7.3 L2 Gain Analysis.- 7.4 Conclusions.- II: Neural Networks and Signal Processing.- 8 Approximation of Input-Output Maps using Gaussian Radial Basis Functions.- 8.1 Introduction.- 8.2 Preliminaries.- 8.3 Radial Basis Function Approximations of Input-Output Maps.- 8.4 An Example.- 8.5 Related Results and Comments.- 9 Blind Source Recovery: A State-Space Formulation.- 9.1 Introduction.- 9.2 Optimization Framework for BSR.- 9.3 Extensions to the Natural Gradient.- 9.4 Simulation Results.- 9.5 Conclusions.- 9.6 Appendix: MIMO Canonical Form.- 10 Direct Neural Dynamic Programming.- 10.1 Introduction.- 10.2 ADP Models and Algorithms.- 10.3 Direct Neural Dynamic Programming (NDP).- 10.4 A Control Problem: Helicopter Command Tracking.- 10.5 Conclusions.- 11 Online Approximation-Based Aircraft State Estimation.- 11.1 Introduction.- 11.2 Aircraft Dynamics and Model Structure.- 11.3 Approximator Definition.- 11.4 On-Line Approximation-Based Estimation.- 11.5 Prediction Error-Based Learning.- 11.6 Lyapunov Analysis: Prediction Error.- 11.7 Implementation Issues.- 11.8 Conclusions.- 11.9 Appendix: Aircraft Notation.- 12 Evolutionary Multiobjective Optimization: Qualitative Analysis and Design Implementation.- 12.1 Introduction.- 12.2 Evolutionary Multiobjective Optimization Algorithms.- 12.3 Dynamic Multiobjective Evolutionary Algorithm (DMOEA).- 12.4 Comparative Study.- 12.5 Robustness Study.- 12.6 Conclusions.- 13 Set-Membership Adaptive Filtering.- 13.1 Introduction.- 13.2 Problem Formulation.- 13.3 Optimal Bounding Ellipsoid (OBE) Algorithms.- 13.4 Set-Membership NLMS (SM-NLMS) Algorithm.- 13.5 Conclusions.- III: Power Systems and Control Systems.- 14 Trajectory Sensitivity Theory in Nonlinear Dynamical Systems: Some Power System Applications.- 14.1 Introduction.- 14.2 Trajectory Sensitivity Analysis (TSA).- 14.3 Trajectory Sensitivity Theory for DAE Model.- 14.4 Stability-Constrained Optimal Power Flow Formulation.- 14.5 Transmission Protection System Vulnerability to Angle Stability.- 14.6 Conclusions.- 15 Emergency Control and Special Protection Systems in Large Electric Power Systems.- 15.1 Introduction.- 15.2 Controlled Islanding.- 15.3 Load-Shedding Scheme.- 15.4 Simulation Result.- 15.5 Other Forms of System Protection Schemes.- 16 Power System Stability: New Opportunities for Control.- 16.1 Introduction.- 16.2 Power System Stability.- 16.3 Challenges and Opportunities.- 16.4 Conclusions.- 17 Data Fusion Modeling for Groundwater Systems using Generalized Kalman Filtering.- 17.1 Introduction.- 17.2 Background.- 17.3 Mathematical Motivation.- 17.4 Approaches.- 17.5 Application at Savannah River Site.- 17.6 Conclusions.- 18 (Control, Output) Synthesis: Algebraic Paradigms.- 18.1 Introduction.- 18.2 Notation and Preliminaries.- 18.3 Problem Statement.- 18.4 NDP: The Abstract Kernel Problem.- 18.5 The Design Morphism.- 18.6 Output Feedback Synthesis (OFS).- 18.7 Good Unity Feedback Synthesis (GUSF).- 18.8 The Zeros of T(s).- 18.9 Conclusions.- 19 The Adaptive Dynamic Programming Theorem.- 19.1 Introduction.- 19.2 Adaptive Dynamic Programming Algorithm.- 19.3 Proof of the Adaptive Dynamic Programming Theorem.- 19.4 Conclusions.- 20 Reliability of SCADA Systems in Offshore Oil and Gas Platforms.- 20.1 Introduction.- 20.2 Conventional and Deepwater Platforms.- 20.3 Fault Tree and Reliability Analysis.- 20.4 Conclusions.- 21 Power Control and Call Admission Control for DS-CDMA Cellular Networks.- 21.1 Introduction.- 21.2 Calculation of Power Control Setpoints.- 21.3 Fixed and Adaptive Call Admission Control Algorithms.- 21.4 Simulation Results.- 21.5 Conclusions.