Lecture 9- Analysis of Adaptive Properties of Adaptive Systems Systems 1. Introduction Theme: Adaptive systems are nonlinear. 2. Nonlinear Dynamics What can we say about their behavior? 3. Adaptation of Feedforward Gain 1. Introduction 4. Stability of dSTR 2. Nonlinear dynamics 5. Averaging 3. Time variability 6. Applicatins of Averaging 4. Stability of STR 7. Robustness 5. Summary 8. Conclusions 1 Introduction 2. Nonlinear Dynamics Investigate a given system Structure of equations · What can be done Convergence Equilibria Convergence rate Local properties Improved algorithms Global properti General principles · A simple example Understand behavior · Structural stability Can difficulties occur? Unification Structures Identifiability Excitation Achievable performance O K.J.Astrom and BWittenmarkLecture 9 – Analysis of Adaptive Systems Theme: Adaptive systems are nonlinear. What can we say about their behavior? 1. Introduction 2. Nonlinear dynamics 3. Time variability 4. Stability of STR 5. Summary Properties of Adaptive Systems 1. Introduction 2. Nonlinear Dynamics 3. Adaptation of Feedforward Gain 4. Stability of DSTR 5. Averaging 6. Applicatins of Averaging 7. Robustness 8. Conclusions 1. Introduction • Investigate a given system – Stability – Convergence – Convergence rate • Improved algorithms • General principles – Understand behavior – Can difficulties occur? – Unification – Structures – Identifiability – Excitation – Achievable performance 2. Nonlinear Dynamics • Structure of equations • What can be done? – Equilibria – Local properties – Global properties • A simple example • Structural stability c K. J. Åström and B. Wittenmark 1