Trends in Nonlinear and Adaptive Control: A Tribute to Laurent Praly for his 65th Birthday

Preface
Contents
1 Almost Feedback Linearization via Dynamic Extension: a Paradigm for Robust Semiglobal Stabilization of Nonlinear MIMO Systems
	1.1 Foreword
	1.2 Invertibility and Feedback Linearization
	1.3 Normal Forms of Uniformly Invertible Nonlinear Systems
		1.3.1 Normal Forms
		1.3.2 Strongly Minimum-Phase Systems
	1.4 Robust (Semiglobal) Stabilization via Almost Feedback Linearization
		1.4.1 Standing Assumptions
		1.4.2 The Nominal Linearizing Feedback
		1.4.3 Robust Feedback Design
	1.5 Application to the Problem of Output Regulation
	1.6 An Illustrative Example
	References
2 Continuous-Time Implementation of Reset Control Systems
	2.1 Introduction
	2.2 Objective and Primary Assumption
	2.3 Continuous-Time Implementation and Main Result
	2.4 Examples and Simulations
		2.4.1 Example 2.1 Revisited
		2.4.2 A Clegg Integrator Controlling a Single Integrator System
		2.4.3 A Bank of Clegg Integrators Controlling a Strictly Passive System
		2.4.4 A Bank of Stable FOREs Controlling a Detectable Passive System
	2.5 Conclusion
	References
3 On the Role of Well-Posedness in Homotopy Methods for the Stability Analysis of Nonlinear Feedback Systems
	3.1 Introduction
	3.2 Signal Spaces
		3.2.1 Examples of Signal Spaces
		3.2.2 Composite Signals
	3.3 Systems, Controllability, and Causality
		3.3.1 Controllability
		3.3.2 Input/Output Systems, Causality, and Hemicontinuity
	3.4 Stability and Gain of IO Systems
		3.4.1 Finite-Gain Stability
		3.4.2 Relationships Between Gain, Small-Signal Gain, and Norm Gain
		3.4.3 Stability Robustness in the Gap Topology
		3.4.4 Stability via Homotopy
	3.5 Stability of Interconnections
		3.5.1 Well-Posed Interconnections
		3.5.2 Regular Systems
		3.5.3 Integral Quadratic Constraints
	3.6 Summary
	3.7 Appendix
	References
4 Design of Heterogeneous Multi-agent System for Distributed Computation
	4.1 Introduction
	4.2 Strong Diffusive State Coupling
		4.2.1 Finding the Number of Agents Participating in the Network
		4.2.2 Distributed Least-Squares Solver
		4.2.3 Distributed Median Solver
		4.2.4 Distributed Optimization: Optimal Power Dispatch
	4.3 Strong Diffusive Output Coupling
		4.3.1 Synchronization of Heterogeneous Liénard Systems
		4.3.2 Distributed State Estimation
	4.4 General Description of Blended Dynamics
		4.4.1 Distributed State Observer with Rank-Deficient Coupling
	4.5 Robustness of Emergent Collective Behavior
	4.6 More than Linear Coupling
		4.6.1 Edge-Wise Funnel Coupling
		4.6.2 Node-Wise Funnel Coupling
	References
5 Contributions to the Problem of High-Gain Observer Design for Hyperbolic Systems
	5.1 Introduction
	5.2 Problem Description and Solutions
		5.2.1 Triangular Form for Observer Design
		5.2.2 The High-Gain Observer Design Problem
	5.3 Observer Design for Systems with a Single Velocity
		5.3.1 Problem Statement and Requirements
		5.3.2 Direct Solvability of the H-GODP
	5.4 Observer Design for Systems with Distinct Velocities
		5.4.1 System Requirements and Main Approach
		5.4.2 Indirect Solvability of the H-GODP
	5.5 Conclusion
	References
6 Robust Adaptive Disturbance Attenuation
	6.1 Introduction
	6.2 Problem Formulation and Objectives
		6.2.1 Preliminaries and Notation
	6.3 Known Stable Plants: SISO Systems
		6.3.1 Discrete-Time Systems
		6.3.2 Continuous-Time Systems
	6.4 Known Stable Plants: MIMO Systems
		6.4.1 Discrete-Time Systems
		6.4.2 Continuous-Time Systems
	6.5 Unknown Minimum-Phase Plants: SISO Systems
		6.5.1 Non-adaptive Case: Known Plant and Known Disturbance Frequencies
		6.5.2 Adaptive Case: Unknown Plant and Unknown Disturbance
	6.6 Numerical Simulation
		6.6.1 SISO Discrete-Time Systems with Known Plant Model
		6.6.2 SISO Continuous-Time Systems with Known Plant Model
		6.6.3 MIMO Discrete-Time Systems with Known Plant Model
		6.6.4 SISO Discrete-Time Systems with Unknown Plant Model
	6.7 Conclusion
	References
7 Delay-Adaptive Observer-Based Control for Linear Systems with Unknown Input Delays
	7.1 Introduction
		7.1.1 Adaptive Control for Time-Delay Systems and PDEs
		7.1.2 Results in This Chapter: Adaptive Control for Uncertain Linear Systems with Input Delays
	7.2 Adaptive Control for Linear Systems with Discrete Input Delays
		7.2.1 Global Stabilization under Uncertain Plant State
		7.2.2 Global Stabilization Under Uncertain Delay
		7.2.3 Local Stabilization Under Uncertain Delay and Actuator State
	7.3 Observer-Based Adaptive Control for Linear Systems with Discrete Input Delays
	7.4 Adaptive Control for Linear Systems with Distributed Input Delays
	7.5 Beyond the Results Given Here
	References
8 Adaptive Control for Systems with Time-Varying Parameters—A Survey
	8.1 Introduction
	8.2 Motivating Examples and Preliminary Result
		8.2.1 Parameter in the Feedback Path
		8.2.2 Parameter in the Input Path
		8.2.3 Preliminary Result: State-Feedback Design for Unmatched Parameters
	8.3 Output-Feedback Design
		8.3.1 System Reparameterization
		8.3.2 Inverse Dynamics
		8.3.3 Filter Design
		8.3.4 Controller Design
	8.4 Simulations
	8.5 Conclusions
	References
9 Robust Reinforcement Learning for Stochastic Linear Quadratic Control with Multiplicative Noise
	9.1 Introduction
	9.2 Problem Formulation and Preliminaries
	9.3 Robust Policy Iteration
	9.4 Multi-trajectory Optimistic Least-Squares Policy Iteration
	9.5 An Illustrative Example
	9.6 Conclusions
	References
Index