Nonlinear Control

Introduction to Nonlinear Control

Stability, Control Design, and Estimation

Christopher M. Kellett

Philipp Braun

Princeton University Press

Link to Publisher

An introductory text on the analysis, control, and estimation of nonlinear systems, appropriate for advanced undergraduate and graduate students

Praise

“This one-of-a-kind textbook succeeds in the seemingly impossible task of making nonlinear control systems analysis and design accessible to undergraduate students, and does that with authority and wit. An essential companion for instructors as well as researchers in the field of nonlinear control.”

—Andrea Serrani, The Ohio State University

“Class-tested, calibrated for the 2020s, and as comprehensive as appropriate for an introductory full-year course. Accessible and a launchpad into virtually all the most ubiquitous nonlinear control and estimation techniques.”

—Miroslav Krstic, coauthor of PDE Control of String-Actuated Motion

Content of the Book

Part I: Dynamical Systems

  • Nonlinear Systems – Fundamentals
    • State Space Models
    • Control Loops, Controller Design & Examples
  • Nonlinear Systems – Stability Notions
    • Stability Notions
    • Comparison Principle
    • Stability by Lyapunov’s Second Method
    • Region of Attraction
    • Converse Theorems
    • Invariance Theorems
  • Linear Systems and Linearization
    • Linear Systems Review
    • Linearization
    • Time-Varying Systems
    • Numerical Calculations of Lyapunov Functions
    • Systems with Inputs
  • Frequency Domain Analysis
    • Fundamental Results in the Frequency Domain
    • Stability Analysis in the Frequency Domain
  • Discrete Time Systems
    • Discrete Time Systems – Fundamentals
    • Sampling: From Continuous to Discrete Time
    • Stability Notions
    • Controllability and Observability
  • Absolute Stability
    • A Commonly Ignored Design Issue
    • Historical Perspective on the Lur’e Problem
    • Sufficient Conditions for Absolute Stability
  • Input-to-State Stability
    • Motivation & Definition
    • Lyapunov Characterizations
    • Integral-to-Integral Estimates and L2-gain
    • Integral ISS and Nonlinear L2-gain
    • Dissipativity and Passivity

Part II: Controller Design

  • LMI Based Controller and Antiwindup Designs
    • L2-Gain Optimization for Linear Systems
    • Systems with Saturation
    • Regional Analysis
    • Antiwindup Synthesis
  • Control Lyapunov Functions
    • Control Affine Systems
    • ISS Redesign via LgV Damping
    • Sontag’s Universal Formula
    • Backstepping
    • Forwarding
    • Stabilizability & Control Lyapunov Functions
  • Sliding Mode Control
    • Finite-Time Stability
    • Basic Sliding Mode Control
    • A More General Structure
    • Estimating the Disturbance
    • Output Tracking
  • Adaptive Control
    • Motivating Examples and Challenges
    • Model Reference Adaptive Control
    • Adaptive Control for Nonlinear Systems
  • Differential Geometric Methods
    • Introductory Examples
    • Zero Dynamics and Relative Degree
    • Feedback Linearization
  • Output Regulation
    • Linear Output Regulation
    • Robust Linear Output Regulation
    • Nonlinear Output Regulation
  • Optimal Control
    • Optimal Control – Continuous Time Setting
    • Optimal Control – Discrete Time Setting
    • From Infinite to Finite Dimensional Optimization
  • Model Predictive Control
    • The Basic MPC formulation
    • MPC Closed-Loop Analysis
    • Model Predictive Control Schemes
    • Implementational Aspects of MPC

Part III: Observer Design and Estimation

Forum