Nonlinear Control / Hassan K. Khalil Pearson

Fundamentos de Sistemas No Lineales: Modelos, equilibrio, linealización.

Análisis de Estabilidad de Lyapunov: Teoremas, funciones de Lyapunov, estabilidad asintótica.

Control por Retroalimentación de Estado: Linearización por retroalimentación, control de modos deslizantes.

Diseño de Controladores No Lineales: Control robusto, control adaptativo.

Sistemas de Tiempo Discreto No Lineales.

Sistemas Singulares y Teoremas de Perturbación Singular.

Control de Sistemas de Parámetros Variantes en el Tiempo (LTI y LPV).

Diseño Basado en Paso-Atrás (Backstepping).

Teoría del Observador No Lineal.

Sistemas de Conmutación y Salto (Switched Systems and Jump Systems).
Examples of Nonlinear Systems: Real-world examples from various fields such as robotics, biology, and economics.

Mathematical Foundations: Basic concepts such as system representation, state-space models, and system dynamics.

Chapter 2: Mathematical Preliminaries
Differential Equations: Review of ordinary differential equations (ODEs) that describe nonlinear systems.

Lyapunov Stability Theory: Introduction to Lyapunov's second method for stability analysis.

Nonlinear System Representations: Techniques for representing nonlinear systems and their properties.

Chapter 3: Stability of Nonlinear Systems
Lyapunov Stability: In-depth analysis of Lyapunov stability, including local and global stability, asymptotic stability, and exponential stability.

LaSalle's Invariance Principle: A powerful method for analyzing the stability of nonlinear systems.

Practical Stability Analysis: Applying Lyapunov's methods to real-world nonlinear systems.

Chapter 4: Feedback Linearization
Concept of Feedback Linearization: The process of transforming nonlinear systems into linear ones using state feedback.

Controllability and Observability: Conditions for feedback linearization, including discussions of system controllability and observability.

Practical Applications: Examples where feedback linearization simplifies control design for nonlinear systems.

Chapter 5: Control Lyapunov Functions
Control Lyapunov Functions (CLFs): Using Lyapunov functions to design stabilizing controllers for nonlinear systems.

Design of Stabilizing Controllers: Practical steps for creating controllers that ensure system stability using CLFs.

Example Applications: Application of CLFs in robotic systems and autonomous vehicles.

Chapter 6: Nonlinear Control Design Techniques
Sliding Mode Control: Explanation of sliding mode control, a technique for robustly controlling nonlinear systems.

Backstepping Method: A method for systematically designing control laws for nonlinear systems.

Small-Gain Theorem: A tool for analyzing stability and robustness in the presence of nonlinearities.

Chapter 7: Global Asymptotic Stability
Global Stabilization: Techniques to achieve global stability for nonlinear systems.

Constructing Global Lyapunov Functions: Methods for developing Lyapunov functions that guarantee global asymptotic stability.

Applications: Global stabilization in practical systems like robotics and aerospace.

Chapter 8: Control in the Presence of Disturbances
Robust Control Design: Design strategies for nonlinear systems that remain stable and performant under disturbances.

Input-Output Stability: Analysis of stability from an input-output perspective, especially for systems subject to external disturbances.

Disturbance Rejection: Strategies for rejecting disturbances in practical nonlinear systems.

Chapter 9: Control of Underactuated Systems
Underactuated Systems: Introduction to systems with fewer actuators than degrees of freedom (common in robotics, aerospace, etc.).

Control Strategies for Underactuated Systems: Techniques for stabilizing and controlling such systems despite limited actuation.

Examples: Application to systems like helicopters, drones, and bipedal robots.

Chapter 10: Applications of Nonlinear Control
Robotic Systems: Application of nonlinear control strategies in robotics, including trajectory tracking and stabilization.

Aerospace Systems: Nonlinear control in the context of aircraft, spacecraft, and satellite systems.

Automobile Systems: Application of nonlinear control in advanced driver assistance systems (ADAS) and autonomous vehicles.

Biological Systems: Use of nonlinear control in biological models and processes, such as in cell biology or metabolic networks.

Chapter 11: Advanced Topics
Nonlinear Systems with Time-Delays: Analysis and control of nonlinear systems that involve time delays.

H-infinity Control for Nonlinear Systems: Advanced methods for robust control using the H-infinity approach in nonlinear systems.

Passivity-Based Control: Control design based on the passivity property of systems to achieve stability and robustness.

Appendices
Mathematical Tools: A review of key mathematical tools used throughout the book, including matrix theory, differential equations, and control theory.

Bibliography: References to seminal and recent research papers and textbooks in the field of nonlinear control.

"Nonlinear Control" de Hassan K. Khalil es una obra fundamental que ofrece una introducción rigurosa y completa a la teoría de control no lineal. El autor aborda desde los conceptos básicos de los sistemas no lineales hasta técnicas avanzadas de análisis de estabilidad y diseño de controladores, como la linealización por retroalimentación, el control de modos deslizantes y el diseño basado en Lyapunov. El libro se distingue por su enfoque claro y sistemático, proporcionando las herramientas matemáticas y conceptuales necesarias para entender y resolver problemas complejos en sistemas de control no lineales. Es un recurso indispensable para quienes buscan profundizar en esta área de la ingeniería de control.

Ingeniería Mecatrónica

Ingeniería Electrónica