Nonlinear Control Theory and Application

Course Overview

In practice, nearly all systems are nonlinear, while linear systems are simplified or approximated nonlinear systems. However, there are also essentially nonlinear systems that cannot be analyzed and controlled using linearization methods. This course enhances students’ ability to solve nonlinear system problems by teaching basic analysis methods of nonlinear systems, feedback system analysis methods, modern analysis, and nonlinear feedback controller design methods.

Starting from control theory, the course helps engineering students master basic knowledge of engineering mathematics such as nonlinear system characteristics and classical stability analysis methods. Using basic marine engineering problems as examples, it cultivates the ability to apply them to practical engineering systems. Through repeated conversion between engineering concepts and theoretical knowledge, it trains graduate students’ abstract thinking in mathematical expression of engineering concepts and their ability to concretize abstract control theories, achieving mutual promotion between theory and reality.

Instructor

Zhengru Ren, Assistant Professor

Course Information

• Credits: 2
• Total Hours: 32 hours (32 hours of lectures)
• Semester: 2023-2024 Spring Semester (Weeks 1-16)
• Weekly Hours: 2
• Assessment Method: Examination
• Applicable Majors: Open to all departments, priority given to students from the Marine Engineering Research Institute
• Course Type: Professional Basic Course
• Teaching Language: Chinese

Application Reasons and Course Objectives

Currently, marine engineering problems are mainly solved through passive control by optimizing structures, which is costly, has limited application scope, and has short operation windows. Automation and intelligence based on active control are the future development trends in the field of marine engineering equipment, and are currently popular research and industrial directions.

Marine engineering automation is based on a deep understanding of marine engineering backgrounds and needs, comprehensively applying control theory to guide the research and development of marine engineering equipment. Its talent training needs to overcome the huge differences in knowledge systems between the marine engineering discipline, which is mainly based on mechanics education, and the control theory discipline, which is mainly based on mathematics education. Therefore, it is necessary to teach more in-depth control theory knowledge on the basis of traditional mechanics education.

“Nonlinear Systems” (or “Nonlinear Control Theory”) is an advanced professional basic course in the field of automation. Although the Marine Engineering Institute and Shenzhen International Graduate School have great demand for automation control research, Shenzhen International Graduate School has not yet offered this course, so there is an urgent need to fill this gap.

Through studying this course, it aims to help graduate students acquire basic and advanced theoretical knowledge of nonlinear systems. Through repeated conversion between engineering concepts and theoretical knowledge, it trains graduate students’ abstract thinking in mathematical expression of engineering concepts and their ability to concretize abstract control theories, achieving mutual promotion between theory and reality.

Comparison with Similar Courses

This course is a further extension of the newly opened course “Guidance, Navigation and Control of Dynamic Positioning Systems”, focusing on nonlinear systems with strong theoretical depth. The course content is mainly based on theoretical explanation and derivation.

Nonlinear systems is a basic course offered in various universities and is an indispensable basic course in the field of marine engineering automatic control. Taking the Marine Technology program at Norwegian University of Science and Technology as a reference, master’s students in the Marine Cybernetics direction can choose the course “TTK4150-Nonlinear systems” offered by the School of Control. Through the basic theoretical study of this course, it can effectively support the study of professional courses offered by the School of Marine Technology (including Marine Control System 1 and Marine Control System 2), and subsequent courses such as “Guidance, Navigation and Control of Vehicles”.

Currently, there are fewer automation-related basic courses offered in Shenzhen International Graduate School, with only the course “Linear System” offered by Professor Xu Feng (not offered this academic year). This course is a study of a wider range of nonlinear systems based on linear system theory.

Prerequisites

Linear Algebra, Guidance, Navigation and Control of Dynamic Positioning Systems

Course Content

This course teaches nonlinear system problems starting from practical problems in the marine engineering field. First, it teaches the mathematical knowledge involved in the course study. The basic analysis part teaches the basic concepts and basic analysis methods of nonlinear systems; the feedback system analysis part teaches input-output stability, passivity, and frequency domain analysis of feedback systems; the modern analysis part teaches the basic concepts of modern stability analysis, the stability of perturbed systems, perturbation theory and averaging, and singular perturbation theory; the nonlinear feedback control part teaches feedback linearization and presents several nonlinear design tools such as sliding mode control, Lyapunov redesign, backstepping design method, passivity-based control, and high-gain observer.

The course is mainly divided into the following three parts:

1. Stability Analysis of Input-free Systems

• Basic mathematical knowledge involved (2 hours)
• Basic concepts and basic analysis methods of nonlinear systems (2 hours)
• Lyapunov direct and indirect methods
• Feedback system analysis part (2 hours)
• Input-output stability
• Passivity
• Frequency domain analysis of feedback systems
• Basic concepts of nonlinear system stability analysis (2 hours)
• Stability of perturbed systems
• Perturbation theory and averaging
• Singular perturbation theory

2. Active Control Strategy Design Based on System Stability

• Feedback linearization control (2 hours)
• Sliding mode control (2 hours)
• Passivity-based control and high-gain observer, etc. (2 hours)

3. Backstepping Control for Nonlinear Ordinary Differential Equations

• Backstepping design method (2 hours)
• Finite-time control (2 hours)
• Adaptive backstepping control, neural networks, fuzzy systems (2 hours)
• State constraint: Barrier Lyapunov function (2 hours)
• Unknown disturbance: projection, disturbance-rejection (2 hours)
• Time-delay effects (2 hours)
• Input nonlinearity (2 hours)
• Pure feedback system, Nussbaum, tanh (2 hours)
• Event-trigger system

Textbooks and References

Main Textbooks

[1] Khalil H K . Nonlinear Systems Third Edition[J]. Upper Saddle River Nj Prentice Hall Inc, 2002. [2] Ioannou, Petros & Sun, Jing. (1995). Robust Adaptive Control.