Robust Safety-Critical Control
Theory, Application and Experiments
1st Edition
Will be published approx. on 22. December 2026
Book
Hardback
352 pages
978-1-394-40018-8 (ISBN)
Description
Practical tools and techniques to achieve objectives in safety-critical control
This book offers a systematic framework for the safety-critical control of nonlinear uncertain systems, with key contributions such as the development of novel small-gain synthesis and feasible-set reshaping techniques to address interactions between the nominal controlled system and dynamic uncertainties. Incorporating recent advancements in the field, this book showcases the strengths of the proposed framework by tackling key theoretical challenges in safety-critical control across multiple benchmark systems. It further highlights the real-world impact of the developed methods and algorithms through practical applications involving vehicles, quadrotors, and robotic manipulators. All results are supported by laboratory experiments with clear explanations.
Written by a team of highly qualified authors, Robust Safety-Critical Control includes:
Insights into the challenges of designing controllers that maintain safety while achieving desired objectives, in the presence of uncertainties, nonlinear dynamics, and multiple constraints
A mathematical foundation for robust safety-critical control, presented in the appendices covering quadratic optimization, Lyapunov stability theory, input-to-state stability, and the nonlinear small-gain theorem
Chapter-by-chapter problem formulations and detailed, rigorous developments of the theory and methods, guiding the reader through the process of addressing the fundamental challenges
Comprehensive system setups for safety-critical control simulations and experiments
Ready-to-use code implementations for key algorithms, including the feasible-reshaping technique and small-gain control methods
Robust Safety-Critical Control is an excellent reference for researchers and graduate students in systems and control, robotics, transportation and AI seeking to expand their knowledge bases. The text is also highly valuable for engineers and practitioners in control engineering, civil and urban engineering, robotics, and manufacturing.
This book offers a systematic framework for the safety-critical control of nonlinear uncertain systems, with key contributions such as the development of novel small-gain synthesis and feasible-set reshaping techniques to address interactions between the nominal controlled system and dynamic uncertainties. Incorporating recent advancements in the field, this book showcases the strengths of the proposed framework by tackling key theoretical challenges in safety-critical control across multiple benchmark systems. It further highlights the real-world impact of the developed methods and algorithms through practical applications involving vehicles, quadrotors, and robotic manipulators. All results are supported by laboratory experiments with clear explanations.
Written by a team of highly qualified authors, Robust Safety-Critical Control includes:
Insights into the challenges of designing controllers that maintain safety while achieving desired objectives, in the presence of uncertainties, nonlinear dynamics, and multiple constraints
A mathematical foundation for robust safety-critical control, presented in the appendices covering quadratic optimization, Lyapunov stability theory, input-to-state stability, and the nonlinear small-gain theorem
Chapter-by-chapter problem formulations and detailed, rigorous developments of the theory and methods, guiding the reader through the process of addressing the fundamental challenges
Comprehensive system setups for safety-critical control simulations and experiments
Ready-to-use code implementations for key algorithms, including the feasible-reshaping technique and small-gain control methods
Robust Safety-Critical Control is an excellent reference for researchers and graduate students in systems and control, robotics, transportation and AI seeking to expand their knowledge bases. The text is also highly valuable for engineers and practitioners in control engineering, civil and urban engineering, robotics, and manufacturing.
More details
Language
English
Place of publication
United States
Publishing group
John Wiley & Sons Inc
Target group
Professional and scholarly
ISBN-13
978-1-394-40018-8 (9781394400188)
Copyright in bibliographic data and cover images is held by Nielsen Book Services Limited or by the publishers or by their respective licensors: all rights reserved.
Schweitzer Classification
Persons
Tengfei Liu is a Professor at Northeastern University, China. He has been deeply engaged in developing and applying nonlinear control methods to engineering systems.
Si Wu is a Postdoctoral Researcher at the State Key Laboratory of Synthetical Automation for Industrial Processes, Northeastern University, China, and a key contributor to the feasible-set reshaping technique for safety-critical control.
Zhi Liu is a PhD student at Northeastern University, China, focusing on developing safety-critical control methods for mechanical systems that fully leverage their inherent energy properties.
Zhong-Ping Jiang is an Institute Professor at New York University, USA. He has made seminal contributions to stability theory, nonlinear control, robust adaptive dynamic programming, learning-based control, and their applications to information, mechanical, transportation and biological systems.
Si Wu is a Postdoctoral Researcher at the State Key Laboratory of Synthetical Automation for Industrial Processes, Northeastern University, China, and a key contributor to the feasible-set reshaping technique for safety-critical control.
Zhi Liu is a PhD student at Northeastern University, China, focusing on developing safety-critical control methods for mechanical systems that fully leverage their inherent energy properties.
Zhong-Ping Jiang is an Institute Professor at New York University, USA. He has made seminal contributions to stability theory, nonlinear control, robust adaptive dynamic programming, learning-based control, and their applications to information, mechanical, transportation and biological systems.
Content
Contents
1 Introduction
1.1 Characterization of Safety for Dynamical Systems
1.2 Robust Safety
1.3 Safety-Critical Control: A Quadratic Programming Approach
1.4 A Practical Scenario of Robust Safety-Critical Control
1.5 Challenges
1.6 Outline of This Book
1.7 Notes
2 Safety-Critical Control Subject to Dynamic Uncertainties: A Nonlinear Small-Gain Approach
2.1 Problem Formulation
2.2 Robust Safety-Critical Controller Design
2.3 Interaction Between Velocity Tracking and Safety
2.4 Small-Gain Synthesis for Safety of the Closed-Loop System
2.5 Simulation and Experiment
2.6 Notes
3 Safety-Critical Control Under Multiple Constraints: A Feasible-
Set Reshaping Technique
3.1 Problem Formulation
3.2 Trial of Directly Extending the Safety Margin
3.3 A Feasible-Set Reshaping Technique for Robust Safety-Critical Control
3.4 Interaction Between Velocity Tracking and Safety
3.5 Small-Gain Synthesis for Safety of the Closed-Loop System
3.6 Simulation and Experiment
3.7 Notes
4 Safety-Critical Control in Cluttered Environments: Set-Valued Measurement and Feasible-Set Reshaping
4.1 Problem Formulation
4.2 A Continuous, Reactive Safety-Critical Controller
4.3 Safety of the Closed-Loop System
4.4 Special Case: An Integrator-Like Mobile Robot
4.5 Simulation and Experiment
4.6 Notes
5 Safety-Critical Control of Multi-Agent Systems: Feasible-Set Reshaping and Nonlinear Small-Gain Synthesis
5.1 Problem Formulation
5.2 Trials with Standard Designs
5.3 Feasible-Set Reshaping and Controller Design
5.4 Properties of the Proposed Design and Proofs
5.5 Small-Gain Analysis for Safety of the Multi-Agent System
5.6 Tuning the Safety-Critical Controllers
5.7 Numerical Simulation and Experiment
5.8 Notes
6 Safety-Critical Control of Euler-Lagrange Systems: Incorporating
Barrier and Energy Functions
6.1 Problem Formulation
6.2 Outer Loop: Safety-Oriented Controller Design
6.3 Inner Loop: Velocity-Tracking Controller Design
6.4 Safety Verification: Incorporating Barrier and Energy Functions
6.5 Numerical Simulation and Experiment
6.6 Notes
7 Safety-Critical Control of Cascade Systems: Towards a Constructive
Control Framework
7.1 Problem Formulation
7.2 Design Ingredient: Plants with Relative Degree One
7.3 Design Ingredient: Refined Feasible-Set Reshaping
7.4 Constructive Design for Plants in the Cascade Form
7.5 Experiment: VTOL Taking Off in a Narrow Space
7.6 Notes
A Mathematical Preliminaries
A.1 Real Vectors and Matrices
A.2 Basis and Positive Basis
A.3 Sets and Convexity
A.4 Continuity, Differentiability and Convexity of Functions
A.5 Comparison Functions
A.6 Nonsmooth Analysis
A.7 Set Invariance
B Quadratic Programming
B.1 Quadratic Optimisation Problems
B.2 Lipschitz Continuity of QP Solutions
C Lyapunov Stability, Input-to-State Stability, and the Nonlinear
Small-Gain Theorem
C.1 Lyapunov Stability Theory
C.2 Input-to-State Stability
C.3 The Nonlinear Small-Gain Theorem
1 Introduction
1.1 Characterization of Safety for Dynamical Systems
1.2 Robust Safety
1.3 Safety-Critical Control: A Quadratic Programming Approach
1.4 A Practical Scenario of Robust Safety-Critical Control
1.5 Challenges
1.6 Outline of This Book
1.7 Notes
2 Safety-Critical Control Subject to Dynamic Uncertainties: A Nonlinear Small-Gain Approach
2.1 Problem Formulation
2.2 Robust Safety-Critical Controller Design
2.3 Interaction Between Velocity Tracking and Safety
2.4 Small-Gain Synthesis for Safety of the Closed-Loop System
2.5 Simulation and Experiment
2.6 Notes
3 Safety-Critical Control Under Multiple Constraints: A Feasible-
Set Reshaping Technique
3.1 Problem Formulation
3.2 Trial of Directly Extending the Safety Margin
3.3 A Feasible-Set Reshaping Technique for Robust Safety-Critical Control
3.4 Interaction Between Velocity Tracking and Safety
3.5 Small-Gain Synthesis for Safety of the Closed-Loop System
3.6 Simulation and Experiment
3.7 Notes
4 Safety-Critical Control in Cluttered Environments: Set-Valued Measurement and Feasible-Set Reshaping
4.1 Problem Formulation
4.2 A Continuous, Reactive Safety-Critical Controller
4.3 Safety of the Closed-Loop System
4.4 Special Case: An Integrator-Like Mobile Robot
4.5 Simulation and Experiment
4.6 Notes
5 Safety-Critical Control of Multi-Agent Systems: Feasible-Set Reshaping and Nonlinear Small-Gain Synthesis
5.1 Problem Formulation
5.2 Trials with Standard Designs
5.3 Feasible-Set Reshaping and Controller Design
5.4 Properties of the Proposed Design and Proofs
5.5 Small-Gain Analysis for Safety of the Multi-Agent System
5.6 Tuning the Safety-Critical Controllers
5.7 Numerical Simulation and Experiment
5.8 Notes
6 Safety-Critical Control of Euler-Lagrange Systems: Incorporating
Barrier and Energy Functions
6.1 Problem Formulation
6.2 Outer Loop: Safety-Oriented Controller Design
6.3 Inner Loop: Velocity-Tracking Controller Design
6.4 Safety Verification: Incorporating Barrier and Energy Functions
6.5 Numerical Simulation and Experiment
6.6 Notes
7 Safety-Critical Control of Cascade Systems: Towards a Constructive
Control Framework
7.1 Problem Formulation
7.2 Design Ingredient: Plants with Relative Degree One
7.3 Design Ingredient: Refined Feasible-Set Reshaping
7.4 Constructive Design for Plants in the Cascade Form
7.5 Experiment: VTOL Taking Off in a Narrow Space
7.6 Notes
A Mathematical Preliminaries
A.1 Real Vectors and Matrices
A.2 Basis and Positive Basis
A.3 Sets and Convexity
A.4 Continuity, Differentiability and Convexity of Functions
A.5 Comparison Functions
A.6 Nonsmooth Analysis
A.7 Set Invariance
B Quadratic Programming
B.1 Quadratic Optimisation Problems
B.2 Lipschitz Continuity of QP Solutions
C Lyapunov Stability, Input-to-State Stability, and the Nonlinear
Small-Gain Theorem
C.1 Lyapunov Stability Theory
C.2 Input-to-State Stability
C.3 The Nonlinear Small-Gain Theorem