Robust Safety-Critical Control

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.

• List of Figures xiList of Table xviAbout the Authors xviiPreface xixNotations xxiiiAcronyms xxviiAbout the Companion Website xxix1 Introduction 11.1 Characterization of Safety for Dynamical Systems 21.2 Robust Safety 91.3 Safety-critical Control: A Quadratic Programming Approach 121.4 A Practical Scenario of Robust Safety-critical Control 181.5 Challenges 281.6 Outline of this Book 331.7 Notes 372 Safety-critical Control Subject to Dynamic Uncertainties: A Nonlinear Small-gain Approach 412.1 Problem Formulation 422.2 Robust Safety-critical Controller Design 452.3 Interaction Between Velocity Tracking and Safety 542.4 Small-gain Synthesis for Safety of the Closed-loop System 582.5 Simulation and Experiment 662.6 Notes 703 Safety-critical Control Under Multiple Constraints: A Feasible-set Reshaping Technique 733.1 Problem Formulation 743.2 Trial of Directly Extending the Safety Margin 773.3 A Feasible-set Reshaping Technique for Robust Safety-critical Control 803.4 Interaction Between Velocity Tracking and Safety 923.5 Small-gain Synthesis for Safety of the Closed-loop System 973.6 Simulation and Experiment 1013.7 Notes 1074 Safety-critical Control in Cluttered Environments: Set-valued Measurement and Feasible-set Reshaping 1114.1 Problem Formulation 1124.2 A Continuous, Reactive Safety-critical Controller 1164.3 Safety of the Closed-loop System 1214.4 Special Case: An Integrator-like Mobile Robot 1244.5 Simulation and Experiment 1254.6 Notes 1375 Safety-critical Control of Multi-agent Systems: Feasible-set Reshaping and Nonlinear Small-gain Synthesis 1395.1 Problem Formulation 1405.2 Trials with Standard Designs 1435.3 Feasible-set Reshaping and Controller Design 1465.4 Properties of the Proposed Design and Proofs 1495.5 Small-gain Analysis for Safety of the Multi-agent System 1625.6 Tuning the Safety-critical Controllers 1665.7 Numerical Simulation and Experiment 1685.8 Notes 1716 Safety-critical Control of Euler–Lagrange Systems: Incorporating Barrier and Energy Functions 1736.1 Problem Formulation 1746.2 Outer Loop: Safety-oriented Controller Design 1786.3 Inner Loop: Velocity-tracking Controller Design 1906.4 Safety Verification: Incorporating Barrier and Energy Functions 1926.5 Numerical Simulation and Experiment 1986.6 Notes 2047 Safety-critical Control of Cascade Systems: Towards a Constructive Control Framework 2077.1 Problem Formulation 2087.2 Design Ingredient: Plants with Relative-degree-one 2137.3 Design Ingredient: Refined Feasible-set Reshaping 2187.4 Constructive Design for Plants in the Cascade Form 2257.5 Experiment: VTOL Taking Off in a Narrow Space 2347.6 Notes 240A Mathematical Preliminaries 243A.1 Real Vectors and Matrices 243A.2 Basis and Positive Basis 245A.3 Sets and Convexity 249A.4 Continuity, Differentiability, and Convexity of Functions 251A.5 Comparison Functions 255A.6 Nonsmooth Analysis 256A.7 Set Invariance 260B Quadratic Programming 263B.1 Quadratic Optimization Problems 263B.2 Lipschitz Continuity of QP Solutions 264C Lyapunov Stability, Input-to-state Stability, and the Nonlinear Small-gain Theorem 269C.1 Lyapunov Stability Theory 269C.2 Input-to-state Stability 273C.3 The Nonlinear Small-gain Theorem 277References 285Index 299