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Intro; Supervisorâ#x80;#x99;s Foreword; Parts of this thesis have been published in the following articlesRefereed Journal PapersZ. Sun, S. Mou, B. D. O. Anderson, and A. S. Morse. Rigid motions of 3-D undirected formations with mismatch between desired distances. IEEE Transactions on Automatic Control, vol. 62, No. 8, pp. 4151â#x80;#x93;4158, 2017.Z. Sun, M.-C. Park, B. D. O. Anderson, and H.-S. Ahn. Distributed stabilization control of rigid formations with prescribed orientation. Automatica, vol. 78, No. 4, pp. 250â#x80;#x93;257, 2017. Full versio; Acknowledgements; Contents; 1 Introduction
1.1 Research Background: Cooperative Control and Networked Systems1.2 Introduction and Literature Review; 1.2.1 Different Approaches on Formation Shape Control; 1.2.2 Coordinate Frame Requirement in Formation Control; 1.2.3 Equilibrium and Stability Analysis on Rigid Formation Control Systems; 1.2.4 Some Practical Issues in Rigid Formation Control; 1.2.5 Agent Dynamical Model: Beyond Single-Integrator Models; 1.3 Thesis Outline and Statements of Collaborations; References; 2 Theoretical Preliminaries; 2.1 Notations; 2.2 Preliminary on Graph Theory; 2.3 Preliminary on Rigidity Theory
2.3.1 Definitions and Properties2.3.2 Rigidity Matrix and Related Results; 2.4 Gradient Systems; 2.4.1 Definitions and Properties; 2.4.2 Real Analyticity and Local Minimum; 2.5 Gradient Descent Control Law for Rigid Formation Stabilization; References; Part I Formation Control Systems: Equilibrium and Stability Analysis; 3 Invariance Principles and Equilibrium Analysis for Formation Shape Control Systems; 3.1 Introduction; 3.1.1 Background and Related Work; 3.1.2 Chapter Organization; 3.2 Problem Setup and Motion Equations; 3.3 Rank-Preserving Property for Formation Systems
3.3.1 Proof of the Rank-Preserving Property3.3.2 Consequences of the Rank-Preserving Property; 3.4 Stability Analysis for Degenerate Equilibria; 3.4.1 The Equilibrium Set; 3.4.2 Eigenvalue Property of E and the Hessian; 3.4.3 Degenerate Equilibria are Unstable; 3.5 Concluding Remarks; 3.6 Appendix: Background on Rank-Preserving Matrix Flow; References; 4 Exponential Stability for Formation Control Systems with Generalized Controllers; 4.1 Introduction; 4.1.1 Background and Related Work; 4.1.2 Chapter Organization; 4.2 Exponential Stability for Minimally Rigid Formations
4.2.1 Review of Special Controllers in the Literature4.2.2 Convergence Analysis; 4.2.3 Properties of the Formation Control System with Generalized Controllers; 4.3 Exponential Stability for Non-minimally Rigid Formations; 4.4 Simulation Examples; 4.5 Concluding Remarks; References; Part II Formation Control Systems: Some Practical Considerations; 5 Robustness Issues for 3-D Undirected Formations with Distance Mismatches; 5.1 Introduction; 5.1.1 Background and Related Work; 5.1.2 Chapter Organization; 5.2 Motion Equations with Distance Mismatches
1.1 Research Background: Cooperative Control and Networked Systems1.2 Introduction and Literature Review; 1.2.1 Different Approaches on Formation Shape Control; 1.2.2 Coordinate Frame Requirement in Formation Control; 1.2.3 Equilibrium and Stability Analysis on Rigid Formation Control Systems; 1.2.4 Some Practical Issues in Rigid Formation Control; 1.2.5 Agent Dynamical Model: Beyond Single-Integrator Models; 1.3 Thesis Outline and Statements of Collaborations; References; 2 Theoretical Preliminaries; 2.1 Notations; 2.2 Preliminary on Graph Theory; 2.3 Preliminary on Rigidity Theory
2.3.1 Definitions and Properties2.3.2 Rigidity Matrix and Related Results; 2.4 Gradient Systems; 2.4.1 Definitions and Properties; 2.4.2 Real Analyticity and Local Minimum; 2.5 Gradient Descent Control Law for Rigid Formation Stabilization; References; Part I Formation Control Systems: Equilibrium and Stability Analysis; 3 Invariance Principles and Equilibrium Analysis for Formation Shape Control Systems; 3.1 Introduction; 3.1.1 Background and Related Work; 3.1.2 Chapter Organization; 3.2 Problem Setup and Motion Equations; 3.3 Rank-Preserving Property for Formation Systems
3.3.1 Proof of the Rank-Preserving Property3.3.2 Consequences of the Rank-Preserving Property; 3.4 Stability Analysis for Degenerate Equilibria; 3.4.1 The Equilibrium Set; 3.4.2 Eigenvalue Property of E and the Hessian; 3.4.3 Degenerate Equilibria are Unstable; 3.5 Concluding Remarks; 3.6 Appendix: Background on Rank-Preserving Matrix Flow; References; 4 Exponential Stability for Formation Control Systems with Generalized Controllers; 4.1 Introduction; 4.1.1 Background and Related Work; 4.1.2 Chapter Organization; 4.2 Exponential Stability for Minimally Rigid Formations
4.2.1 Review of Special Controllers in the Literature4.2.2 Convergence Analysis; 4.2.3 Properties of the Formation Control System with Generalized Controllers; 4.3 Exponential Stability for Non-minimally Rigid Formations; 4.4 Simulation Examples; 4.5 Concluding Remarks; References; Part II Formation Control Systems: Some Practical Considerations; 5 Robustness Issues for 3-D Undirected Formations with Distance Mismatches; 5.1 Introduction; 5.1.1 Background and Related Work; 5.1.2 Chapter Organization; 5.2 Motion Equations with Distance Mismatches