Cooperative Control of Multi-Agent Systems: An Optimal and Robust Perspective

Contents
About the authors
Preface
Acknowledgments
1 Introduction
	1.1 Background
		1.1.1 Motivations
		1.1.2 Control architectures and strategies
		1.1.3 Related applications
	1.2 Overview of related works
		1.2.1 Consensus control
			1.2.1.1 Basic concept
			1.2.1.2 Optimal cooperative control
			1.2.1.3 Robust cooperative control
		1.2.2 Formation control
		1.2.3 Other related research
		1.2.4 Future research topics
	1.3 Objectives of this book
	1.4 Book outline
2 Preliminaries
	2.1 Matrix theory
	2.2 Stability theory
	2.3 Basic algebraic graph theory
		2.3.1 Basic definitions
		2.3.2 Graph matrices
		2.3.3 Properties
	2.4 Useful lemmas on inequalities
3 Optimal consensus control of multiple integrator systems
	3.1 Problem formulation
	3.2 Optimal consensus control with obstacle avoidance for single-integrator case
		3.2.1 Optimal consensus algorithm: single-integrator case
		3.2.2 Numerical examples
			3.2.2.1 Consensus without obstacles on the trajectories of agents
			3.2.2.2 Consensus with multiple obstacles on the trajectories of agents
	3.3 Optimal consensus control with obstacle avoidance for double-integrator case
		3.3.1 Optimal consensus algorithm: double-integrator case
		3.3.2 Numerical examples
			3.3.2.1 Consensus without obstacles on the trajectories of the agents
			3.3.2.2 Consensus with multiple obstacles on the trajectories of the agents
	3.4 Conclusion remarks
4 Optimal cooperative tracking and flocking of multi-agent systems
	4.1 Optimal rendezvous and cooperative tracking control with obstacle avoidance
		4.1.1 Problem formulation
		4.1.2 Optimal rendezvous algorithm with obstacle avoidance
		4.1.3 Numerical examples
			A. Rendezvous without obstacles on the trajectories of agents
			B. Rendezvous with two obstacles on the trajectory of agents
		4.1.4 Extension to cooperative tracking problem with obstacle avoidance
			4.1.4.1 Cooperative tracking algorithm with obstacle avoidance
			4.1.4.2 Numerical examples
				A. Cooperative tracking of a reference with constant velocity
				B. Cooperative tracking of a dynamic reference trajectory
	4.2 Optimal flocking control design with obstacle avoidance
		4.2.1 Problem formulation
		4.2.2 Optimal flocking control algorithm design
		4.2.3 Numerical examples
			A. Flocking with velocity alignment and navigation
			B. Flocking with velocity alignment, navigation, and cohesion
			C. Flocking with velocity alignment, navigation, cohesion, and obstacle/ collision avoidance
	4.3 Conclusion remarks
5 Optimal formation control of multiple UAVs
	5.1 Problem formulation
	5.2 Integrated optimal control approach to formation control problem
	5.3 Numerical examples
		5.3.1 Formation control without obstacles on the trajectories of UAVs
		5.3.2 Formation control with two obstacles on the trajectories of UAVs
	5.4 Conclusion remarks
6 Optimal coverage control of multi-robot systems
	6.1 Problem formulation
		6.1.1 Voronoi tessellation and locational optimization
		6.1.2 Potential field method for collision avoidance
	6.2 Coverage controller design with known density function
		6.2.1 Coverage controller design
		6.2.2 Numerical examples
	6.3 Coverage controller design with density function estimation
		6.3.1 Estimation based coverage controller design
		6.3.2 Numerical examples
	6.4 Conclusion remarks
7 Robust consensus control of multi-agent systems with input delay
	7.1 Problem formulation
	7.2 Consensus of Lipschitz nonlinear systems with input delay: model reduction method
		7.2.1 Stability analysis for single nonlinear system
		7.2.2 Consensus analysis
		7.2.3 Controller design
	7.3 Consensus of Lipschitz nonlinear systems with input delay: truncated predictor feedback method
		7.3.1 Finite-dimensional consensus controller design
		7.3.2 Overview of truncated predictor feedback approach
		7.3.3 Consensus analysis
	7.4 Numerical examples
		7.4.1 A circuit example
		7.4.2 Numerical examples
	7.5 Conclusion remarks
8 Robust consensus control of multi-agent systems with disturbance rejection
	8.1 Problem formulation
	8.2 Disturbance rejection for a directed graph
		8.2.1 Consensus controller design with disturbance rejection
		8.2.2 Consensus analysis
	8.3 Fully distributed consensus disturbance rejection
		8.3.1 Local information based disturbance rejection controller
		8.3.2 Consensus analysis
	8.4 Disturbance rejection in leader-follower format
		8.4.1 Leader-follower disturbance rejection controller
		8.4.2 Consensus analysis
	8.5 Numerical examples
	8.6 Conclusion remarks
9 Robust consensus control of nonlinear odd power integrator systems
	9.1 Problem formulation
	9.2 Distributed controller for nonlinear odd power integrator systems
	9.3 Numerical examples
		9.3.1 Perturbed case
		9.3.2 Perturbation-free case
	9.4 Conclusion remarks
10 Robust cooperative control of networked negative-imaginary systems
	10.1 Problem formulation
		10.1.1 NI system definition
		10.1.2 Typical results for NI systems
	10.2 Robust consensus control for multi-NI systems
		10.2.1 Homogeneous NI systems
		10.2.2 Robust output feedback consensus algorithm for homogeneous multi-agent systems
		10.2.3 Convergence set study
		10.2.4 Numerical examples
			10.2.4.1 Multiple single-integrator systems
			10.2.4.2 Multiple double-integrator systems
			10.2.4.3 Multiple flexible structures systems
	10.3 Robust consensus control of heterogeneous multi-NI systems
		10.3.1 Heterogeneous NI systems
		10.3.2 Robust output feedback consensus algorithm for heterogeneous multi-agent systems
			10.3.2.1 NI plants without free body dynamics
			10.3.2.2 NI plants with free body dynamics
		10.3.3 Numerical examples
			10.3.3.1 Two lightly damped and one undamped flexible structures
			10.3.3.2 One single integrator, one double integrator, one undamped and one lightly damped flexible structure
	10.4 Extension to robust cooperative control
	10.5 Conclusion remarks
Bibliography
Index