This paper provides a theoretical framework for analysis of consensus algorithms for multi-agent networked systems with an emphasis on the role of directed information flow, robustness to changes in network topology due to link/node failures, time-delays, and performance guarantees. An overview of basic concepts of information consensus in networks and methods of convergence and performance analysis for the algorithms are provided. Our analysis framework is based on tools from matrix theory, algebraic graph theory, and control theory. We discuss the connections between consensus problems in networked dynamic systems and diverse applications including synchronization of coupled oscillators, flocking, formation control, fast consensus in small-world networks, Markov processes and gossip-based algorithms, load balancing in networks, rendezvous in space, distributed sensor fusion in sensor networks, and belief propagation. We establish direct connections between spectral and structural properties of complex networks and the speed of information diffusion of consensus algorithms. A brief introduction is provided on networked systems with nonlocal information flow that are considerably faster than distributed systems with lattice-type nearest neighbor interactions. Simulation results are presented that demonstrate the role of small-world effects on the speed of consensus algorithms and cooperative control of multivehicle formations

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Consensus and Cooperation in Networked Multi-Agent Systems

By a switched system, we mean a hybrid dynamical system consisting of a family of continuous-time subsystems and a rule that orchestrates the switching between them. The article surveys developments in three basic problems regarding stability and design of switched systems. These problems are: stability for arbitrary switching sequences, stability for certain useful classes of switching sequences, and construction of stabilizing switching sequences. We also provide motivation for studying these problems by discussing how they arise in connection with various questions of interest in control theory and applications.

Basic problems in stability and design of switched systems

This paper presents control and coordination algorithms for groups of vehicles. The focus is on autonomous vehicle networks performing distributed sensing tasks where each vehicle plays the role of a mobile tunable sensor. The paper proposes gradient descent algorithms for a class of utility functions which encode optimal coverage and sensing policies. The resulting closed-loop behavior is adaptive, distributed, asynchronous, and verifiably correct.

Coverage control for mobile sensing networks

With the continuous increase in complexity and expense of industrial systems, there is less tolerance for performance degradation, productivity decrease, and safety hazards, which greatly necessitates to detect and identify any kinds of potential abnormalities and faults as early as possible and implement real-time fault-tolerant operation for minimizing performance degradation and avoiding dangerous situations. During the last four decades, fruitful results have been reported about fault diagnosis and fault-tolerant control methods and their applications in a variety of engineering systems. The three-part survey paper aims to give a comprehensive review of real-time fault diagnosis and fault-tolerant control, with particular attention on the results reported in the last decade. In this paper, fault diagnosis approaches and their applications are comprehensively reviewed from model- and signal-based perspectives, respectively.

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A Survey of Fault Diagnosis and Fault-Tolerant Techniques—Part I: Fault Diagnosis With Model-Based and Signal-Based Approaches

Series Preface * Preface to the Third Edition * 1 Linear Systems * 2 Nonlinear Systems: Local Theory * 3 Nonlinear Systems: Global Theory * 4 Nonlinear Systems: Bifurcation Theory * References * Index

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Differential Equations and Dynamical Systems

Decentralized overlapping control of a formation of unmanned aerial vehicles

In this paper we present a theoretical and experimental result on the control of multi-agent non-holonomic systems. We design and implement a novel decentralized control scheme that achieves dynamic formation control and collision avoidance for a group of non-holonomic robots. First, we derive a feedback law using Lyapunov-type analysis that guarantees collision avoidance and tracking of a reference trajectory for a single robot. Then we extend this result to the case of multiple non-holonomic robots, and show how different multi-agent problems, such as formation control and leader-follower control, can be addressed in this framework. Finally, we combine the above results to address the problem of coordinated tracking for a group of agents. We give extensive experimental results that validate the effectiveness of our results in all three cases.

Formation Control and Collision Avoidance for Multi-agent Non-holonomic Systems: Theory and Experiments

This paper studies the problem of dynamically covering a given region in the plane using a set of mobile sensor agents. A novel problem formulation is proposed that addresses a number of important multiagent missions. The coverage goal, which is to cover a given search domain using multiple mobile sensors such that each point is surveyed until a certain preset level is achieved, is formulated in a mathematically precise problem statement. A control law is developed that guarantees to meet the coverage goal. This control law is modified to guarantee that a partially connected fleet also attains the coverage goal. Finally, a collision avoidance component is added to the controller to guarantee that the agents do not collide. The new controller is shown to safely achieve coverage. Several numerical examples are provided to illustrate the main results.

Effective Coverage Control for Mobile Sensor Networks With Guaranteed Collision Avoidance

We consider the problem of distributed convergence to a Nash equilibrium in a noncooperative game where the players generate their actions based only on online measurements of their individual cost functions, corrupted with additive measurement noise. Exact analytical forms and/or parameters of the cost functions, as well as the current actions of the players may be unknown. Additionally, the players' actions are subject to linear dynamic constraints. We propose an algorithm based on discrete-time stochastic extremum seeking using sinusoidal perturbations and prove its almost sure convergence to a Nash equilibrium. We show how the proposed algorithm can be applied to solving coordination problems in mobile sensor networks, where motion dynamics of the players can be modeled as: 1) single integrators (velocity-actuated vehicles), 2) double integrators (force-actuated vehicles), and 3) unicycles (a kinematic model with nonholonomic constraints). Examples are given in which the cost functions are selected such that the problems of connectivity control, formation control, rendezvous and coverage control are solved in an adaptive and distributed way. The methodology is illustrated through simulations.

Distributed Seeking of Nash Equilibria With Applications to Mobile Sensor Networks

We present a decentralized optimization method for solving the coordination problem of interconnected nonlinear discrete-time dynamic systems with multiple decision makers. The optimization framework embeds the inherent structure in which each decision maker has a mathematical model that captures only the local dynamics and the associated interconnecting global constraints. A globally convergent algorithm based on sequential local optimizations is presented. Under assumptions of differentiability and linear independence constraint qualification, we show that the method results in global convergence to /spl epsiv/-feasible Nash solutions that satisfy the Karush-Kuhn-Tucker necessary conditions for Pareto-optimality. We apply this methodology to a multiple unmanned air vehicle system, with kinematic aircraft models, coordinating in a common airspace with separation requirements between the aircraft.

Dusan M. Stipanovic

Papers

Decentralized overlapping control of a formation of unmanned aerial vehicles

Formation Control and Collision Avoidance for Multi-agent Non-holonomic Systems: Theory and Experiments

Effective Coverage Control for Mobile Sensor Networks With Guaranteed Collision Avoidance

Distributed Seeking of Nash Equilibria With Applications to Mobile Sensor Networks

Decentralized optimization, with application to multiple aircraft coordination