Discrete Networked Dynamic Systems: Analysis and Performance provides a high-level treatment of a general class of linear discrete-time dynamic systems interconnected over an information network, exchanging relative state measurements or output measurements. It presents a systematic analysis of the material and provides an account to the math development in a unified way.
The topics in this book are structured along four dimensions: Agent, Environment, Interaction, and Organization, while keeping global (system-centered) and local (agent-centered) viewpoints.
The focus is on the wide-sense consensus problem in discrete networked dynamic systems. The authors rely heavily on algebraic graph theory and topology to derive their results. It is known that graphs play an important role in the analysis of interactions between multiagent/distributed systems. Graph-theoretic analysis provides insight into how topological interactions play a role in achieving coordination among agents. Numerous types of graphs exist in the literature, depending on the edge set of G. A simple graph has no self-loop or edges. Complete graphs are simple graphs with an edge connecting any pair of vertices. The vertex set in a bipartite graph can be partitioned into disjoint non-empty vertex sets, whereby there is an edge connecting every vertex in one set to every vertex in the other set. Random graphs have fixed vertex sets, but the edge set exhibits stochastic behavior modeled by probability functions. Much of the studies in coordination control are based on deterministic/fixed graphs, switching graphs, and random graphs.
Author(s): Magdi S. Mahmoud, Yuanqing Xia
Publisher: Academic Press
Year: 2020
Language: English
Pages: 484
City: London
Front Cover
Discrete Networked Dynamic Systems
Copyright
Contents
About the authors
Preface
Acknowledgement
1 Mathematical background and examples
1.1 Introduction
1.2 Mathematical background
1.2.1 Basic notions
1.2.2 Signal norms
1.2.3 Vector norms
1.2.4 Matrix norms
1.2.5 Singular value decomposition
1.2.6 System norms
1.2.7 Brief overview of matrix theory
1.2.8 Estimation of spectrum of complex matrices
1.2.9 Spectral radius
1.2.10 Row-stochastic matrices
1.2.11 Products of stochastic matrices
1.2.12 Kronecker products and vec
1.2.13 Matrix lemmas
1.3 Elements of algebraic graphs
1.3.1 Graph theory
1.3.2 Undirected graphs
1.3.3 Main graphs
1.3.4 Graph operations
1.3.5 Basic properties
1.3.6 Connectivity properties of digraphs
1.3.7 Properties of adjacency matrices
1.3.8 Laplacian spectrum of graphs
1.4 Lyapunov stability
1.4.1 Preliminaries
1.4.2 Input-to-state stability properties
1.4.3 More on the lemma of Lyapunov
1.5 Minimum mean square estimate
1.5.1 Standard results
1.6 Motivating problems
1.6.1 Wireless sensor networks
1.6.2 Distributed parameter estimation
1.6.3 Population dynamics
1.6.4 Distributed control systems
1.6.5 Bipartite distributed control systems
1.7 Notes
References
2 Structural and performance patterns
2.1 Introduction
2.2 Discrete networked dynamic systems
2.2.1 Linear time-invariant systems
2.2.2 Preliminary view
2.2.3 Problem statement
2.3 System properties
2.3.1 Glimpse of stability
2.3.2 Controllability and observability
2.3.3 Stabilizability and detectability
2.4 Controllability Gramian
2.4.1 H2-norm of homogeneous discrete networked dynamic systems
2.4.2 Observability Gramian
2.4.3 Homogeneous and heterogeneous discrete networked dynamic systems
2.5 Observability properties of discrete networked dynamic systems
2.5.1 Homogeneous systems
2.5.2 Heterogeneous systems
2.5.3 Necessary and sufficient conditions
2.6 Index of homogeneity and heterogeneity
2.6.1 DNDS index of homogeneity
2.6.2 DNDS index of heterogeneity
2.7 Agent feedback stability
2.7.1 Computation of the H2-norm
2.7.2 Agent state feedback control
2.7.3 Linear matrix inequality-based formulation
2.8 Synthesis schemes of discrete networked dynamic systems
2.8.1 Local agent control for fixed topology
2.8.2 H2 control design
2.9 H∞ performance and robust topology design
2.9.1 Relative sensing network model
2.9.2 Graph-theoretic bounds on H∞ performance
2.9.3 Homogeneous RSN H∞ performance
2.9.4 Bounds on the heterogeneous RSN H∞ performance
2.9.5 Robust synthesis of relative sensing networks
2.10 Notes
References
3 Consensus of systems over graphs
3.1 Dynamic consensus protocol
3.1.1 Preliminaries
3.1.2 Discrete consensus region
3.1.3 Simulation example 3.1
3.1.4 Networks with neutrally stable agents
3.1.5 Simulation example 3.2
3.1.6 Networks with unstable agents
3.1.7 Simulation example 3.3
3.1.8 Application to formation control
3.1.9 Simulation example 3.4
3.2 Multiagent systems with diverse time delays
3.2.1 Introduction
3.2.2 Preliminaries
3.2.3 Dynamic model
3.2.4 Design results
3.2.5 Simulation example 3.5
3.3 Decentralized consensus prediction
3.3.1 Formulation of the problem
3.3.2 Distributed asymptotic consensus
3.3.3 Finite-time computation
3.4 Performance of agreement protocol
3.4.1 Introduction
3.4.2 The edge Laplacian
3.4.3 Performance bounds for consensus
3.4.4 Spanning trees
3.4.5 k-Regular graphs
3.4.6 Cycle contributions
3.4.7 Sensor placement with H2 performance
3.5 Scalable consensus conditions
3.5.1 Integrator agents over delayless networks
3.5.2 Consentability
3.5.3 Effect of input delay
3.6 Notes
References
4 Energy-based cooperative control
4.1 Dissipative cooperative output synchronization
4.1.1 Introduction
4.1.2 Problem preliminaries and formulation
4.1.3 Design results
4.1.4 Event-triggered protocol
4.1.5 Simulation example 4.1
4.2 Passivity analysis of time delay systems
4.2.1 Introduction
4.2.2 System formulation
4.2.3 Stability results
4.2.4 Simulation example 4.2
4.2.5 Simulation example 4.3
4.2.6 Simulation example 4.4
4.3 Consensus tracking of saturated systems
4.3.1 Introduction
4.3.2 Problem statement
4.3.3 Control design
4.3.4 Simulation example 4.5
4.4 Notes
References
5 Performance of consensus algorithms
5.1 Introduction
5.2 The agreement algorithm
5.3 Performance and robustness of averaging algorithms
5.3.1 Simulation example 5.1
5.3.2 Convergence rate and eigenvalues
5.3.3 Linear quadratic control
5.3.4 Performance with noise
5.4 Leader following consensus
5.4.1 Review
5.4.2 Problem formulation
5.4.3 Design result
5.4.4 Simulation example 5.2
5.5 Stochastic approximation algorithms
5.5.1 Problem formulation
5.5.2 The measurement model
5.5.3 The algorithm
5.5.4 Simulation example 5.3
5.6 Notes
References
6 Event-based coordination control
6.1 Event-based tracking control
6.1.1 Introduction
6.1.2 Problem statement
6.1.3 Design results
6.1.4 Simulation example 6.1
6.2 Discrete two-timescale systems
6.2.1 Preliminaries
6.2.2 Global analytic results
6.2.3 Nonsingular transformation
6.2.4 Event-based control
6.2.5 Event-based conditions
6.2.6 Self-triggered control
6.2.7 Simulation example 6.2
6.3 Networks of two-timescale systems
6.3.1 Synchronization using local information
6.3.2 Control design
6.3.3 Simulation example 6.3
6.4 Consensus of multiagent delay systems with adversaries
6.4.1 Adversary model
6.4.2 Delay-robust resilient consensus
6.4.3 Delay-robust f-local resilient consensus protocol
6.4.4 Stability analysis
6.4.5 Simulation example 6.4
6.5 Notes
References
7 Advanced approaches to multiagent coordination
7.1 Synchronization of stochastic dynamic networks
7.1.1 Problem formulation
7.1.2 Design results
7.1.3 Simulation example 7.1
7.2 Observer-based consensus protocols
7.2.1 Problem formulation
7.3 Event-based tracking control
7.3.1 Introduction
7.3.2 Problem statement
7.3.3 Design results
7.3.4 Simulation example 7.2
7.4 Robust output regulation
7.4.1 Network model
7.4.2 Consensus protocol
7.4.3 Simulation example 7.3
7.5 Distributed networked control
7.5.1 Introduction
7.5.2 Problem statement
7.5.3 Distributed feedback scheme
7.5.4 Reliable observer-based protocol
7.5.5 Design procedure
7.5.6 Simulation example 7.4
7.6 Notes
References
8 State estimation techniques
8.1 Asynchronous multirate multismart sensors
8.1.1 Introduction
8.1.2 Problem formulation
8.1.3 Lossy channel
8.1.4 Dealing with delay
8.1.5 Fusion algorithm
8.1.6 Simulation example 8.1
8.1.7 Simulation example 8.2
8.2 Nonlinear state estimation
8.2.1 Introduction
8.2.2 Problem formulation
8.2.3 Analytic results
8.2.4 Design algorithm
8.2.5 Simulation example 8.3
8.3 Distributed filtering with saturation
8.3.1 Problem formulation
8.3.2 Design results
8.3.3 Simulation example 8.4
8.4 Notes
References
9 Advanced distributed filtering
9.1 Self-tuning Kalman filtering
9.1.1 Multisensor data fusion
9.1.2 Information fusion estimation
9.1.3 Problem formulation
9.1.4 Self-tuning distributed Kalman fusion filter
9.1.5 Distributed self-tuning Kalman filter without feedback
9.1.6 Optimality of self-tuning Kalman filter with feedback
9.1.7 Global optimality of the feedback filtering fusion
9.1.8 Simulation example 9.1
9.2 Kalman filtering with intermittent communications
9.2.1 Problem formulation
9.2.2 Impact of packet loss/intermittent communications
9.2.3 Modified centralized multisensor system
9.2.4 Process data collection
9.2.5 Model of the coupled-tank system
9.2.6 Evaluation of results
9.3 Information-based algorithms
9.3.1 Introduction
9.3.2 Problem formulation
9.4 Covariance intersection
9.5 Information-based covariance intersection filter
9.5.1 Algorithm
9.5.2 Complete feedback case
9.5.3 Partial feedback case
9.5.4 Weighted covariance
9.5.5 Weighted covariance filter algorithm
9.5.6 Weighted covariance filter: complete feedback case
9.5.7 Partial feedback case
9.5.8 Kalman-like particle filter
9.5.9 Kalman-like particle filter algorithm
9.5.10 Complete feedback case
9.5.11 Kalman-like particle filter: partial feedback case
9.5.12 Measurement fusion algorithm
9.5.13 Measurement fusion method
9.5.14 State vector fusion method
9.5.15 Functional equivalence results
9.6 Simulation example 9.2
9.6.1 Evaluation of results
9.6.2 Covariance intersection filter
9.6.3 Weighted covariance filter
9.6.4 Kalman-like particle filter
9.6.5 Mean square error comparison
9.7 Notes
References
Index
Back Cover
