Large-Scale Dynamic Systems: Stability and Structure

Large-Scale Dynamic Systems: Stability and Structure

by Dragoslav D. Siljak


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The unique interdisciplinary approach examines relationship between stability and structure of complex dynamic systems.  Its application ranges from competitive-cooperative models in ecology and economics to control of spacecraft and power systems.The author, a Professor of Electrical Engineering at California's Santa Clara University, defines large-scale systems as nonlinear and time-varying interaction of dynamic subsystems.  Stability of the overall system is determined from stability properties of the subsystems and the nature of their interconnections.  The concept of decentralized control and estimation is introduced for efficient stabilization and optimization of complex systems using local subsystem feedback and vector Liapunov methods.  Decentrally stabilized large systems are robust to uncertainty in the interconnection structure and environmental fluctuations.  Appropriate for graduate students studying multi-agent systems in engineering, ecology, economics, and sustainability of complex systems; this volume is also a valuable resource for engineers working in control of spacecraft, large power networks, and networked multi-robot systems.

Product Details

ISBN-13: 9780486462851
Publisher: Dover Publications
Publication date: 11/12/2007
Series: Dover Civil and Mechanical Engineering Series
Pages: 448
Product dimensions: 5.30(w) x 8.40(h) x 0.90(d)

Table of Contents

Preface     ix
Errata     xv
Introduction: Stability, Complexity, Reliability     1
Competition     2
Structure     5
Stability     9
Comparison Principle     15
Connective Stability     17
Cooperation     20
Decomposition     24
Aggregation     32
Decentralization     42
Synthesis     49
References     58
Analysis: Connective Stability     63
Structural Perturbations     65
Connective Stability     68
Differential Inequalities     74
Vector Liapunov Functions     81
Large-Scale Dynamic Systems     88
Partial Connective Stability     113
Connective Instability     126
Regions of Connective Stability     132
References     138
Synthesis: Decentralized Control     145
Reachability, Vulnerability, and Condensations     147
Decentralization     165
Stabilization     171
Estimation     192
Optimization     199
References     214
Economics:Competitive Equilibrium     219
Commodities and Prices: Demand Functions     222
A Dynamic Model     225
Connective Stability: Linear Case     228
Connective Stability: Nonlinear Case     234
Nonstationary Models: Moving Equilibrium     241
A Stochastic Model     250
Discrete Models     254
Composite Commodities: A Hierarchic Model     260
References     263
Ecology: Multispecies Communities     269
Linear Constant Models     271
Nonlinear Models: Linearization     276
Nonlinear Matrix Models     279
Stability Regions     285
Lotka-Volterra Model     287
Instability     294
Environmental Fluctuations     297
Stochastic Models: Stability     302
Stochastic Models: Instability     312
Hierarchic Models     315
References     322
Engineering: Spacecraft Control Systems     327
Large Space Telescope: A Model     328
Bilinear Systems: Local Stabilization     335
Stabilization of LST     338
Optimal Control of LST     340
Maximization of Structural Parameters     343
Stabilization of the Skylab     352
References     361
Engineering: Power Systems     363
Transient Stability     364
A Model and Decomposition     366
Subsystem Analysis     369
Stability Region     374
Three-Machine System     378
Automatic Generation Control     379
A Decentralized Model     381
Regulator Design     384
References     390
Matrices     394
References     406
Index     409

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