Hybrid Dynamical Systems (eBook)

Modeling, Stability, and Robustness

Rafal Goebel, Ricardo G. Sanfelice, Andrew R. Teel (Autoren)

eBook Download: EPUB

2012
232 Seiten
Princeton University Press (Verlag)
978-1-4008-4263-6 (ISBN)

Infos

Hybrid dynamical systems exhibit continuous and instantaneous changes, having features of continuous-time and discrete-time dynamical systems. Filled with a wealth of examples to illustrate concepts, this book presents a complete theory of robust asymptotic stability for hybrid dynamical systems that is applicable to the design of hybrid control algorithms--algorithms that feature logic, timers, or combinations of digital and analog components. With the tools of modern mathematical analysis, Hybrid Dynamical Systems unifies and generalizes earlier developments in continuous-time and discrete-time nonlinear systems. It presents hybrid system versions of the necessary and sufficient Lyapunov conditions for asymptotic stability, invariance principles, and approximation techniques, and examines the robustness of asymptotic stability, motivated by the goal of designing robust hybrid control algorithms. This self-contained and classroom-tested book requires standard background in mathematical analysis and differential equations or nonlinear systems. It will interest graduate students in engineering as well as students and researchers in control, computer science, and mathematics.

Autor

Rafal Goebel is an assistant professor in the Department of Mathematics and Statistics at Loyola University, Chicago. Ricardo G. Sanfelice is an assistant professor in the Department of Aerospace and Mechanical Engineering at the University of Arizona. Andrew R. Teel is a professor in the Electrical and Computer Engineering Department at the University of California, Santa Barbara.

Produkt-Details

• Erscheint lt. Verlag: 18.3.2012
• Zusatzinfo: 45 line illus.
• Verlagsort: Princeton
• Sprache: englisch
• Themenwelt: Mathematik / Informatik ► Mathematik ► Algebra
• Themenwelt: Mathematik / Informatik ► Mathematik ► Analysis
• Themenwelt: Mathematik / Informatik ► Mathematik ► Angewandte Mathematik
• Themenwelt: Technik
• Schlagworte: absolute continuity • algorithm • angular frequency • Approximation • Arbitrarily large • asymptotic stability • Bolzano–Weierstrass theorem • boundedness • Classical control theory • closed sets • combination • compact sets • Compact space • conical approximation • conical hybrid system • Continuity Properties • continuous function • Continuous function (set theory) • Continuous Time • continuous-time systems • Contradiction • Control Theory • convex function • convex set • corollary • data structure • detection • Differentiable function • differential equation • Differential Equations • differential inclusion • differential inclusions • Differentiation under the integral sign • Discrete Time • Discrete time and continuous time • Discrete-time systems • Dissipation • Domain of a function • Double integrator • Dynamical system • Dynamical Systems • Embedding • empty set • Equation • Equilibrium Point • Equilibrium Points • estimation • Euclidean space • existential quantification • flow map • flow set • Generalized Solutions • graphical convergence • hausdorff distance • Hermes solutions • hybrid arcs • hybrid automaton • hybrid control algorithms • hybrid dynamical systems • hybrid feedback control • Hybrid Models • hybrid system • hybrid time domains • Hysteresis • Inductance • Infimum and supremum • Initial Condition • Initial point • Integrator • invariance principles • jump map • jump set • Krasovskii regularization • Krasovskii solutions • Limit of a sequence • Limit point • _-limit sets • Limit superior and limit inferior • Linear Function • Linearization • Linear map • Lipschitz continuity • Local boundedness • Lyapunov conditions • Lyapunov function • Lyapunov functions • Lyapunov-like functions • Lyapunov stability • Mathematical Optimization • Measurement • Modeling • modeling frameworks • Monotonic Function • Newton's cradle • nonlinear system • Nonlinear Systems • Norm (mathematics) • Notation • Numerical simulations • output function • Parameter • parametrization • partial derivative • Pointwise • pre-asymptotically stable sets • pre-asymptotic stability • precompact solutions • Quantity • Quantization (signal processing) • Quasinorm • Rate of Convergence • regularity properties • Regularization (mathematics) • Requirement • resistor • Robustness • Sampling (signal processing) • Semi-continuity • Sequence • servomechanism • set convergence • Set (mathematics) • set-valued analysis • Set-valued mappings • smoothing • smooth Lyapunov function • Smoothness • solution concept • Special case • Stability Theory • state measurement error • state perturbations • State Space • state variable • step function • subsequence • Subset • switching signals • Switching systems • Symmetric matrix • tangent cone • Theorem • Thyristor • time domain • Timer • transient response • uniform asymptotic stability • uniform boundedness • uniform convergence • uniqueness • Variable (mathematics) • well-posed hybrid systems • Well-Posedness • Well-posed Problems • Without loss of generality • Zero-order hold • ω-limit sets
• ISBN-10: 1-4008-4263-8 / 1400842638
• ISBN-13: 978-1-4008-4263-6 / 9781400842636