Two-Dimensional Hybrid Dynamical Systems

2000 ◽  
pp. 105-218
Author(s):  
Alexey S. Matveev ◽  
Andrey V. Savkin
Keyword(s):  
Dynamical Systems ◽  
Hybrid Dynamical Systems ◽  
Two Dimensional

Integrable two-dimensional dynamical systems and the characteristic Lie algebras

2007 ◽  
Vol 5 ◽  
pp. 195-200
Author(s):  
A.V. Zhiber ◽  
O.S. Kostrigina
Keyword(s):  
Dynamical System ◽  
Dynamical Systems ◽  
Lie Algebra ◽  
Lie Algebras ◽  
Second Order ◽  
System Of Equations ◽  
Two Dimensional ◽  
Finite Dimensional ◽  
Dimensional Dynamical System

In the paper it is shown that the two-dimensional dynamical system of equations is Darboux integrable if and only if its characteristic Lie algebra is finite-dimensional. The class of systems having a full set of fist and second order integrals is described.

scholarly journals The Salted Kalman Filter: Kalman filtering on hybrid dynamical systems

Automatica ◽  
2021 ◽  
Vol 131 ◽  
pp. 109752
Author(s):  
Nathan J. Kong ◽  
J. Joe Payne ◽  
George Council ◽  
Aaron M. Johnson
Keyword(s):  
Kalman Filter ◽  
Dynamical Systems ◽  
Kalman Filtering ◽  
Hybrid Dynamical Systems

A STUDY OF BIFURCATIONS IN A CIRCULAR REAL CELLULAR AUTOMATON

1993 ◽  
Vol 03 (02) ◽  
pp. 293-321 ◽  
Author(s):  
JÜRGEN WEITKÄMPER
Keyword(s):  
Hopf Bifurcation ◽  
Dynamical Systems ◽  
Cellular Automata ◽  
Cellular Automaton ◽  
Parallel Computers ◽  
Discrete Dynamical Systems ◽  
Two Dimensional ◽  
Bifurcation Structure ◽  
Logistic Mapping ◽  
Henon Mapping

Real cellular automata (RCA) are time-discrete dynamical systems on ℝN. Like cellular automata they can be obtained from discretizing partial differential equations. Due to their structure RCA are ideally suited to implementation on parallel computers with a large number of processors. In a way similar to the Hénon mapping, the system we consider here embeds the logistic mapping in a system on ℝN, N>1. But in contrast to the Hénon system an RCA in general is not invertible. We present some results about the bifurcation structure of such systems, mostly restricting ourselves, due to the complexity of the problem, to the two-dimensional case. Among others we observe cascades of cusp bifurcations forming generalized crossroad areas and crossroad areas with the flip curves replaced by Hopf bifurcation curves.

scholarly journals Identification of a Class of Hybrid Dynamical Systems

2020 ◽  
Vol 53 (2) ◽  
pp. 875-882
Author(s):  
Stefano Massaroli ◽  
Federico Califano ◽  
Angela Faragasso ◽  
Mattia Risiglione ◽  
Atsushi Yamashita ◽  
...  
Keyword(s):  
Dynamical Systems ◽  
Hybrid Dynamical Systems

scholarly journals Stability analysis and controller synthesis for hybrid dynamical systems

2010 ◽  
Vol 368 (1930) ◽  
pp. 4937-4960 ◽  
Author(s):  
W. P. M. H. Heemels ◽  
B. De Schutter ◽  
J. Lunze ◽  
M. Lazar
Keyword(s):  
Dynamical Systems ◽  
Mathematical Models ◽  
Hybrid Systems ◽  
Discrete Event ◽  
Research Area ◽  
Hybrid Dynamical Systems ◽  
Technological Systems ◽  
Analysis And Synthesis ◽  
Control Community ◽  
The One

Wherever continuous and discrete dynamics interact, hybrid systems arise. This is especially the case in many technological systems in which logic decision-making and embedded control actions are combined with continuous physical processes. Also for many mechanical, biological, electrical and economical systems the use of hybrid models is essential to adequately describe their behaviour. To capture the evolution of these systems, mathematical models are needed that combine in one way or another the dynamics of the continuous parts of the system with the dynamics of the logic and discrete parts. These mathematical models come in all kinds of variations, but basically consist of some form of differential or difference equations on the one hand and automata or other discrete-event models on the other hand. The collection of analysis and synthesis techniques based on these models forms the research area of hybrid systems theory, which plays an important role in the multi-disciplinary design of many technological systems that surround us. This paper presents an overview from the perspective of the control community on modelling, analysis and control design for hybrid dynamical systems and surveys the major research lines in this appealing and lively research area.

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