Adaptive stabilizing state feedback controllers of uncertain dynamical systems with multiple time delays

2000 ◽  
Vol 45 (9) ◽  
pp. 1697-1701 ◽  
Author(s):  
H. Wu
Keyword(s):  
Dynamical Systems ◽  
Time Delays ◽  
State Feedback ◽  
Multiple Time ◽  
Feedback Controllers ◽  
Uncertain Dynamical Systems ◽  
Multiple Time Delays

scholarly journals Delayed dynamical systems: networks, chimeras and reservoir computing

2019 ◽  
Vol 377 (2153) ◽  
pp. 20180123 ◽  
Author(s):  
Joseph D. Hart ◽  
Laurent Larger ◽  
Thomas E. Murphy ◽  
Rajarshi Roy
Keyword(s):  
Time Delay ◽  
Dynamical Systems ◽  
System Dynamics ◽  
Coupled Oscillators ◽  
Time Delays ◽  
Delay Systems ◽  
Multiple Time ◽  
Reservoir Computing ◽  
Multiple Time Delays ◽  
Network Topologies

We present a systematic approach to reveal the correspondence between time delay dynamics and networks of coupled oscillators. After early demonstrations of the usefulness of spatio-temporal representations of time-delay system dynamics, extensive research on optoelectronic feedback loops has revealed their immense potential for realizing complex system dynamics such as chimeras in rings of coupled oscillators and applications to reservoir computing. Delayed dynamical systems have been enriched in recent years through the application of digital signal processing techniques. Very recently, we have showed that one can significantly extend the capabilities and implement networks with arbitrary topologies through the use of field programmable gate arrays. This architecture allows the design of appropriate filters and multiple time delays, and greatly extends the possibilities for exploring synchronization patterns in arbitrary network topologies. This has enabled us to explore complex dynamics on networks with nodes that can be perfectly identical, introduce parameter heterogeneities and multiple time delays, as well as change network topologies to control the formation and evolution of patterns of synchrony. This article is part of the theme issue ‘Nonlinear dynamics of delay systems’.

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