Supervisory Control of Dynamical Systems With Uncertain Time Delays

2010 ◽  
Vol 132 (6) ◽  
Author(s):  
Bo Song ◽  
Jian-Qiao Sun
Keyword(s):  
Time Delay ◽  
Dynamical Systems ◽  
Supervisory Control ◽  
Time Delays ◽  
Control Algorithm ◽  
Control Design ◽  
Theoretical Work ◽  
Mapping Method ◽  
Upper And Lower Bounds ◽  
Uncertain Time

A study of controlling dynamical systems with uncertain and varying time delays is presented in this paper. The uncertain time delay is assumed to fall in a range with known upper and lower bounds. We apply the supervisory control algorithm to deal with uncertainties in the time delay. An index is defined for each of the predetermined controls for a discrete set of time delays sampled from the range. Based on this index, a hysteretic switching rule selects a control from the predetermined controls with optimal feedback gains. Each predetermined control must be stable for any time delay in the range. Two control design methods are discussed, namely, the mapping method and a higher order approach. Examples of linear systems are used to demonstrate the theoretical work.

Supervisory Control of Dynamical Systems With Uncertain Time Delays

2009 ◽  
Author(s):  
Bo Song ◽  
Jian-Qiao Sun
Keyword(s):  
Time Delay ◽  
Dynamical Systems ◽  
Supervisory Control ◽  
Time Delays ◽  
Linear Time ◽  
Theoretical Work ◽  
Linear Time Invariant ◽  
Uncertain Time ◽  
Linear Time Invariant System ◽  
Time Invariant

This paper presents a study of controlling dynamical systems with uncertain and varying time delays. We apply the supervisory control algorithm to handle uncertainties in time delay. The hysteretic switching rule selects control gains out of the set of pre-determined optimal feedback gains for certain time delays in a range with known lower and upper bounds. The criterion is to judge when the system stays stable for any gains being selected and has a smaller switching index when the uncertain time delay varies in a known interval. A linear time-invariant system is used as an example to demonstrate the theoretical work.

Optimally designed Lyapunov–Krasovskii terminal costs for robust stable–feasible model predictive control of uncertain time-delay nonlinear dynamical systems

2020 ◽  
pp. 095965182095219
Author(s):  
S Yaqubi ◽  
MR Homaeinezhad
Keyword(s):  
Time Delay ◽  
Dynamical Systems ◽  
Model Predictive Control ◽  
Predictive Control ◽  
Robust Stability ◽  
Control Algorithm ◽  
Nonlinear Dynamical Systems ◽  
Prediction Horizon ◽  
Delay Effects ◽  
Uncertain Time

This article details a new Model Predictive Control algorithm ensuring robust stability and control feasibility for uncertain nonlinear multi-input multi-output dynamical systems considering uncertain time-delay effects. The proposed control algorithm is based on construction of a Lyapunov–Krasovskii functional as terminal cost. Incorporation of this terminal cost into the Model Predictive Control optimization problem and calculation of the associated admissible set result in robust feasibility and robust stability of closed-loop system in presence of uncertain time-delay effects and bounded disturbance signals. The Lyapunov–Krasovskii functional term is constructed with respect to predicted sliding functions over the prediction horizon and considers the effects of dynamical variations over the prediction horizon in generation of control inputs. As dynamical variations are investigated in a sample-to-sample basis, feasible sliding regions are updated at each sample as well. Finally, based on expression of sliding functions as a combination of dynamical variations and input-based terms, required control inputs are calculated in the admissible bound by the optimization algorithm. Construction of control scheme on this basis permits straightforward calculation of robust stability and feasibility conditions for a general class of uncertain nonlinear system in finite prediction horizon whereas in the previous works, often-restrictive conditions were considered for the investigated dynamical systems. Numerical illustrations indicate precision and efficiency of control algorithm and improved stability and convergence rate for multivariable nonlinear dynamical systems considering uncertain time-delay effects. Finally, hardware-in-the-loop implementation indicates applicability of the proposed scheme in real-time control applications particularly in case appropriate compromises between optimality and calculation speed are considered.

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’.

scholarly journals Determination of the time scale of photoemission from the measurement of spin polarization

2018 ◽  
Vol 5 (6) ◽  
Author(s):  
Mauro Fanciulli ◽  
Hugo Dil
Keyword(s):  
Experimental Data ◽  
Time Delay ◽  
Matrix Element ◽  
Spin Polarization ◽  
Time Delays ◽  
Upper And Lower Bounds ◽  
Recent Experimental Data ◽  
The Matrix ◽  
Phase Term

The Eisenbud-Wigner-Smith (EWS) time delay of photoemission depends on the phase term of the matrix element describing the transition. Because of an interference process between partial channels, the photoelectrons acquire a spin polarization which is also related to the phase term. The analytical model for estimating the time delay by measuring the spin polarization is reviewed in this manuscript. In particular, the distinction between scattering EWS and interfering EWS time delay will be introduced, providing an insight in the chronoscopy of photoemission. The method is applied to the recent experimental data for Cu(111) presented in M. Fanciulli et al., PRL 118, 067402 (2017), allowing to give better upper and lower bounds and estimates for the EWS time delays.

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