Dynamical complexities of forced impacting systems

1992 ◽  
Vol 338 (1651) ◽  
pp. 547-556 ◽  
Keyword(s):  
Dynamical System ◽  
Discrete Time ◽  
Continuous Time ◽  
Linear Oscillator ◽  
Nonlinear Behaviour ◽  
Engineering Applications ◽  
Poincaré Maps ◽  
The Impact ◽  
Derivatives Of ◽  
Impacting Systems

The model of a forced linear oscillator with instantaneous impacts at one or two stops is discussed. The nonlinearities introduced by the instantaneous impact rule are sufficient to cause typical nonlinear behaviour. The impact rule is discontinuous, introducing discontinuities into discrete time Poincaré maps defined from the continuous time dynamical system. Discontinuities also exist in the derivatives of these maps. The implications of these discontinuities are discussed and their relevance to engineering applications is assessed with suggestions for further research.

scholarly journals Optimal measurement budget allocation for Kalman prediction over a finite time horizon by genetic algorithms

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Antoine Aspeel ◽  
Axel Legay ◽  
Raphaël M. Jungers ◽  
Benoit Macq
Keyword(s):  
Genetic Algorithm ◽  
Discrete Time ◽  
Continuous Time ◽  
Estimation Error ◽  
Budget Allocation ◽  
Finite Horizon ◽  
Time Step ◽  
Optimal Measurement ◽  
Discrete Time Dynamical System ◽  
The Impact

AbstractIn this paper, we address the problem of optimal measurement budget allocation to estimate the state of a linear discrete-time dynamical system over a finite horizon. More precisely, our aim is to select the measurement times in order to minimize the variance of the estimation error over a finite horizon. In addition, we investigate the closely related problem of finding a trade-off between number of measurements and signal to noise ratio.First, the optimal measurement budget allocation problem is reduced to a deterministic combinatorial program. Then, we propose a genetic algorithm implementing a count preserving crossover to solve it. On the theoretical side, we provide a one-dimensional analysis that indicates that the benefit of using irregular measurements grows when the system is unstable or when the process noise becomes important. Then, using the duality between estimation and control, we show that the problem of selecting optimal control times for a linear quadratic regulator can be reduced to our initial problem.Finally, numerical implementations demonstrate that using measurement times optimized by our genetic algorithm gives better estimate than regularly spaced measurements. Our method is applied to a discrete version of a continuous-time system and the impact of the discretization time step is studied. It reveals good convergence properties, showing that our method is well suited to both continuous-time and discrete-time setups.

Latent heat storage for hot beverages

2019 ◽  
Vol 13 (3) ◽  
pp. 5653-5664
Author(s):  
M. S. M. Al-Jethelah ◽  
H. S. Dheyab ◽  
S. Khudhayer ◽  
T. K. Ibrahim ◽  
A. T. Al-Sammarraie
Keyword(s):  
Latent Heat ◽  
Food Industry ◽  
Heat Storage ◽  
Food Storage ◽  
Thermal Engineering ◽  
Engineering Applications ◽  
Latent Heat Storage ◽  
The Impact ◽  
Encapsulated Phase Change Material ◽  
Change Material

Latent heat storage has shown a great potential in many engineering applications. The utilization of latent heat storage has been extended from small scales to large scales of thermal engineering applications. In food industry, latent heat has been applied in food storage. Another potential application of latent heat storage is to maintain hot beverages at a reasonable drinking temperature for longer periods. In the present work, a numerical calculation was performed to investigate the impact of utilizing encapsulated phase change material PCM on the temperature of hot beverage. The PCM was encapsulated in rings inside the cup. The results showed that the encapsulated PCM reduced the coffee temperature to an acceptable temperature in shorter time. In addition, the PCM maintained the hot beverage temperature at an acceptable drinking temperature for rational time.

Design of Programmable Wideband Low Pass Filter with Continuous-Time/Discrete-Time Hybrid Architecture

2017 ◽  
Vol E100.C (10) ◽  
pp. 858-865 ◽  
Author(s):  
Yohei MORISHITA ◽  
Koichi MIZUNO ◽  
Junji SATO ◽  
Koji TAKINAMI ◽  
Kazuaki TAKAHASHI
Keyword(s):  
Discrete Time ◽  
Continuous Time ◽  
Hybrid Architecture ◽  
Pass Filter ◽  
Low Pass Filter ◽  
Low Pass

scholarly journals Time to Intervene: A Continuous-Time Approach to Network Analysis and Centrality

Psychometrika ◽  
2021 ◽  
Author(s):  
Oisín Ryan ◽  
Ellen L. Hamaker
Keyword(s):  
Network Analysis ◽  
Discrete Time ◽  
Continuous Time ◽  
Centrality Measures ◽  
Time Interval ◽  
Direct Effects ◽  
Network Approach ◽  
Var Models ◽  
Auto Regressive ◽  
Conceptual Shift

AbstractNetwork analysis of ESM data has become popular in clinical psychology. In this approach, discrete-time (DT) vector auto-regressive (VAR) models define the network structure with centrality measures used to identify intervention targets. However, VAR models suffer from time-interval dependency. Continuous-time (CT) models have been suggested as an alternative but require a conceptual shift, implying that DT-VAR parameters reflect total rather than direct effects. In this paper, we propose and illustrate a CT network approach using CT-VAR models. We define a new network representation and develop centrality measures which inform intervention targeting. This methodology is illustrated with an ESM dataset.

scholarly journals Trajectory representation and landmark projection for continuous-time structure from motion

2019 ◽  
Vol 38 (6) ◽  
pp. 686-701 ◽  
Author(s):  
Hannes Ovrén ◽  
Per-Erik Forssén
Keyword(s):  
Structure From Motion ◽  
Continuous Time ◽  
Spline Interpolation ◽  
Time Structure ◽  
Robot Arm ◽  
Good Sense ◽  
Trajectory Representation ◽  
Inertial Measurements ◽  
Derivatives Of ◽  
Fusion Framework

This paper revisits the problem of continuous-time structure from motion, and introduces a number of extensions that improve convergence and efficiency. The formulation with a [Formula: see text]-continuous spline for the trajectory naturally incorporates inertial measurements, as derivatives of the sought trajectory. We analyze the behavior of split spline interpolation on [Formula: see text] and on [Formula: see text], and a joint spline on [Formula: see text], and show that the latter implicitly couples the direction of translation and rotation. Such an assumption can make good sense for a camera mounted on a robot arm, but not for hand-held or body-mounted cameras. Our experiments in the Spline Fusion framework show that a split spline on [Formula: see text] is preferable over an [Formula: see text] spline in all tested cases. Finally, we investigate the problem of landmark reprojection on rolling shutter cameras, and show that the tested reprojection methods give similar quality, whereas their computational load varies by a factor of two.

On quasi-stationary distributions in absorbing continuous-time finite Markov chains

1967 ◽  
Vol 4 (1) ◽  
pp. 192-196 ◽  
Author(s):  
J. N. Darroch ◽  
E. Seneta
Keyword(s):  
Markov Chains ◽  
Discrete Time ◽  
Continuous Time ◽  
Present Note ◽  
Time Parameter ◽  
Stationary Distributions ◽  
Finite State ◽  
Absorbing Markov Chains ◽  
Finite Markov Chains ◽  
Finite State Space

In a recent paper, the authors have discussed the concept of quasi-stationary distributions for absorbing Markov chains having a finite state space, with the further restriction of discrete time. The purpose of the present note is to summarize the analogous results when the time parameter is continuous.

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