scholarly journals Tracking control of ship course system using new six-step zead (Zhang et al discretization) formula with high precision

Filomat ◽  
2020 ◽  
Vol 34 (15) ◽  
pp. 5059-5071
Author(s):  
Jinjin Guo ◽  
Yunong Zhang ◽  
Binbin Qiu
Keyword(s):  
High Precision ◽  
Discrete Time ◽  
Tracking Control ◽  
Truncation Error ◽  
Sampling Period ◽  
Fourth Power ◽  
Scs Model ◽  
The Stability ◽  
Theoretical Analyses ◽  
Discrete Time Models

In this paper, firstly, a new six-step Zhang et al discretization (SSZeaD) formula is proposed, which is with the truncation error proportional to the fourth power of sampling period. Then, the SSZeaD formula is used to discretize a ship course system (SCS) for tracking control, and thus the SSZeaD-type SCS model is developed. For comparison purposes, the classical Euler forward formula (EFF) with the truncation error proportional to the first power of sampling period is also used to discretize the SCS, and thus the EFF-type SCS model is obtained. Besides, there is an important parameter called stepsize, which is closely related to the stability and the precision of the above two discrete-time models. In view of the importance of the stepsize, the effective stepsize domains of these two discrete-time models are confirmed by theoretical analyses. Finally, numerical experimental results well verify the higher tracking precision of the SSZeaD-type SCS model as compared with the EFF-type SCS model.

scholarly journals STOCHASTIC AND DISCRETE TIME MODELS OF LONG-RANGE TURBULENT TRANSPORT IN THE SCRAPE-OFF LAYER

2005 ◽  
Vol 19 (28) ◽  
pp. 4195-4218
Author(s):  
D. VOLCHENKOV ◽  
R. LIMA
Keyword(s):  
Discrete Time ◽  
Probability Distribution Function ◽  
Particle Flux ◽  
Particle Density ◽  
Turbulent Transport ◽  
Time Model ◽  
Stochastic Perturbations ◽  
The Stability ◽  
Stochastic Time ◽  
Discrete Time Models

The two dimensional stochastic time model of scrape-off layer (SOL) turbulent transport is studied. The instability arisen in the system with respect to the stochastic perturbations of both either density or vorticity reveals itself in the strong outward bursts of particle density propagating ballistically across the SOL. The stability and possible stabilization of the cross-field turbulent system depend very much upon the reciprocal correlation time between density and vorticity fluctuations. The probability distribution function (pdf) of the particle flux for the large magnitudes of flux events can be modeled with a simple discrete time toy model of random walks concluding at a boundary. The spectra of wandering times feature the pdf of particle flux in the model and qualitatively reproduce the experimental statistics of transport events.

Dynamics of Continuous Time and Related Discrete Time Economic Models / Dynamische Modelle mit stetiger Zeit und verwandte zeitdiskrete Modelle

1994 ◽  
Vol 213 (3) ◽  
Author(s):  
Herman J. Nieuwenhuis ◽  
Lambert Schoonbeek
Keyword(s):  
Discrete Time ◽  
Continuous Time ◽  
Economic Model ◽  
Dynamic Behaviour ◽  
Economic Models ◽  
Econometric Models ◽  
Stability Behaviour ◽  
Complex Eigenvalues ◽  
The Stability ◽  
Discrete Time Models

SummaryWe compare the dynamic behaviour of a given linear economic model with continuous time and two discrete time models derived from it. The latter two models with discrete time play an important role in the literature on econometric models with continuous time. We analyze and compare the eigenvalues of the models, and obtain results with respect to the stability behaviour and the periods of oscillations that arise in the case of complex eigenvalues.

scholarly journals Distributed Tracking Control for Discrete-Time Multiagent Systems with Novel Markovian Switching Topologies

2017 ◽  
Vol 2017 ◽  
pp. 1-10
Author(s):  
Hongbin Wang ◽  
Zhen Zhou ◽  
Zhongquan Hu
Keyword(s):  
Multiagent Systems ◽  
Discrete Time ◽  
Tracking Control ◽  
Sampling Period ◽  
Consensus Algorithm ◽  
Switching Topology ◽  
Tracking Errors ◽  
Control Gain ◽  
Leader Following ◽  
Coordinated Tracking

Distributed discrete-time coordinated tracking control problem is investigated for multiagent systems in the ideal case, where agents with a fixed graph combine with a leader-following group, aiming to expand the function of the traditional one in some scenes. The modified union switching topology is derived from a set of Markov chains to the edges by introducing a novel mapping. The issue on how to guarantee all the agents tracking the leader is solved through a PD-like consensus algorithm. The available sampling period and the feasible control gain are calculated in terms of the trigonometric function theory, and the mean-square bound of tracking errors is provided finally. Simulation example is presented to demonstrate the validity of the theoretical results.

CHAOTIC CONTROL USING FUZZY MODEL-BASED METHODS

2002 ◽  
Vol 12 (08) ◽  
pp. 1827-1841 ◽  
Author(s):  
KUANG-YOW LIAN ◽  
PETER LIU ◽  
TSU-CHENG WU ◽  
WEI-CHI LIN
Keyword(s):  
Discrete Time ◽  
Continuous Time ◽  
Tracking Control ◽  
Chaotic Systems ◽  
Reference Model ◽  
Fuzzy Model ◽  
Step Method ◽  
Fuzzy Models ◽  
Error System ◽  
The Stability

In this paper, we propose a fuzzy tracking control for chaotic systems with immeasurable states. First we represent the chaotic and reference systems into T–S fuzzy models. Some properties concerning the premise variable selection and controller placement for chaotic systems are discussed. When considering immeasurable states, an observer is designed along with the controller to track a reference model which is a fixed point, a stable nonlinear system, or a chaotic system. For different premise variables between the plant and reference models, a robust approach is used to deal with the problem. The conditions for dealing with the stability of the overall error system are formulated into LMIs. Since the simultaneous solution to both the controller and observer gains with disturbances are not trivial, a two-step method is utilized. The methodology proposed above is applied to both continuous-time and discrete-time chaotic systems. Two well-known examples, the Chua's circuit for continuous-time and Hénon map for discrete-time, are used in numerical simulations and DSP-based experiments. The results verify the validity of theoretical derivations.

scholarly journals On the Stability of the Endemic Equilibrium of A Discrete-Time Networked Epidemic Model

2020 ◽  
Vol 53 (2) ◽  
pp. 2576-2581
Author(s):  
Fangzhou Liu ◽  
Shaoxuan CUI ◽  
Xianwei Li ◽  
Martin Buss
Keyword(s):  
Discrete Time ◽  
Epidemic Model ◽  
Endemic Equilibrium ◽  
The Stability

scholarly journals Semiglobal exponential input-to-state stability of sampled-data systems based on approximate discrete-time models

Automatica ◽  
2021 ◽  
Vol 131 ◽  
pp. 109742
Author(s):  
Alexis J. Vallarella ◽  
Paula Cardone ◽  
Hernan Haimovich
Keyword(s):  
Discrete Time ◽  
Data Systems ◽  
Sampled Data ◽  
Discrete Time Models

scholarly journals High-Precision RTT-Based Indoor Positioning System Using RCDN and RPN

Sensors ◽  
2021 ◽  
Vol 21 (11) ◽  
pp. 3701
Author(s):  
Ju-Hyeon Seong ◽  
Soo-Hwan Lee ◽  
Won-Yeol Kim ◽  
Dong-Hoan Seo
Keyword(s):  
High Precision ◽  
Distance Estimation ◽  
Sampling Period ◽  
Multipath Fading ◽  
Indoor Positioning ◽  
Positioning System ◽  
Positioning Systems ◽  
Positioning Errors ◽  
Location Determination ◽  
Indoor Positioning System

Wi-Fi round-trip timing (RTT) was applied to indoor positioning systems based on distance estimation. RTT has a higher reception instability than the received signal strength indicator (RSSI)-based fingerprint in non-line-of-sight (NLOS) environments with many obstacles, resulting in large positioning errors due to multipath fading. To solve these problems, in this paper, we propose high-precision RTT-based indoor positioning system using an RTT compensation distance network (RCDN) and a region proposal network (RPN). The proposed method consists of a CNN-based RCDN for improving the prediction accuracy and learning rate of the received distances and a recurrent neural network-based RPN for real-time positioning, implemented in an end-to-end manner. The proposed RCDN collects and corrects a stable and reliable distance prediction value from each RTT transmitter by applying a scanning step to increase the reception rate of the TOF-based RTT with unstable reception. In addition, the user location is derived using the fingerprint-based location determination method through the RPN in which division processing is applied to the distances of the RTT corrected in the RCDN using the characteristics of the fast-sampling period.

scholarly journals Stability of a one-dimensional morphoelastic model for post-burn contraction

2021 ◽  
Vol 83 (3) ◽  
Author(s):  
Ginger Egberts ◽  
Fred Vermolen ◽  
Paul van Zuijlen
Keyword(s):  
Wound Healing ◽  
Residual Stresses ◽  
Truncation Error ◽  
Signaling Molecules ◽  
Discrete Problem ◽  
One Dimensional ◽  
Stability Constraint ◽  
Biological Interpretation ◽  
The Stability ◽  
The One

AbstractTo deal with permanent deformations and residual stresses, we consider a morphoelastic model for the scar formation as the result of wound healing after a skin trauma. Next to the mechanical components such as strain and displacements, the model accounts for biological constituents such as the concentration of signaling molecules, the cellular densities of fibroblasts and myofibroblasts, and the density of collagen. Here we present stability constraints for the one-dimensional counterpart of this morphoelastic model, for both the continuous and (semi-) discrete problem. We show that the truncation error between these eigenvalues associated with the continuous and semi-discrete problem is of order $${{\mathcal {O}}}(h^2)$$ O ( h 2 ) . Next we perform numerical validation to these constraints and provide a biological interpretation of the (in)stability. For the mechanical part of the model, the results show the components reach equilibria in a (non) monotonic way, depending on the value of the viscosity. The results show that the parameters of the chemical part of the model need to meet the stability constraint, depending on the decay rate of the signaling molecules, to avoid unrealistic results.

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