scholarly journals Nonlinear Min-Cost-Pursued Route-Swapping Dynamic System

2013 ◽  
Vol 2013 ◽  
pp. 1-10 ◽  
Author(s):  
Wenyi Zhang ◽  
Wei Guan ◽  
Jihui Ma ◽  
Tao Wang
Keyword(s):  
Discrete Time ◽  
Continuous Time ◽  
User Equilibrium ◽  
Adjustment Process ◽  
Rational Behavior ◽  
Traffic Network ◽  
Selfish Routing ◽  
Numerical Examples ◽  
The Stability ◽  
Routing Games

This study proposes a nonlinear min-cost-pursued swapping dynamic (NMSD) system to model the evolution of selfish routing games on traffic network where travelers only swap from previous costly routes to the least costly ones. NMSD is a rational behavior adjustment process with stationary link flow pattern being the Wardrop user equilibrium. NMSD is able to prevent two behavioral deficiencies suffered by the existing min-cost-oriented models and keep solution invariance. NMSD relaxes the homogeneous user assumption, and the continuous-time NMSD (CNMSD) and discrete-time NMSD (DNMSD) share the same revision protocol. Moreover, CNMSD is Lyapunov-stable. Two numerical examples are conducted. The first one is designed to characterize the NMSD-conducted network traffic evolution and test the stability of day-to-day NMSD. The second one aims to explore the impacts of network scale on the stability of route-swaps conducted by pairwise and min-cost-pursed swapping behaviors.

Stability of real-time hybrid simulation involving time-varying delay and direct integration algorithms

2021 ◽  
pp. 107754632110016
Author(s):  
Liang Huang ◽  
Cheng Chen ◽  
Shenjiang Huang ◽  
Jingfeng Wang
Keyword(s):  
Real Time ◽  
Discrete Time ◽  
Continuous Time ◽  
Hybrid Simulation ◽  
Time Varying ◽  
Discrete Time System ◽  
Time System ◽  
Integration Algorithms ◽  
The Stability ◽  
Continuous Time System

Stability presents a critical issue for real-time hybrid simulation. Actuator delay might destabilize the real-time test without proper compensation. Previous research often assumed real-time hybrid simulation as a continuous-time system; however, it is more appropriately treated as a discrete-time system because of application of digital devices and integration algorithms. By using the Lyapunov–Krasovskii theory, this study explores the convoluted effect of integration algorithms and actuator delay on the stability of real-time hybrid simulation. Both theoretical and numerical analysis results demonstrate that (1) the direct integration algorithm is preferably used for real-time hybrid simulation because of its computational efficiency; (2) the stability analysis of real-time hybrid simulation highly depends on actuator delay models, and the actuator model that accounts for time-varying characteristic will lead to more conservative stability; and (3) the integration step is constrained by the algorithm and structural frequencies. Moreover, when the step is small, the stability of the discrete-time system will approach that of the corresponding continuous-time system. The study establishes a bridge between continuous- and discrete-time systems for stability analysis of real-time hybrid simulation.

scholarly journals Pinning Synchronization of Nonlinearly Coupled Complex Dynamical Networks on Time Scales

2020 ◽  
Vol 2020 ◽  
pp. 1-12
Author(s):  
Fang-Di Kong
Keyword(s):  
Time Scales ◽  
Discrete Time ◽  
Control Strategy ◽  
Continuous Time ◽  
General Framework ◽  
Pinning Control ◽  
Complex Dynamical Networks ◽  
Dynamical Networks ◽  
Numerical Examples ◽  
Synchronization Problem

In this paper, we study the synchronization problem for nonlinearly coupled complex dynamical networks on time scales. To achieve synchronization for nonlinearly coupled complex dynamical networks on time scales, a pinning control strategy is designed. Some pinning synchronization criteria are established for nonlinearly coupled complex dynamical networks on time scales, which guarantee the whole network can be pinned to some desired state. The model investigated in this paper generalizes the continuous-time and discrete-time nonlinearly coupled complex dynamical networks to a unique and general framework. Moreover, two numerical examples are given for illustration and verification of the obtained results.

scholarly journals Practical and asymptotic stability of fractional discrete-time scalar systems described by a new model

2016 ◽  
Vol 26 (4) ◽  
pp. 441-452 ◽  
Author(s):  
Andrzej Ruszewski
Keyword(s):  
Asymptotic Stability ◽  
Discrete Time ◽  
Sufficient Conditions ◽  
Numerical Examples ◽  
New Model ◽  
The Stability ◽  
Partition Method ◽  
Necessary And Sufficient ◽  
Time Linear ◽  
Linear Scalar

Abstract The stability problems of fractional discrete-time linear scalar systems described by the new model are considered. Using the classical D-partition method, the necessary and sufficient conditions for practical stability and asymptotic stability are given. The considerations are il-lustrated by numerical examples.

scholarly journals Entwurf von zeitkontinuierlichen ΣΔ-Modulatoren – Äquivalenz zwischen zeitkontinuierlichen und zeitdiskreten Systemen

2007 ◽  
Vol 5 ◽  
pp. 221-224
Author(s):  
J. Anders ◽  
W. Mathis ◽  
M. Ortmanns
Keyword(s):  
Stability Analysis ◽  
Discrete Time ◽  
Input Signal ◽  
Continuous Time ◽  
Wird Eine ◽  
Loop Delay ◽  
Discrete Time Systems ◽  
Excess Loop Delay ◽  
The Stability ◽  
Time Systems

Abstract. Im vorliegenden Artikel wird eine vollstängige, d.h. unter Einbeziehung des Eingangssignals, Äquivalenz zwischen zeitkontinuierlichen und zeitdiskreten ΣΔ-Modulatoren im Zustandsraum hergeleitet. Es wird ebenfalls gezeigt, wie eine wichtige Nichtidealität, das sog. "excess loop delay", in den Berechnungen berücksichtigt werden kann. Die dargestellte Methode dient dazu, den Entwurf und dabei vor allem die Stabilitätsuntersuchungen, von zeitkontinuierlichen ΣΔs auf die bereits empirisch intensiv erforschten zeitdiskreten Systeme zurückzuführen. In the article at hand a complete equivalency, i.e. including the input signal, between continuous-time and discrete-time ΣΔ-modulators in state-space is derived. In addition, it is shown, how one can incorporate the important non-ideality of "excess loop delay" into the formalism. The method introduced is supposed to facilitate the design, especially the stability analysis part of the design, of continuous-time ΣΔs by making use of the empirically thoroughly examined discrete-time systems.

scholarly journals Descriptor fractional linear systems with regular pencils

2013 ◽  
Vol 23 (2) ◽  
pp. 309-315 ◽  
Author(s):  
Tadeusz Kaczorek
Keyword(s):  
Laplace Transform ◽  
Linear Systems ◽  
Discrete Time ◽  
Continuous Time ◽  
The State ◽  
Transition Matrices ◽  
State Equations ◽  
Numerical Examples ◽  
The Laplace Transform ◽  
Time Linear

Methods for finding solutions of the state equations of descriptor fractional discrete-time and continuous-time linear systems with regular pencils are proposed. The derivation of the solution formulas is based on the application of the Z transform, the Laplace transform and the convolution theorems. Procedures for computation of the transition matrices are proposed. The efficiency of the proposed methods is demonstrated on simple numerical examples.

Discrete time methods for simulating continuous time Markov chains

1976 ◽  
Vol 8 (04) ◽  
pp. 772-788 ◽  
Author(s):  
Arie Hordijk ◽  
Donald L. Iglehart ◽  
Rolf Schassberger
Keyword(s):  
Central Limit Theorem ◽  
Limit Theorem ◽  
Markov Chains ◽  
Confidence Intervals ◽  
Discrete Time ◽  
Continuous Time ◽  
Statistical Efficiency ◽  
Numerical Examples ◽  
The Central Limit Theorem ◽  
Continuous Time Markov Chains

This paper discusses several problems which arise when the regenerative method is used to analyse simulations of Markov chains. The first problem involves calculating the variance constant which appears in the central limit theorem used to obtain confidence intervals. Knowledge of this constant is very helpful in evaluating simulation methodologies. The second problem is to devise a method for simulating continuous time Markov chains without having to generate exponentially distributed holding times. Several methods are presented and compared. Numerical examples are given to illustrate the computional and statistical efficiency of these methods.

Dynamics of Supply Chains: A Multilevel (Logistical–Informational–Financial) Network Perspective

2002 ◽  
Vol 29 (6) ◽  
pp. 795-818 ◽  
Author(s):  
Anna Nagurney ◽  
Ke Ke ◽  
Jose Cruz ◽  
Kitty Hancock ◽  
Frank Southworth
Keyword(s):  
Dynamical System ◽  
Stability Analysis ◽  
Supply Chains ◽  
Discrete Time ◽  
Equilibrium Solution ◽  
Adjustment Process ◽  
Financial Network ◽  
Numerical Examples ◽  
Space And Time

In this paper, we propose a multilevel network perspective for the conceptualization of the dynamics underlying supply chains in the presence of competition. The multilevel network consists of: the logistical network, the informational network, and the financial network. We describe the behavior of the network decisionmakers, which are spatially separated and which consist of the manufacturers and producing firms, the retailers, and the consumers located at the demand markets. We propose a projected dynamical system, along with stability analysis results, that captures the adjustments of the commodity shipments and the prices over space and time. A discrete-time adjustment process is described and implemented in order to illustrate in several numerical examples the evolution of the commodity shipments and prices to the equilibrium solution.

Stability analysis of nonlinear impulsive switched positive systems

2022 ◽  
Vol 0 (0) ◽  
Author(s):  
Yanzi Lin ◽  
Ping Zhao
Keyword(s):  
Discrete Time ◽  
Continuous Time ◽  
Function Method ◽  
Sufficient Conditions ◽  
Average Dwell Time ◽  
Positive Systems ◽  
Lyapunov Function Method ◽  
The Stability ◽  
Switched Positive Systems ◽  
Time Linear

Abstract In this paper, the global asymptotic stability (GAS) of continuous-time and discrete-time nonlinear impulsive switched positive systems (NISPS) are studied. For continuous-time and discrete-time NISPS, switching signals and impulse signals coexist. For both of these systems, using the multiple max-separable Lyapunov function method and average dwell-time (ADT) method, some sufficient conditions on GAS are given. Based on these, the GAS criteria are also given for continuous-time and discrete-time linear impulsive switched positive systems (LISPS). From our criteria, the stability of the systems can be judged directly from the characteristics of the system functions, switching signals and impulse signals of the systems. Finally, simulation examples verify the validity of the results.

scholarly journals Comparison of approximation methods of positive stable continuous-time linear systems by positive stable discrete-time systems

2013 ◽  
Vol 62 (2) ◽  
pp. 345-355 ◽  
Author(s):  
Tadeusz Kaczorek
Keyword(s):  
Linear Systems ◽  
Discrete Time ◽  
Continuous Time ◽  
Electrical Circuit ◽  
Approximation Methods ◽  
Asymptotically Stable ◽  
Numerical Examples ◽  
Discrete Time Systems ◽  
Time Systems ◽  
Time Linear

Abstract The positive asymptotically stable continuous-time linear systems are approximated by corresponding asymptotically stable discrete-time linear systems. Two methods of the approximation are presented and the comparison of the methods is addressed. The considerations are illustrated by three numerical examples and an example of positive electrical circuit.

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