scholarly journals Continuous and Discrete-Time Optimal Controls for an Isolated Signalized Intersection

2017 ◽  
Vol 2017 ◽  
pp. 1-11 ◽  
Author(s):  
Jiyuan Tan ◽  
Xiangyun Shi ◽  
Zhiheng Li ◽  
Kaidi Yang ◽  
Na Xie ◽  
...  
Keyword(s):  
Optimal Control ◽  
Discrete Time ◽  
Continuous Time ◽  
Optimal Controls ◽  
Time Model ◽  
Control Plan ◽  
Analytic Proof ◽  
Planning Models ◽  
Gradient Descent Algorithm ◽  
Time Planning

A classical control problem for an isolated oversaturated intersection is revisited with a focus on the optimal control policy to minimize total delay. The difference and connection between existing continuous-time planning models and recently proposed discrete-time planning models are studied. A gradient descent algorithm is proposed to convert the optimal control plan of the continuous-time model to the plan of the discrete-time model in many cases. Analytic proof and numerical tests for the algorithm are also presented. The findings shed light on the links between two kinds of models.

scholarly journals Dividend Moments in the Dual Risk Model: Exact and Approximate Approaches

2008 ◽  
Vol 38 (02) ◽  
pp. 399-422 ◽  
Author(s):  
Eric C.K. Cheung ◽  
Steve Drekic
Keyword(s):  
Differential Equations ◽  
Laplace Transform ◽  
Size Distribution ◽  
Discrete Time ◽  
Continuous Time ◽  
Risk Model ◽  
Time Model ◽  
Jump Size ◽  
Time Of Ruin ◽  
The Time Of Ruin

In the classical compound Poisson risk model, it is assumed that a company (typically an insurance company) receives premium at a constant rate and pays incurred claims until ruin occurs. In contrast, for certain companies (typically those focusing on invention), it might be more appropriate to assume expenses are paid at a fixed rate and occasional random income is earned. In such cases, the surplus process of the company can be modelled as a dual of the classical compound Poisson model, as described in Avanzi et al. (2007). Assuming further that a barrier strategy is applied to such a model (i.e., any overshoot beyond a fixed level caused by an upward jump is paid out as a dividend until ruin occurs), we are able to derive integro-differential equations for the moments of the total discounted dividends as well as the Laplace transform of the time of ruin. These integro-differential equations can be solved explicitly assuming the jump size distribution has a rational Laplace transform. We also propose a discrete-time analogue of the continuous-time dual model and show that the corresponding quantities can be solved for explicitly leaving the discrete jump size distribution arbitrary. While the discrete-time model can be considered as a stand-alone model, it can also serve as an approximation to the continuous-time model. Finally, we consider a generalization of the so-called Dickson-Waters modification in optimal dividends problems by maximizing the difference between the expected value of discounted dividends and the present value of a fixed penalty applied at the time of ruin.

Birth and death processes with random environments in continuous time

1981 ◽  
Vol 18 (01) ◽  
pp. 19-30 ◽  
Author(s):  
Robert Cogburn ◽  
William C. Torrez
Keyword(s):  
Discrete Time ◽  
Random Environment ◽  
Continuous Time ◽  
Death Process ◽  
Random Environments ◽  
Birth And Death Process ◽  
Time Model ◽  
Birth And Death Processes ◽  
Discrete Time Model ◽  
Extinction Probabilities

A generalization to continuous time is given for a discrete-time model of a birth and death process in a random environment. Some important properties of this process in the continuous-time setting are stated and proved including instability and extinction conditions, and when suitable absorbing barriers have been defined, methods are given for the calculation of extinction probabilities and the expected duration of the process.

scholarly journals Discrete-Time First-Order Plus Dead-Time Model-Reference Trade-off PID Control Design

2019 ◽  
Vol 9 (16) ◽  
pp. 3220 ◽  
Author(s):  
Ryo Kurokawa ◽  
Takao Sato ◽  
Ramon Vilanova ◽  
Yasuo Konishi
Keyword(s):  
Discrete Time ◽  
Pid Control ◽  
Continuous Time ◽  
Dead Time ◽  
Design Method ◽  
Control Design ◽  
The Other ◽  
Time Model ◽  
Trade Off ◽  
First Order

The present study proposes a novel proportional-integral-derivative (PID) control design method in discrete time. In the proposed method, a PID controller is designed for first-order plus dead-time (FOPDT) systems so that the prescribed robust stability is accomplished. Furthermore, based on the control performance, the relationship between the servo performance and the regulator performance is a trade-off relationship, and hence, these items are not simultaneously optimized. Therefore, the proposed method provides an optimal design method of the PID parameters for optimizing the reference tracking and disturbance rejection performances, respectively. Even though such a trade-off design method is being actively researched for continuous time, few studies have examined such a method for discrete time. In conventional discrete time methods, the robust stability is not directly prescribed or available systems are restricted to systems for which the dead-time in the continuous time model is an integer multiple of the sampling interval. On the other hand, in the proposed method, even when a discrete time zero is included in the controlled plant, the optimal PID parameters are obtained. In the present study, as well as the other plant parameters, a zero in the FOPDT system is newly normalized, and then, a universal design method is obtained for the FOPDT system with the zero. Finally, the effectiveness of the proposed method is demonstrated through numerical examples.

scholarly journals Optimal Control Strategy for a Discrete Time Smoking Model with Specific Saturated Incidence Rate

2018 ◽  
Vol 2018 ◽  
pp. 1-10 ◽  
Author(s):  
Abderrahim Labzai ◽  
Omar Balatif ◽  
Mostafa Rachik
Keyword(s):  
Optimal Control ◽  
Incidence Rate ◽  
Discrete Time ◽  
Control Strategy ◽  
Optimal Controls ◽  
Optimization Strategy ◽  
Optimal Control Strategy ◽  
Saturated Incidence Rate ◽  
Saturated Incidence ◽  
Heavy Smokers

The aim of this paper is to study and investigate the optimal control strategy of a discrete mathematical model of smoking with specific saturated incidence rate. The population that we are going to study is divided into five compartments: potential smokers, light smokers, heavy smokers, temporary quitters of smoking, and permanent quitters of smoking. Our objective is to find the best strategy to reduce the number of light smokers, heavy smokers, and temporary quitters of smoking. We use three control strategies which are awareness programs through media and education, treatment, and psychological support with follow-up. Pontryagins maximum principle in discrete time is used to characterize the optimal controls. The numerical simulation is carried out using MATLAB. Consequently, the obtained results confirm the performance of the optimization strategy.

scholarly journals Predicting IBNYR Events and Delays II. Discrete Time

1990 ◽  
Vol 20 (1) ◽  
pp. 93-111 ◽  
Author(s):  
William S. Jewell
Keyword(s):  
Discrete Time ◽  
Continuous Time ◽  
Bayesian Method ◽  
Predictive Accuracy ◽  
Random Delay ◽  
Continuous Time Model ◽  
Practical Situation ◽  
Time Model ◽  
Numerical Example ◽  
Exposure Interval

AbstractAn IBNYR event is one that occurs randomly during some fixed exposure interval and incurs a random delay before it is reported. A previous paper developed a continuous-time model of the IBNYR process in which both the Poisson rate at which events occur and the parameters of the delay distribution are unknown random quantities; a full-distributional Bayesian method was then developed to predict the number of unreported events. Using a numerical example, the success of this approach was shown to depend upon whether or not the occurrence dates were available in addition to the reporting dates. This paper considers the more usual practical situation in which only discretized epoch information is available; this leads to a loss of predictive accuracy, which is investigated by considering various levels of quantization for the same numerical example.

scholarly journals Likelihood-based estimation of continuous-time epidemic models from time-series data: application to measles transmission in London

2008 ◽  
Vol 5 (25) ◽  
pp. 885-897 ◽  
Author(s):  
Simon Cauchemez ◽  
Neil M Ferguson
Keyword(s):  
Time Series ◽  
Discrete Time ◽  
Continuous Time ◽  
Generation Time ◽  
Data Augmentation ◽  
Time Series Data ◽  
Observation Interval ◽  
Series Data ◽  
Time Model ◽  
Similar Time

We present a new statistical approach to analyse epidemic time-series data. A major difficulty for inference is that (i) the latent transmission process is partially observed and (ii) observed quantities are further aggregated temporally. We develop a data augmentation strategy to tackle these problems and introduce a diffusion process that mimicks the susceptible–infectious–removed (SIR) epidemic process, but that is more tractable analytically. While methods based on discrete-time models require epidemic and data collection processes to have similar time scales, our approach, based on a continuous-time model, is free of such constraint. Using simulated data, we found that all parameters of the SIR model, including the generation time, were estimated accurately if the observation interval was less than 2.5 times the generation time of the disease. Previous discrete-time TSIR models have been unable to estimate generation times, given that they assume the generation time is equal to the observation interval. However, we were unable to estimate the generation time of measles accurately from historical data. This indicates that simple models assuming homogenous mixing (even with age structure) of the type which are standard in mathematical epidemiology miss key features of epidemics in large populations.

scholarly journals Extreme stability and almost periodicity in continuous and discrete neuronal models with finite delays

2002 ◽  
Vol 44 (2) ◽  
pp. 261-282 ◽  
Author(s):  
S. Mohamad ◽  
K. Gopalsamy
Keyword(s):  
Discrete Time ◽  
Continuous Time ◽  
Model Neuron ◽  
Sufficient Conditions ◽  
External Stimulus ◽  
Input Stimulus ◽  
Time System ◽  
Time Model ◽  
Discrete Time Model ◽  
Continuous Time System

We consider the dynamical characteristics of a continuous-time isolated Hopfield-type neuron subjected to an almost periodic external stimulus. The model neuron is assumed to be dissipative having finite time delays in the process of encoding the external input stimulus and recalling the encoded pattern associated with the external stimulus. By using non-autonomous Halanay-type inequalities we obtain sufficient conditions for the hetero-associative stable encoding of temporally non-uniform stimuli. A brief study of a discrete-time model derived from the continuous-time system is given. It is shown that the discrete-time model preserves the stability conditions of the continuous-time system.

Optimal Control of Time-Delayed Linear Systems With the Method of Continuous Time Approximation

2008 ◽  
Author(s):  
Jian-Qiao Sun ◽  
Bo Song
Keyword(s):  
Optimal Control ◽  
Output Feedback ◽  
Continuous Time ◽  
Output Feedback Control ◽  
Optimal Controls ◽  
Feedback Controls ◽  
Time Approximation ◽  
Dimensional State Space ◽  
Delayed System ◽  
Space Formulation

This paper presents optimal control studies of delayed dynamical systems with the help of a method of continuous time approximation (CTA). The CTA method proposes a continuous time approximation of the delayed portion of the response leading to a high and finite dimensional state space formulation of the time-delayed system. Optimal controls of the system such as LQR and output feedback controls are readily designed with the existing design tools. In the paper, we present an output feedback control by means of the mapping approach studied previously. In order to accomplish the objective of control design, we also examine various discretization schemes of the CTA method in frequency domain.

scholarly journals Dividend Moments in the Dual Risk Model: Exact and Approximate Approaches

2008 ◽  
Vol 38 (2) ◽  
pp. 399-422 ◽  
Author(s):  
Eric C.K. Cheung ◽  
Steve Drekic
Keyword(s):  
Differential Equations ◽  
Laplace Transform ◽  
Size Distribution ◽  
Discrete Time ◽  
Continuous Time ◽  
Risk Model ◽  
Time Model ◽  
Jump Size ◽  
Time Of Ruin ◽  
The Time Of Ruin

In the classical compound Poisson risk model, it is assumed that a company (typically an insurance company) receives premium at a constant rate and pays incurred claims until ruin occurs. In contrast, for certain companies (typically those focusing on invention), it might be more appropriate to assume expenses are paid at a fixed rate and occasional random income is earned. In such cases, the surplus process of the company can be modelled as a dual of the classical compound Poisson model, as described in Avanzi et al. (2007). Assuming further that a barrier strategy is applied to such a model (i.e., any overshoot beyond a fixed level caused by an upward jump is paid out as a dividend until ruin occurs), we are able to derive integro-differential equations for the moments of the total discounted dividends as well as the Laplace transform of the time of ruin. These integro-differential equations can be solved explicitly assuming the jump size distribution has a rational Laplace transform. We also propose a discrete-time analogue of the continuous-time dual model and show that the corresponding quantities can be solved for explicitly leaving the discrete jump size distribution arbitrary. While the discrete-time model can be considered as a stand-alone model, it can also serve as an approximation to the continuous-time model. Finally, we consider a generalization of the so-called Dickson-Waters modification in optimal dividends problems by maximizing the difference between the expected value of discounted dividends and the present value of a fixed penalty applied at the time of ruin.

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