Abstract: This paper is interested in two difficulties encountered in practice when observing a continuous time process. The first is that we cannot observe a process over a time interval; we only take discrete observations. The second is the process frequently observed with a constant additive error. It is important to give an estimator of the spectral density of such a process taking into account the additive observation error and the choice of the discrete observation times. In this work, we propose an estimator based on the spectral smoothing of the periodogram by the polynomial Jackson kernel reducing the additive error. In order to solve the aliasing phenomenon, this estimator is constructed from observations taken at well-chosen times so as to reduce the estimator to the field where the spectral density is not zero. We show that the proposed estimator is asymptotically unbiased and consistent. Thus we obtain an estimate solving the two difficulties concerning the choice of the instants of observations of a continuous time process and the observations affected by a constant error.
Abstract: This work focuses on the symmetric alpha stable process with continuous time frequently used in modeling the signal with indefinitely growing variance, often observed with an unknown additive error. The objective of this paper is to estimate this error from discrete observations of the signal. For that, we propose a method based on the smoothing of the observations via Jackson polynomial kernel and taking into account the width of the interval where the spectral density is non-zero. This technique allows avoiding the “Aliasing phenomenon” encountered when the estimation is made from the discrete observations of a process with continuous time. We have studied the convergence rate of the estimator and have shown that the convergence rate improves in the case where the spectral density is zero at the origin. Thus, we set up an estimator of the additive error that can be subtracted for approaching the original signal without error.
Abstract: Assessing several individuals intensively over time
yields intensive longitudinal data (ILD). Even though ILD provide
rich information, they also bring other data analytic challenges. One
of these is the increased occurrence of missingness with increased
study length, possibly under non-ignorable missingness scenarios.
Multiple imputation (MI) handles missing data by creating several
imputed data sets, and pooling the estimation results across imputed
data sets to yield final estimates for inferential purposes. In this
article, we introduce dynr.mi(), a function in the R package,
Dynamic Modeling in R (dynr). The package dynr provides a suite
of fast and accessible functions for estimating and visualizing the
results from fitting linear and nonlinear dynamic systems models in
discrete as well as continuous time. By integrating the estimation
functions in dynr and the MI procedures available from the R
package, Multivariate Imputation by Chained Equations (MICE), the
dynr.mi() routine is designed to handle possibly non-ignorable
missingness in the dependent variables and/or covariates in a
user-specified dynamic systems model via MI, with convergence
diagnostic check. We utilized dynr.mi() to examine, in the context
of a vector autoregressive model, the relationships among individuals’
ambulatory physiological measures, and self-report affect valence
and arousal. The results from MI were compared to those from
listwise deletion of entries with missingness in the covariates.
When we determined the number of iterations based on the
convergence diagnostics available from dynr.mi(), differences in
the statistical significance of the covariate parameters were observed
between the listwise deletion and MI approaches. These results
underscore the importance of considering diagnostic information in
the implementation of MI procedures.
Abstract: In this paper, we studied the effect of supplementary premium on the optimal portfolio policy in a defined contribution (DC) pension scheme with refund of premium clauses. This refund clause allows death members’ next of kin to withdraw their relative’s accumulated wealth during the accumulation period. The supplementary premium is to help sustain the scheme and is assumed to be stochastic. We considered cases when the remaining wealth is equally distributed and when it is not equally distributed among the remaining members. Next, we considered investments in cash and equity to help increase the remaining accumulated funds to meet up with the retirement needs of the remaining members and composed the problem as a continuous time mean-variance stochastic optimal control problem using the actuarial symbol and established an optimization problem from the extended Hamilton Jacobi Bellman equations. The optimal portfolio policy, the corresponding optimal fund size for the two assets and also the efficient frontier of the pension members for the two cases was obtained. Furthermore, the numerical simulations of the optimal portfolio policies with time were presented and the effect of the supplementary premium on the optimal portfolio policy was discussed and observed that the supplementary premium decreases the optimal portfolio policy of the risky asset (equity). Secondly we observed a disparity between the optimal policies for the two cases.
Abstract: In this paper, we propose a condition-based
maintenance policy for multi-unit systems considering the
existence of economic dependency among units. We consider a
system composed of N identical units, where each unit deteriorates
independently. Deterioration process of each unit is modeled as a
three-state continuous time homogeneous Markov chain with two
working states and a failure state. The average production rate of
units varies in different working states and demand rate of the
system is constant. Units are inspected at equidistant time epochs,
and decision regarding performing maintenance is determined by the
number of units in the failure state. If the total number of units in the
failure state exceeds a critical level, maintenance is initiated, where
units in failed state are replaced correctively and deteriorated state
units are maintained preventively. Our objective is to determine the
optimal number of failed units to initiate maintenance minimizing
the long run expected average cost per unit time. The problem is
formulated and solved in the semi-Markov decision process (SMDP)
framework. A numerical example is developed to demonstrate the
proposed policy and the comparison with the corrective maintenance
policy is presented.
Abstract: Equivalent circuit models (ECMs) are widely used in
battery management systems in electric vehicles and other battery
energy storage systems. The battery dynamics and the model
parameters vary under different working conditions, such as different
temperature and state of charge (SOC) levels, and therefore online
parameter identification can improve the modelling accuracy. This
paper presents a way of online ECM parameter identification using a
continuous time (CT) estimation method. The CT estimation method
has several advantages over discrete time (DT) estimation methods
for ECM parameter identification due to the widely separated battery
dynamic modes and fast sampling. The presented method can be used
for online SOC estimation. Test data are collected using a lithium ion
cell, and the experimental results show that the presented CT method
achieves better modelling accuracy compared with the conventional
DT recursive least square method. The effectiveness of the presented
method for online SOC estimation is also verified on test data.
Abstract: Traveling Wave Ultrasonic Motor (TWUM) is a compact, precise, and silent actuator generating high torque at low speed without gears. Moreover, the TWUM has a high holding torque without supply, which makes this motor as an attractive solution for holding position of robotic arms. However, their nonlinear dynamics, and the presence of load-dependent dead zones often limit their use. Those issues can be overcome in closed loop with effective and precise controllers. In this paper, robust H-infinity (H∞) and discrete time RST position controllers are presented. The H∞ controller is designed in continuous time with additional weighting filters to ensure the robustness in the case of uncertain motor model and external disturbances. Robust RST controller based on the pole placement method is also designed and compared to the H∞. Simulink model of TWUM is used to validate the stability and the robustness of the two proposed controllers.
Abstract: A continuous time model of the interaction between
crop insect pests and naturally beneficial pest enemies is created
using a set of simultaneous, non-linear, ordinary differential
equations incorporating natural death rates based on the Weibull
distribution. The crop pest is present in all its life-cycle stages of:
egg, larva, pupa and adult. The beneficial insects, parasitoid wasps,
may be present in either or all parasitized: eggs, larva and pupa.
Population modelling is used to estimate the quantity of the natural
pest enemies that should be introduced into the pest infested
environment to suppress the pest population density to an
economically acceptable level within a prescribed number of days.
The results obtained illustrate the effect of different combinations of
parasitoid wasps, using the Pascal distribution to estimate their
success in parasitizing different pest developmental stages, to deliver
pest control to a sustainable level. Effective control, within a
prescribed number of days, is established by the deployment of two
or all three species of wasps, which partially destroy pest: egg, larvae
and pupae stages. The selected scenarios demonstrate effective
sustainable control of the pest in less than thirty days.
Abstract: This work evaluates the ability of OBT for detecting parametric faults in continuous-time filters. To this end, we adopt two filters with quite different topologies as cases of study and a previously reported statistical fault model. In addition, we explore the behavior of the test schemes when a particular test condition is changed. The new data reported here, obtained from a fault simulation process, reveal a lower performance of OBT not observed in previous work using single-deviation faults, even under the change in the test condition.
Abstract: This paper proposes a new obstacle and collision
avoidance control laws for a three-dimensional swarm of boids.
The swarm exhibit collective emergent behaviors whilst avoiding the
obstacles in the workspace. While flocking, animals group up in order
to do various tasks and even a greater chance of evading predators. A
generalized algorithms for attraction to the centroid, inter-individual
swarm avoidance and obstacle avoidance is designed in this paper.
We present a set of new continuous time-invariant velocity control
laws is presented which is formulated via the Lyapunov-based control
scheme. The control laws proposed in this paper also ensures practical
stability of the system. The effectiveness of the proposed control laws
is demonstrated via computer simulations
Abstract: In this paper, we propose a solution to the motion
planning and control problem for a swarm of three-dimensional
boids. The swarm exhibit collective emergent behaviors within the
vicinity of the workspace. The capability of biological systems
to autonomously maneuver, track and pursue evasive targets in a
cluttered environment is vastly superior to any engineered system. It
is considered an emergent behavior arising from simple rules that are
followed by individuals and may not involve any central coordination.
A generalized, yet scalable algorithm for attraction to the centroid
and inter-individual swarm avoidance is proposed. We present a set
of new continuous time-invariant velocity control laws, formulated via
the Lyapunov-based control scheme for target attraction and collision
avoidance. The controllers provide a collision-free trajectory. The
control laws proposed in this paper also ensures practical stability
of the system. The effectiveness of the control laws is demonstrated
via computer simulations.
Abstract: This paper presents a new methodology to study power and energy consumption in mechatronic systems early in the development process. This new approach makes use of two modeling languages to represent and simulate embedded control software and electromechanical subsystems in the discrete event and continuous time domain respectively within a single co-model. This co-model enables an accurate representation of power and energy consumption and facilitates the analysis and development of both software and electro-mechanical subsystems in parallel. This makes the engineers aware of energy-wise implications of different design alternatives and enables early trade-off analysis from the beginning of the analysis and design activities.
Abstract: Spatial and mobile computing evolves. This paper
describes a smart modeling platform called “GeoSEMA". This
approach tends to model multidimensional GeoSpatial Evolutionary
and Mobile Agents. Instead of 3D and location-based issues, there
are some other dimensions that may characterize spatial agents, e.g.
discrete-continuous time, agent behaviors. GeoSEMA is seen as a
devoted design pattern motivating temporal geographic-based
applications; it is a firm foundation for multipurpose and
multidimensional special-based applications. It deals with
multipurpose smart objects (buildings, shapes, missiles, etc.) by
stimulating geospatial agents.
Formally, GeoSEMA refers to geospatial, spatio-evolutive and
mobile space constituents where a conceptual geospatial space model
is given in this paper. In addition to modeling and categorizing
geospatial agents, the model incorporates the concept of inter-agents
event-based protocols. Finally, a rapid software-architecture
prototyping GeoSEMA platform is also given. It will be
implemented/ validated in the next phase of our work.
Abstract: The main aim of this study is to describe and introduce a method of numerical analysis in obtaining approximate solutions for the SIR-SI differential equations (susceptible-infectiverecovered for human populations; susceptible-infective for vector populations) that represent a model for dengue disease transmission. Firstly, we describe the ordinary differential equations for the SIR-SI disease transmission models. Then, we introduce the numerical analysis of solutions of this continuous time, discrete space SIR-SI model by simplifying the continuous time scale to a densely populated, discrete time scale. This is followed by the application of this numerical analysis of solutions of the SIR-SI differential equations to the estimation of relative risk using continuous time, discrete space dengue data of Kuala Lumpur, Malaysia. Finally, we present the results of the analysis, comparing and displaying the results in graphs, table and maps. Results of the numerical analysis of solutions that we implemented offers a useful and potentially superior model for estimating relative risks based on continuous time, discrete space data for vector borne infectious diseases specifically for dengue disease.
Abstract: The growth and interconnection of power networks in many regions has invited complicated techniques for energy management services (EMS). State estimation techniques become a powerful tool in power system control centers, and that more information is required to achieve the objective of EMS. For the online state estimator, assuming the continuous time is equidistantly sampled with period Δt, processing events must be finished within this period. Advantage of Kalman Filtering (KF) algorithm in using system information to improve the estimation precision is utilized. Computational power is a major issue responsible for the achievement of the objective, i.e. estimators- solution at a small sampled period. This paper presents the optimum utilization of processors in a state estimator based on KF. The model used is presented using Petri net (PN) theory.
Abstract: In this paper, a alternative structure method for
continuous time sigma delta modulator is presented. In this
modulator for implementation of integrators in loop filter second
generation current conveyors are employed. The modulator is
designed in CMOS technology and features low power consumption
(65db),
and with 180khZ bandwidth. Simulation results confirm that this
design is suitable for data converters.
Abstract: In this paper, a novel associative memory model will be proposed and applied to memory retrievals based on the conventional continuous time model. The conventional model presents memory capacity is very low and retrieval process easily converges to an equilibrium state which is very different from the stored patterns. Genetic Algorithms is well-known with the capability of global optimal search escaping local optimum on progress to reach a global optimum. Based on the well-known idea of Genetic Algorithms, this work proposes a heuristic rule to make a mutation when the state of the network is trapped in a spurious memory. The proposal heuristic associative memory show the stored capacity does not depend on the number of stored patterns and the retrieval ability is up to ~ 1.
Abstract: Continuous-time delta-sigma analog digital converter (ADC) for radio frequency identification (RFID) complementary metal oxide semiconductor (CMOS) biosensor has been reported. This delta-sigma ADC is suitable for digital conversion of biosensor signal because of small process variation, and variable input range. As the input range of continuous-time switched current delta-sigma ADC (Dynamic range : 50 dB) can be limited by using current reference, amplification of biosensor signal is unnecessary. The input range is switched to wide input range mode or narrow input range mode by command of current reference. When the narrow input range mode, the input range becomes ± 0.8 V. The measured power consumption is 5 mW and chip area is 0.31 mm^2 using 1.2 um standard CMOS process. Additionally, automatic input range detecting system is proposed because of RFID biosensor applications.