Abstract: Bayesian approach can be used for parameter identification and extraction in state space models and its ability for analyzing sequence of data in dynamical system is proved in different literatures. In this paper, adaptive Kalman filter with Bayesian approach for identification of variances in measurement parameter noise is developed. Next, it is applied for estimation of the dynamical state and measurement data in discrete linear dynamical system. This algorithm at each step time estimates noise variance in measurement noise and state of system with Kalman filter. Next, approximation is designed at each step separately and consequently sufficient statistics of the state and noise variances are computed with a fixed-point iteration of an adaptive Kalman filter. Different simulations are applied for showing the influence of noise variance in measurement data on algorithm. Firstly, the effect of noise variance and its distribution on detection and identification performance is simulated in Kalman filter without Bayesian formulation. Then, simulation is applied to adaptive Kalman filter with the ability of noise variance tracking in measurement data. In these simulations, the influence of noise distribution of measurement data in each step is estimated, and true variance of data is obtained by algorithm and is compared in different scenarios. Afterwards, one typical modeling of nonlinear state space model with inducing noise measurement is simulated by this approach. Finally, the performance and the important limitations of this algorithm in these simulations are explained.
Abstract: A mathematical model for knowledge acquisition in
teaching and learning is proposed. In this study we adopt the
mathematical model that is normally used for disease modelling
into teaching and learning. We derive mathematical conditions which
facilitate knowledge acquisition. This study compares the effects
of dropping out of the course at early stages with later stages of
learning. The study also investigates effect of individual interaction
and learning from other sources to facilitate learning. The study fits
actual data to a general mathematical model using Matlab ODE45
and lsqnonlin to obtain a unique mathematical model that can be
used to predict knowledge acquisition. The data used in this study
was obtained from the tutorial test results for mathematics 2 students
from the Central University of Technology, Free State, South Africa
in the department of Mathematical and Physical Sciences. The study
confirms already known results that increasing dropout rates and
forgetting taught concepts reduce the population of knowledgeable
students. Increasing teaching contacts and access to other learning
materials facilitate knowledge acquisition. The effect of increasing
dropout rates is more enhanced in the later stages of learning
than earlier stages. The study opens up a new direction in further
investigations in teaching and learning using differential equations.
Abstract: Crop yield prediction is a paramount issue in
agriculture. The main idea of this paper is to find out efficient
way to predict the yield of corn based meteorological records.
The prediction models used in this paper can be classified into
model-driven approaches and data-driven approaches, according to
the different modeling methodologies. The model-driven approaches are based on crop mechanistic
modeling. They describe crop growth in interaction with their
environment as dynamical systems. But the calibration process of
the dynamic system comes up with much difficulty, because it
turns out to be a multidimensional non-convex optimization problem.
An original contribution of this paper is to propose a statistical
methodology, Multi-Scenarios Parameters Estimation (MSPE), for the
parametrization of potentially complex mechanistic models from a
new type of datasets (climatic data, final yield in many situations).
It is tested with CORNFLO, a crop model for maize growth. On the other hand, the data-driven approach for yield prediction
is free of the complex biophysical process. But it has some strict
requirements about the dataset.
A second contribution of the paper is the comparison of these
model-driven methods with classical data-driven methods. For this
purpose, we consider two classes of regression methods, methods
derived from linear regression (Ridge and Lasso Regression, Principal
Components Regression or Partial Least Squares Regression) and
machine learning methods (Random Forest, k-Nearest Neighbor,
Artificial Neural Network and SVM regression).
The dataset consists of 720 records of corn yield at county scale
provided by the United States Department of Agriculture (USDA) and
the associated climatic data. A 5-folds cross-validation process and
two accuracy metrics: root mean square error of prediction(RMSEP),
mean absolute error of prediction(MAEP) were used to evaluate the
crop prediction capacity.
The results show that among the data-driven approaches, Random
Forest is the most robust and generally achieves the best prediction
error (MAEP 4.27%). It also outperforms our model-driven approach
(MAEP 6.11%). However, the method to calibrate the mechanistic
model from dataset easy to access offers several side-perspectives.
The mechanistic model can potentially help to underline the stresses
suffered by the crop or to identify the biological parameters of interest
for breeding purposes. For this reason, an interesting perspective is
to combine these two types of approaches.
Abstract: This paper is concerned with a system of
Hamilton-Jacobi-Bellman equations coupled with an autonomous
dynamical system. The mathematical system arises in the differential
game formulation of political economy models as an infinite-horizon
continuous-time differential game with discounted instantaneous
payoff rates and continuously and discretely varying state variables.
The existence of a weak solution of the PDE system is proven and
a computational scheme of approximate solution is developed for a
class of such systems. A model of democratization is mathematically
analyzed as an illustration of application.
Abstract: Propagation of nonlinear acoustic wave in dense electron-positron (e-p) plasmas in the presence of an external magnetic field and stationary ions (to neutralize the plasma background) is studied. By means of the quantum hydrodynamics model and applying the reductive perturbation method, the Zakharov-Kuznetsov equation is derived. Using the bifurcation theory of planar dynamical systems, the compressive structure of electrostatic solitary wave and periodic travelling waves is found. The numerical results show how the ion density ratio, the ion cyclotron frequency, and the direction cosines of the wave vector affect the nonlinear electrostatic travelling waves. The obtained results may be useful to better understand the obliquely nonlinear electrostatic travelling wave of small amplitude localized structures in dense magnetized quantum e-p plasmas and may be applicable to study the particle and energy transport mechanism in compact stars such as the interior of massive white dwarfs etc.
Abstract: This paper considers an H∞ TS fuzzy state-derivative feedback controller for a class of nonlinear dynamical systems. A Takagi-Sugeno (TS) fuzzy model is used to approximate a class of nonlinear dynamical systems. Then, based on a linear matrix inequality (LMI) approach, we design an H∞ TS fuzzy state-derivative feedback control law which guarantees L2-gain of the mapping from the exogenous input noise to the regulated output to be less or equal to a prescribed value. We derive a sufficient condition such that the system with the fuzzy controller is asymptotically stable and H∞ performance is satisfied. Finally, we provide and simulate a numerical example is provided to illustrate the stability and the effectiveness of the proposed controller.
Abstract: This paper presents an optimal state feedback controller based on Linear Quadratic Regulator (LQR) for a two-rotor aero-dynamical system (TRAS). TRAS is a highly nonlinear multi-input multi-output (MIMO) system with two degrees of freedom and cross coupling. There are two parameters that define the behavior of LQR controller: state weighting matrix and control weighting matrix. The two parameters influence the performance of LQR. Particle Swarm Optimization (PSO) is proposed to optimally tune weighting matrices of LQR. The major concern of using LQR controller is to stabilize the TRAS by making the beam move quickly and accurately for tracking a trajectory or to reach a desired altitude. The simulation results were carried out in MATLAB/Simulink. The system is decoupled into two single-input single-output (SISO) systems. Comparing the performance of the optimized proportional, integral and derivative (PID) controller provided by INTECO, results depict that LQR controller gives a better performance in terms of both transient and steady state responses when PSO is performed.
Abstract: Human biological signals (pulse wave and brain wave, etc.) have a rhythm which shows fluctuations. This study investigates the relationship between fluctuations of biological signals which are shown by a finger plethysmogram (i.e., finger pulse wave) in conversation and anthropophobic tendency, and identifies whether the fluctuation could be an index of mental health. 32 college students participated in the experiment. The finger plethysmogram of each subject was measured in the following conversation situations: Fun memory talking/listening situation and regrettable memory talking/ listening situation for three minutes each. Lyspect 3.5 was used to collect the data of the finger plethysmogram. Since Lyspect calculates the Lyapunov spectrum, it is possible to obtain the largest Lyapunov exponent (LLE). LLE is an indicator of the fluctuation and shows the degree to which a measure is going away from close proximity to the track in a dynamical system. Before the finger plethysmogram experiment, each participant took the psychological test questionnaire “Anthropophobic Scale.” The scale measures the social phobia trend close to the consciousness of social phobia. It is revealed that there is a remarkable relationship between the fluctuation of the finger plethysmography and anthropophobic tendency scale in talking about a regrettable story in conversation: The participants (N=15) who have a low anthropophobic tendency show significantly more fluctuation of finger pulse waves than the participants (N=17) who have a high anthropophobic tendency (F (1, 31) =5.66, p
Abstract: For a rigid body sliding on a rough surface, a range of
uncertainty or non-uniqueness of solution could be found, which is
termed: Painlevé paradox. Painlevé paradox is the reason of a wide
range of bouncing motion, observed during sliding of robotic
manipulators on rough surfaces. In this research work, the existence
of the paradox zone during the sliding motion of a two-link (P-R)
robotic manipulator with a unilateral constraint is investigated.
Parametric study is performed to investigate the effect of friction,
link-length ratio, total height and link-mass ratio on the paradox zone.
Abstract: The aim of the present study is to detect the chaotic
behavior in monetary economic relevant dynamical system. The
study employs three different forms of Taylor rules: current, forward,
and backward looking. The result suggests the existence of the
chaotic behavior in all three systems. In addition, the results strongly
represent that using expectations in policy rule especially rational
expectation hypothesis can increase complexity of the system and
leads to more chaotic behavior.
Abstract: In this paper a real-time obstacle avoidance approach
for both autonomous and non-autonomous dynamical systems (DS) is
presented. In this approach the original dynamics of the controller
which allow us to determine safety margin can be modulated.
Different common types of DS increase the robot’s reactiveness in
the face of uncertainty in the localization of the obstacle especially
when robot moves very fast in changeable complex environments.
The method is validated by simulation and influence of different
autonomous and non-autonomous DS such as important
characteristics of limit cycles and unstable DS. Furthermore, the
position of different obstacles in complex environment is explained.
Finally, the verification of avoidance trajectories is described through
different parameters such as safety factor.
Abstract: In this paper, Bayesian online inference in models of
data series are constructed by change-points algorithm, which
separated the observed time series into independent series and study
the change and variation of the regime of the data with related
statistical characteristics. variation of statistical characteristics of time
series data often represent separated phenomena in the some
dynamical system, like a change in state of brain dynamical reflected
in EEG signal data measurement or a change in important regime of
data in many dynamical system. In this paper, prediction algorithm
for studying change point location in some time series data is
simulated. It is verified that pattern of proposed distribution of data
has important factor on simpler and smother fluctuation of hazard
rate parameter and also for better identification of change point
locations. Finally, the conditions of how the time series distribution
effect on factors in this approach are explained and validated with
different time series databases for some dynamical system.
Abstract: In this paper, we considered and applied parametric
modeling for some experimental data of dynamical system. In this
study, we investigated the different distribution of output
measurement from some dynamical systems. Also, with variance
processing in experimental data we obtained the region of
nonlinearity in experimental data and then identification of output
section is applied in different situation and data distribution. Finally,
the effect of the spanning the measurement such as variance to
identification and limitation of this approach is explained.
Abstract: Performance of different filtering approaches depends
on modeling of dynamical system and algorithm structure. For
modeling and smoothing the data the evaluation of posterior
distribution in different filtering approach should be chosen carefully.
In this paper different filtering approaches like filter KALMAN,
EKF, UKF, EKS and smoother RTS is simulated in some trajectory
tracking of path and accuracy and limitation of these approaches are
explained. Then probability of model with different filters is
compered and finally the effect of the noise variance to estimation is
described with simulations results.
Abstract: This paper presents a combination of both robust
nonlinear controller and nonlinear controller for a class of nonlinear
4Y Octorotor UAV using Back-stepping and sliding mode controller.
The robustness against internal and external disturbance and
decoupling control are the merits of the proposed paper. The
proposed controller decouples the Octorotor dynamical system. The
controller is then applied to a 4Y Octortor UAV and its feature will
be shown.
Abstract: This paper proposes the designing direct adaptive
neural controller to apply for a class of a nonlinear pendulum
dynamic system. The radial basis function (RBF) neural adaptive
controller is robust in presence of external and internal uncertainties.
Both the effectiveness of the controller and robustness against
disturbances are importance of this paper. The simulation results
show the promising performance of the proposed controller.
Abstract: The design of a feedback controller, so as to minimize a given performance criterion, for a general non-linear dynamical system is difficult; if not impossible. But for a large class of non-linear dynamical systems, the open loop control that minimizes a performance criterion can be obtained using calculus of variations and Pontryagin’s minimum principle. In this paper, the open loop optimal trajectories, that minimizes a given performance measure, is used to train the neural network whose inputs are state variables of non-linear dynamical systems and the open loop optimal control as the desired output. This trained neural network is used as the feedback controller. In other words, attempts are made here to solve the “inverse optimal control problem” by using the state and control trajectories that are optimal in an open loop sense.
Abstract: A gradient learning method to regulate the trajectories
of some nonlinear chaotic systems is proposed. The method is
motivated by the gradient descent learning algorithms for neural
networks. It is based on two systems: dynamic optimization system
and system for finding sensitivities. Numerical results of several
examples are presented, which convincingly illustrate the efficiency
of the method.
Abstract: In analyzing large scale nonlinear dynamical systems,
it is often desirable to treat the overall system as a collection of
interconnected subsystems. Solutions properties of the large scale
system are then deduced from the solution properties of the
individual subsystems and the nature of the interconnections. In this
paper a new approach is proposed for the stability analysis of large
scale systems, which is based upon the concept of vector Lyapunov
functions and the decomposition methods. The present results make
use of graph theoretic decomposition techniques in which the overall
system is partitioned into a hierarchy of strongly connected
components. We show then, that under very reasonable assumptions,
the overall system is stable once the strongly connected subsystems
are stables. Finally an example is given to illustrate the constructive
methodology proposed.
Abstract: A dynamic of Bertrand duopoly game is analyzed, where players use different production methods and choose their prices with bounded rationality. The equilibriums of the corresponding discrete dynamical systems are investigated. The stability conditions of Nash equilibrium under a local adjustment process are studied. The stability conditions of Nash equilibrium under a local adjustment process are studied. The stability of Nash equilibrium, as some parameters of the model are varied, gives rise to complex dynamics such as cycles of higher order and chaos. On this basis, we discover that an increase of adjustment speed of bounded rational player can make Bertrand market sink into the chaotic state. Finally, the complex dynamics, bifurcations and chaos are displayed by numerical simulation.