Abstract: In this paper we consider a nonlinear feedback control called augmented automatic choosing control (AACC) for nonlinear systems with constrained input. Constant terms which arise from section wise linearization of a given nonlinear system are treated as coefficients of a stable zero dynamics.Parameters included in the control are suboptimally selectedby extremizing a combination of Hamiltonian and Lyapunov functions with the aid of the genetic algorithm. This approach is applied to a field excitation control problem of power system to demonstrate the splendidness of the AACC. Simulation results show that the new controller can improve performance remarkably well.
Abstract: This paper proposes an adaptive sliding mode
controller which combines adaptive control and sliding
mode control to control a nonlinear robotic manipulator
with uncertain parameters. We use an adaptive algorithm
based on the concept of sliding mode control to alleviate the
chattering phenomenon of control input. Adaptive laws are
developed to obtain the gain of switching input and the
boundary layer parameters. The stability and convergence
of the robotic manipulator control system are guaranteed
by applying the Lyapunov theorem. Simulation results
demonstrate that the chattering of control input can be
alleviated effectively. The proposed controller scheme can
assure robustness against a large class of uncertainties and
achieve good trajectory tracking performance.
Abstract: In this paper, an magnetorheological (MR) mount with
fuzzy sliding mode controller (FSMC) is studied for vibration
suppression when the system is subject to base excitations. In recent
years, magnetorheological fluids are becoming a popular material in
the field of the semi-active control. However, the dynamic equation of
an MR mount is highly nonlinear and it is difficult to identify. FSMC
provides a simple method to achieve vibration attenuation of the
nonlinear system with uncertain disturbances. This method is capable
of handling the chattering problem of sliding mode control effectively
and the fuzzy control rules are obtained by using the Lyapunov
stability theory. The numerical simulations using one-dimension and
two-dimension FSMC show effectiveness of the proposed controller
for vibration suppression. Further, the well-known skyhook control
scheme and an adaptive sliding mode controller are also included in
the simulation for comparison with the proposed FSMC.
Abstract: Strict stability can present the rate of decay of the
solution, so more and more investigators are beginning to study the
topic and some results have been obtained. However, there are few
results about strict stability of stochastic differential equations. In
this paper, using Lyapunov functions and Razumikhin technique, we
have gotten some criteria for the strict stability of impulsive stochastic
functional differential equations with markovian switching.
Abstract: This paper considers the design of a motion planner
that will simultaneously accomplish control and motion planning of a
n-link nonholonomic mobile manipulator, wherein, a n-link
holonomic manipulator is coupled with a nonholonomic mobile
platform, within an obstacle-ridden environment. This planner,
derived from the Lyapunov-based control scheme, generates
collision-free trajectories from an initial configuration to a final
configuration in a constrained environment cluttered with stationary
solid objects of different shapes and sizes. We demonstrate the
efficiency of the control scheme and the resulting acceleration
controllers of the mobile manipulator with results through computer
simulations of an interesting scenario.
Abstract: In this paper, different nonlinear dynamics analysis techniques are employed to unveil the rich nonlinear phenomena of the electromagnetic system. In particular, bifurcation diagrams, time responses, phase portraits, Poincare maps, power spectrum analysis, and the construction of basins of attraction are all powerful and effective tools for nonlinear dynamics problems. We also employ the method of Lyapunov exponents to show the occurrence of chaotic motion and to verify those numerical simulation results. Finally, two cases of a chaotic electromagnetic system being effectively controlled by a reference signal or being synchronized to another nonlinear electromagnetic system are presented.
Abstract: This paper considers the robust exponential stability issues for a class of uncertain switched neutral system which delays switched according to the switching rule. The system under consideration includes both stable and unstable subsystems. The uncertainties considered in this paper are norm bounded, and possibly time varying. Based on multiple Lyapunov functional approach and dwell-time technique, the time-dependent switching rule is designed depend on the so-called average dwell time of stable subsystems as well as the ratio of the total activation time of stable subsystems and unstable subsystems. It is shown that by suitably controlling the switching between the stable and unstable modes, the robust stabilization of the switched uncertain neutral systems can be achieved. Two simulation examples are given to demonstrate the effectiveness of the proposed method.
Abstract: An important technique in stability theory for
differential equations is known as the direct method of Lyapunov. In
this work we deal global stability properties of Leptospirosis
transmission model by age group in Thailand. First we consider the
data from Division of Epidemiology Ministry of Public Health,
Thailand between 1997-2011. Then we construct the mathematical
model for leptospirosis transmission by eight age groups. The
Lyapunov functions are used for our model which takes the forms of
an Ordinary Differential Equation system. The globally
asymptotically for equilibrium states are analyzed.
Abstract: Deep Brain Stimulation or DBS is a surgical treatment for Parkinson-s Disease with three stimulation parameters: frequency, pulse width, and voltage. The parameters should be selected appropriately to achieve effective treatment. This selection now, performs clinically. The aim of this research is to study chaotic behavior of recorded tremor of patients under DBS in order to present a computational method to recognize stimulation optimum voltage. We obtained some chaotic features of tremor signal, and discovered embedding space of it has an attractor, and its largest Lyapunov exponent is positive, which show tremor signal has chaotic behavior, also we found out, in optimal voltage, entropy and embedding space variance of tremor signal have minimum values in comparison with other voltages. These differences can help neurologists recognize optimal voltage numerically, which leads to reduce patients' role and discomfort in optimizing stimulation parameters and to do treatment with high accuracy.
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: Functional near infrared spectroscopy (fNIRS) is a
practical non-invasive optical technique to detect characteristic of
hemoglobin density dynamics response during functional activation of
the cerebral cortex. In this paper, fNIRS measurements were made in
the area of motor cortex from C4 position according to international
10-20 system. Three subjects, aged 23 - 30 years, were participated in
the experiment.
The aim of this paper was to evaluate the effects of different motor
activation tasks of the hemoglobin density dynamics of fNIRS signal.
The chaotic concept based on deterministic dynamics is an important
feature in biological signal analysis. This paper employs the chaotic
properties which is a novel method of nonlinear analysis, to analyze
and to quantify the chaotic property in the time series of the
hemoglobin dynamics of the various motor imagery tasks of fNIRS
signal. Usually, hemoglobin density in the human brain cortex is
found to change slowly in time. An inevitable noise caused by various
factors is to be included in a signal. So, principle component analysis
method (PCA) is utilized to remove high frequency component. The
phase pace is reconstructed and evaluated the Lyapunov spectrum, and
Lyapunov dimensions. From the experimental results, it can be
conclude that the signals measured by fNIRS are chaotic.
Abstract: The three-species food web model proposed and investigated by Gakkhar and Naji is known to have chaotic behaviour for a choice of parameters. An attempt has been made to synchronize the chaos in the model using bidirectional coupling. Numerical simulations are presented to demonstrate the effectiveness and feasibility of the analytical results. Numerical results show that for higher value of coupling strength, chaotic synchronization is achieved. Chaos can be controlled to achieve stable synchronization in natural systems.
Abstract: In this paper, the problem of stability criteria of neural networks (NNs) with two-additive time-varying delay compenents is investigated. The relationship between the time-varying delay and its lower and upper bounds is taken into account when estimating the upper bound of the derivative of Lyapunov functional. As a result, some improved delay stability criteria for NNs with two-additive time-varying delay components are proposed. Finally, a numerical example is given to illustrate the effectiveness of the proposed method.
Abstract: The very nonlinear nature of the generator and system
behaviour following a severe disturbance precludes the use of
classical linear control technique. In this paper, a new approach of
nonlinear control is proposed for transient and steady state stability
analysis of a synchronous generator. The control law of the generator
excitation is derived from the basis of Lyapunov stability criterion.
The overall stability of the system is shown using Lyapunov
technique. The application of the proposed controller to simulated
generator excitation control under a large sudden fault and wide
range of operating conditions demonstrates that the new control
strategy is superior to conventional automatic voltage regulator
(AVR), and show very promising results.
Abstract: This paper presents an adaptive nonlinear position
controller with velocity constraint, capable of combining the
input-output linearization technique and Lyapunov stability theory.
Based on the Lyapunov stability theory, the adaptation law of the
proposed controller is derived along with the verification of the overall
system-s stability. Computer simulation results demonstrate that the
proposed controller is robust and it can ensure transient stability of
BLDCM, under the occurrence of a large sudden fault.
Abstract: By using the method of coincidence degree and constructing suitable Lyapunov functional, some sufficient conditions are established for the existence and global exponential stability of antiperiodic solutions for a kind of impulsive Cohen-Grossberg shunting inhibitory cellular neural networks (CGSICNNs) on time scales. An example is given to illustrate our results.
Abstract: This paper investigates the problem of exponential stability for a class of uncertain discrete-time stochastic neural network with time-varying delays. By constructing a suitable Lyapunov-Krasovskii functional, combining the stochastic stability theory, the free-weighting matrix method, a delay-dependent exponential stability criteria is obtained in term of LMIs. Compared with some previous results, the new conditions obtain in this paper are less conservative. Finally, two numerical examples are exploited to show the usefulness of the results derived.
Abstract: This paper derives some new sufficient conditions for
the stability of a class of neutral-type neural networks with discrete
time delays by employing a suitable Lyapunov functional. The
obtained conditions can be easily verified as they can be expressed
in terms of the network parameters only. It is shown that the results
presented in this paper for neutral-type delayed neural networks establish
a new set of stability criteria, and therefore can be considered
as the alternative results to the previously published literature results.
A numerical example is also given to demonstrate the applicability
of our proposed stability criterion.
Abstract: In this paper, a class of generalized bi-directional associative memory (BAM) neural networks with mixed delays is investigated. On the basis of Lyapunov stability theory and contraction mapping theorem, some new sufficient conditions are established for the existence and uniqueness and globally exponential stability of equilibrium, which generalize and improve the previously known results. One example is given to show the feasibility and effectiveness of our results.
Abstract: In this paper, the trajectory tracking problem for carlike mobile robots have been studied. The system comprises of a leader and a follower robot. The purpose is to control the follower so that the leader-s trajectory is tracked with arbitrary desired clearance to avoid inter-robot collision while navigating in a terrain with obstacles. A set of artificial potential field functions is proposed using the Direct Method of Lyapunov for the avoidance of obstacles and attraction to their designated targets. Simulation results prove the efficiency of our control technique.