Abstract: In this work, we investigate the exponential stability of a linear system described by x˙ (t) = Ax(t) − ρBx(t). Here, A generates a semigroup S(t) on a Hilbert space, the operator B is supposed to be of Desch-Schappacher type, which makes the investigation more interesting in many applications. The case of Miyadera-Voigt perturbations is also considered. Sufficient conditions are formulated in terms of admissibility and observability inequalities and the approach is based on some energy estimates. Finally, the obtained results are applied to prove the uniform exponential stabilization of bilinear partial differential equations.
Abstract: Three structure-dependent integration methods have been developed for solving equations of motion, which are second-order ordinary differential equations, for structural dynamics and earthquake engineering applications. Although they generally have the same numerical properties, such as explicit formulation, unconditional stability and second-order accuracy, a different performance is found in solving the free vibration response to either linear elastic or nonlinear systems with high frequency modes. The root cause of this different performance in the free vibration responses is analytically explored herein. As a result, it is verified that a weak instability is responsible for the different performance of the integration methods. In general, a weak instability will result in an inaccurate solution or even numerical instability in the free vibration responses of high frequency modes. As a result, a weak instability must be prohibited for time integration methods.
Abstract: This paper presents parameter estimation of a
single-phase rectifier using extended Kalman filter (EKF). The state
space model has been obtained using Kirchhoff’s current law (KCL)
and Kirchhoff’s voltage law (KVL). The capacitor voltage and diode
current of the circuit have been estimated using EKF. Simulation
results validate the better accuracy of the proposed method as
compared to the least mean square method (LMS). Further, EKF
has the advantage that it can be used for nonlinear systems.
Abstract: A class of implicit systems is known as a more
generalized class of systems than a class of explicit systems. To
establish a control method for such a generalized class of systems, we
adopt model predictive control method which is a kind of optimal
feedback control with a performance index that has a moving
initial time and terminal time. However, model predictive control
method is inapplicable to systems whose all state variables are not
exactly known. In other words, model predictive control method is
inapplicable to systems with limited measurable states. In fact, it
is usual that the state variables of systems are measured through
outputs, hence, only limited parts of them can be used directly. It is
also usual that output signals are disturbed by process and sensor
noises. Hence, it is important to establish a state estimation method
for nonlinear implicit systems with taking the process noise and
sensor noise into consideration. To this purpose, we apply the model
predictive control method and unscented Kalman filter for solving
the optimization and estimation problems of nonlinear implicit
systems, respectively. The objective of this study is to establish a
model predictive control with unscented Kalman filter for nonlinear
implicit systems.
Abstract: Recently, the effectiveness of random dither
quantization method for linear feedback control systems has
been shown in several papers. However, the random dither
quantization method has not yet been applied to nonlinear feedback
control systems. The objective of this paper is to verify the
effectiveness of random dither quantization method for nonlinear
feedback control systems. For this purpose, we consider the attitude
stabilization problem of satellites using discrete-level actuators.
Namely, this paper provides a control method based on the random
dither quantization method for stabilizing the attitude of satellites
using discrete-level actuators.
Abstract: In this paper, we consider the parametrization of the
discrete-time systems without the unit-delay element within the
framework of the factorization approach. In the parametrization,
we investigate the number of required parameters. We consider
single-input single-output systems in this paper. By the investigation,
we find, on the discrete-time systems without the unit-delay element,
three cases that are (1) there exist plants which require only one
parameter and (2) two parameters, and (3) the number of parameters
is at most three.
Abstract: In this paper, the problem of robust model predictive control (MPC) for discrete-time linear systems in linear fractional transformation form with structured uncertainty and norm-bounded disturbance is investigated. The problem of minimization of the cost function for MPC design is converted to minimization of the worst case of the cost function. Then, this problem is reduced to minimization of an upper bound of the cost function subject to a terminal inequality satisfying the l2-norm of the closed loop system. The characteristic of the linear fractional transformation system is taken into account, and by using some mathematical tools, the robust predictive controller design problem is turned into a linear matrix inequality minimization problem. Afterwards, a formulation which includes an integrator to improve the performance of the proposed robust model predictive controller in steady state condition is studied. The validity of the approaches is illustrated through a robust control benchmark problem.
Abstract: This paper presents a design of dynamic feedback
control based on observer for a class of large scale Lipschitz nonlinear
systems. The use of Differential Mean Value Theorem (DMVT) is to
introduce a general condition on the nonlinear functions. To ensure
asymptotic stability, sufficient conditions are expressed in terms of
linear matrix inequalities (LMIs). High performances are shown
through real time implementation with ARDUINO Duemilanove
board to the one-link flexible joint robot.
Abstract: In this paper, a spectral decomposition method is developed for the direct integration of stiff and nonstiff homogeneous linear (ODE) systems with linear, constant, or zero right hand sides (RHSs). The method does not require iteration but obtains solutions at any random points of t, by direct evaluation, in the interval of integration. All the numerical solutions obtained for the class of systems coincide with the exact theoretical solutions. In particular, solutions of homogeneous linear systems, i.e. with zero RHS, conform to the exact analytical solutions of the systems in terms of t.
Abstract: Uncertainties related to fatigue damage estimation of
non-linear systems are highly dependent on the tail behaviour
and extreme values of the stress range distribution. By using
a combination of the First Order Reliability Method (FORM)
and Monte Carlo simulations (MCS), the accuracy of the fatigue
estimations may be improved for the same computational efforts.
The method is applied to a bottom-fixed, monopile-supported large
offshore wind turbine, which is a non-linear and dynamically sensitive
system. Different curve fitting techniques to the fatigue damage
distribution have been used depending on the sea-state dependent
response characteristics, and the effect of a bi-linear S-N curve is
discussed. Finally, analyses are performed on several environmental
conditions to investigate the long-term applicability of this multistep
method. Wave loads are calculated using state-of-the-art theory, while
wind loads are applied with a simplified model based on rotor thrust
coefficients.
Abstract: In population dynamics the study of both, the
abundance and the spatial distribution of the populations in a
given habitat, is a fundamental issue a From ecological point of
view, the determination of the factors influencing such changes
involves important problems. In this paper a mathematical model to
describe the temporal dynamic and the spatiotemporal dynamic of the
interaction of three populations (pollinators, plants and herbivores) is
presented. The study we present is carried out by stages: 1. The
temporal dynamics and 2. The spatio-temporal dynamics. In turn,
each of these stages is developed by considering three cases which
correspond to the dynamics of each type of interaction. For instance,
for stage 1, we consider three ODE nonlinear systems describing
the pollinator-plant, plant-herbivore and plant-pollinator-herbivore,
interactions, respectively. In each of these systems different types of
dynamical behaviors are reported. Namely, transcritical and pitchfork
bifurcations, existence of a limit cycle, existence of a heteroclinic
orbit, etc. For the spatiotemporal dynamics of the two mathematical
models a novel factor are introduced. This consists in considering
that both, the pollinators and the herbivores, move towards those
places of the habitat where the plant population density is high.
In mathematical terms, this means that the diffusive part of the
pollinators and herbivores equations depend on the plant population
density. The analysis of this part is presented by considering pairs of
populations, i. e., the pollinator-plant and plant-herbivore interactions
and at the end the two mathematical model is presented, these models
consist of two coupled nonlinear partial differential equations of
reaction-diffusion type. These are defined on a rectangular domain
with the homogeneous Neumann boundary conditions. We focused
in the role played by the density dependent diffusion term into
the coexistence of the populations. For both, the temporal and
spatio-temporal dynamics, a several of numerical simulations are
included.
Abstract: In this paper, we consider the two-stage compensator
designs of SISO plants. As an investigation of the characteristics of
the two-stage compensator designs, which is not well investigated
yet, of SISO plants, we implement three dimensional visualization
systems of output signals and optimization system for SISO plants by
the parametrization of stabilizing controllers based on the two-stage
compensator design. The system runs on Mathematica by using
“Three Dimensional Surface Plots,” so that the visualization can
be interactively manipulated by users. In this paper, we use the
discrete-time LTI system model. Even so, our approach is the
factorization approach, so that the result can be applied to many
linear models.
Abstract: The spreadsheet engine is exploited via a non-conventional mechanism to enable novel worksheet solver functions for computational calculus. The solver functions bypass inherent restrictions on built-in math and user defined functions by taking variable formulas as a new type of argument while retaining purity and recursion properties. The enabling mechanism permits integration of numerical algorithms into worksheet functions for solving virtually any computational problem that can be modelled by formulas and variables. Several examples are presented for computing integrals, derivatives, and systems of deferential-algebraic equations. Incorporation of the worksheet solver functions with the ubiquitous spreadsheet extend the utility of the latter as a powerful tool for computational mathematics.
Abstract: This paper presents a novel integrated hybrid
approach for fault diagnosis (FD) of nonlinear systems. Unlike most
FD techniques, the proposed solution simultaneously accomplishes
fault detection, isolation, and identification (FDII) within a unified
diagnostic module. At the core of this solution is a bank of adaptive
neural parameter estimators (NPE) associated with a set of singleparameter
fault models. The NPEs continuously estimate unknown
fault parameters (FP) that are indicators of faults in the system. Two
NPE structures including series-parallel and parallel are developed
with their exclusive set of desirable attributes. The parallel scheme is
extremely robust to measurement noise and possesses a simpler, yet
more solid, fault isolation logic. On the contrary, the series-parallel
scheme displays short FD delays and is robust to closed-loop system
transients due to changes in control commands. Finally, a fault
tolerant observer (FTO) is designed to extend the capability of the
NPEs to systems with partial-state measurement.
Abstract: Many problems in science and engineering field require
the solution of shifted linear systems with multiple right hand
sides and multiple shifts. To solve such systems efficiently, the
implicitly restarted global GMRES algorithm is extended in this
paper. However, the shift invariant property could no longer hold over
the augmented global Krylov subspace due to adding the harmonic
Ritz matrices. To remedy this situation, we enforce the collinearity
condition on the shifted system and propose shift implicitly restarted
global GMRES. The new method not only improves the convergence
but also has a potential to simultaneously compute approximate
solution for the shifted systems using only as many matrix vector
multiplications as the solution of the seed system requires. In
addition, some numerical experiments also confirm the effectiveness
of our method.
Abstract: Analysis of real life problems often results in linear
systems of equations for which solutions are sought. The method to
employ depends, to some extent, on the properties of the coefficient
matrix. It is not always feasible to solve linear systems of equations
by direct methods, as such the need to use an iterative method
becomes imperative. Before an iterative method can be employed
to solve a linear system of equations there must be a guaranty that
the process of solution will converge. This guaranty, which must
be determined apriori, involve the use of some criterion expressible
in terms of the entries of the coefficient matrix. It is, therefore,
logical that the convergence criterion should depend implicitly on the
algebraic structure of such a method. However, in deference to this
view is the practice of conducting convergence analysis for Gauss-
Seidel iteration on a criterion formulated based on the algebraic
structure of Jacobi iteration. To remedy this anomaly, the Gauss-
Seidel iteration was studied for its algebraic structure and contrary
to the usual assumption, it was discovered that some property of the
iteration matrix of Gauss-Seidel method is only diagonally dominant
in its first row while the other rows do not satisfy diagonal dominance.
With the aid of this structure we herein fashion out an improved
version of Gauss-Seidel iteration with the prospect of enhancing
convergence and robustness of the method. A numerical section is
included to demonstrate the validity of the theoretical results obtained
for the improved Gauss-Seidel method.
Abstract: In recent years, many researchers are involved in the
field of fuzzy theory. However, there are still a lot of issues to be
resolved. Especially on topics related to controller design such as the
field of robot, artificial intelligence, and nonlinear systems etc.
Besides fuzzy theory, algorithms in swarm intelligence are also a
popular field for the researchers. In this paper, a concept of utilizing
one of the swarm intelligence method, which is called Bacterial-GA
Foraging, to find the stabilized common P matrix for the fuzzy
controller system is proposed. An example is given in in the paper, as
well.
Abstract: In this paper a nonlinear feedback control called augmented automatic choosing control (AACC) for a class of
nonlinear systems with constrained input is presented. When designed
the control, a constant term which arises from linearization of a
given nonlinear system is treated as a coefficient of a stable zero
dynamics. Parameters of the control are suboptimally selected by
maximizing the stable region in the sense of Lyapunov with the aid
of a 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: In this paper, the stability analysis of a GA-Based adaptive fuzzy sliding model controller for a nonlinear system is discussed. First, a nonlinear plant is well-approximated and described with a reference model and a fuzzy model, both involving FLC rules. Then, FLC rules and the consequent parameter are decided on via an Evolved Bat Algorithm (EBA). After this, we guarantee a new tracking performance inequality for the control system. The tracking problem is characterized to solve an eigenvalue problem (EVP). Next, an adaptive fuzzy sliding model controller (AFSMC) is proposed to stabilize the system so as to achieve good control performance. Lyapunov’s direct method can be used to ensure the stability of the nonlinear system. It is shown that the stability analysis can reduce nonlinear systems into a linear matrix inequality (LMI) problem. Finally, a numerical simulation is provided to demonstrate the control methodology.
Abstract: This paper presents a nonparametric identification of
continuous-time nonlinear systems by using a Gaussian process
(GP) model. The GP prior model is trained by artificial bee colony
algorithm. The nonlinear function of the objective system is estimated
as the predictive mean function of the GP, and the confidence
measure of the estimated nonlinear function is given by the predictive
covariance of the GP. The proposed identification method is applied
to modeling of a simplified electric power system. Simulation results
are shown to demonstrate the effectiveness of the proposed method.