Abstract: In this study, the density dependent nonlinear reactiondiffusion
equation, which arises in the insect dispersal models, is
solved using the combined application of differential quadrature
method(DQM) and implicit Euler method. The polynomial based
DQM is used to discretize the spatial derivatives of the problem. The
resulting time-dependent nonlinear system of ordinary differential
equations(ODE-s) is solved by using implicit Euler method. The
computations are carried out for a Cauchy problem defined by a onedimensional
density dependent nonlinear reaction-diffusion equation
which has an exact solution. The DQM solution is found to be in a
very good agreement with the exact solution in terms of maximum
absolute error. The DQM solution exhibits superior accuracy at large
time levels tending to steady-state. Furthermore, using an implicit
method in the solution procedure leads to stable solutions and larger
time steps could be used.
Abstract: This paper proposes the analysis and design of robust
fuzzy control to Stochastic Parametrics Uncertaint Linear systems.
This system type to be controlled is partitioned into several linear
sub-models, in terms of transfer function, forming a convex polytope,
similar to LPV (Linear Parameters Varying) system. Once defined the
linear sub-models of the plant, these are organized into fuzzy Takagi-
Sugeno (TS) structure. From the Parallel Distributed Compensation
(PDC) strategy, a mathematical formulation is defined in the frequency
domain, based on the gain and phase margins specifications,
to obtain robust PI sub-controllers in accordance to the Takagi-
Sugeno fuzzy model of the plant. The main results of the paper are
based on the robust stability conditions with the proposal of one
Axiom and two Theorems.
Abstract: Fuzzy controllers are potential candidates for the
control of nonlinear, time variant and also complicated systems. Anti
lock brake system (ABS) which is a nonlinear system, may not be
easily controlled by classical control methods. An intelligent Fuzzy
control method is very useful for this kind of nonlinear system. A
typical antilock brake system (ABS) by sensing the wheel lockup,
releases the brakes for a short period of time, and then reapplies again
the brakes when the wheel spins up. In this paper, an intelligent fuzzy
ABS controller is designed to adjust slipping performance for variety
of roads. There are tow major sections in the proposing control
system. First section consists of tow Fuzzy-Logic Controllers (FLC)
providing optimal brake torque for both front and rear wheels.
Second section which is also a FLC provides required amount of slip
and torque references properties for different kind of roads.
Simulation results of our proposed intelligent ABS for three different
kinds of road show more reliable and better performance in compare
with two other break systems.
Abstract: The two cart inverted pendulum system is a good
bench mark for testing the performance of system dynamics and
control engineering principles. Devasia introduced this system to
study the asymptotic tracking problem for nonlinear systems. In this
paper the problem of asymptotic tracking of the two-cart with an
inverted-pendulum system to a sinusoidal reference inputs via
introducing a novel method for solving finite-horizon nonlinear
optimal control problems is presented. In this method, an iterative
method applied to state dependent Riccati equation (SDRE) to obtain
a reliable algorithm. The superiority of this technique has been shown
by simulation and comparison with the nonlinear approach.
Abstract: Extended Kalman Filter (EKF) is probably the most
widely used estimation algorithm for nonlinear systems. However,
not only it has difficulties arising from linearization but also many
times it becomes numerically unstable because of computer round off
errors that occur in the process of its implementation. To overcome
linearization limitations, the unscented transformation (UT) was
developed as a method to propagate mean and covariance
information through nonlinear transformations. Kalman filter that
uses UT for calculation of the first two statistical moments is called
Unscented Kalman Filter (UKF). Square-root form of UKF (SRUKF)
developed by Rudolph van der Merwe and Eric Wan to
achieve numerical stability and guarantee positive semi-definiteness
of the Kalman filter covariances. This paper develops another
implementation of SR-UKF for sequential update measurement
equation, and also derives a new UD covariance factorization filter
for the implementation of UKF. This filter is equivalent to UKF but
is computationally more efficient.
Abstract: In the present work, we propose a new projection method for solving the matrix equation AXB = F. For implementing our new method, generalized forms of block Krylov subspace and global Arnoldi process are presented. The new method can be considered as an extended form of the well-known global generalized minimum residual (Gl-GMRES) method for solving multiple linear systems and it will be called as the extended Gl-GMRES (EGl- GMRES). Some new theoretical results have been established for proposed method by employing Schur complement. Finally, some numerical results are given to illustrate the efficiency of our new method.
Abstract: In this paper we consider a nonlinear feedback control
called augmented automatic choosing control (AACC) using the
gradient optimization automatic choosing functions for nonlinear
systems. Constant terms which arise from sectionwise linearization
of a given nonlinear system are treated as coefficients of a stable
zero dynamics. Parameters included in the control are suboptimally
selected by expanding a stable region in the sense of Lyapunov
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: In this paper, we are concerned with the design and
its simulation studies of a modified extremum seeking control for
nonlinear systems. A standard extremum seeking control has a simple
structure, but it takes a long time to reach an optimal operating point.
We consider a modification of the standard extremum seeking control
which is aimed to reach the optimal operating point more speedily
than the standard one. In the modification, PD acceleration term
is added before an integrator making a principal control, so that it
enables the objects to be regulated to the optimal point smoothly. This
proposed method is applied to Monod and Williams-Otto models to
investigate its effectiveness. Numerical simulation results show that
this modified method can improve the time response to the optimal
operating point more speedily than the standard one.
Abstract: In this paper, we give the generalized alternating twostage method in which the inner iterations are accomplished by a generalized alternating method. And we present convergence results of the method for solving nonsingular linear systems when the coefficient matrix of the linear system is a monotone matrix or an H-matrix.
Abstract: Both the minimum energy consumption and
smoothness, which is quantified as a function of jerk, are generally
needed in many dynamic systems such as the automobile and the
pick-and-place robot manipulator that handles fragile equipments.
Nevertheless, many researchers come up with either solely
concerning on the minimum energy consumption or minimum jerk
trajectory. This research paper proposes a simple yet very interesting
when combining the minimum energy and jerk of indirect jerks
approaches in designing the time-dependent system yielding an
alternative optimal solution. Extremal solutions for the cost functions
of the minimum energy, the minimum jerk and combining them
together are found using the dynamic optimization methods together
with the numerical approximation. This is to allow us to simulate
and compare visually and statistically the time history of state inputs
employed by combining minimum energy and jerk designs. The
numerical solution of minimum direct jerk and energy problem are
exactly the same solution; however, the solutions from problem of
minimum energy yield the similar solution especially in term of
tendency.
Abstract: This paper proposes a new parameter identification
method based on Linear Fractional Transformation (LFT). It is
assumed that the target linear system includes unknown parameters.
The parameter deviations are separated from a nominal system via
LFT, and identified by organizing I/O signals around the separated
deviations of the real system. The purpose of this paper is to apply LFT
to simultaneously identify the parameter deviations in systems with
fewer outputs than unknown parameters. As a fundamental example,
this method is implemented to one degree of freedom vibratory system.
Via LFT, all physical parameters were simultaneously identified in this
system. Then, numerical simulations were conducted for this system to
verify the results. This study shows that all the physical parameters of a
system with fewer outputs than unknown parameters can be effectively
identified simultaneously using LFT.
Abstract: The permanent magnet synchronous motor (PMSM) is
very useful in many applications. Vector control of PMSM is popular
kind of its control. In this paper, at first an optimal vector control for
PMSM is designed and then results are compared with conventional
vector control. Then, it is assumed that the measurements are noisy
and linear quadratic Gaussian (LQG) methodology is used to filter
the noises. The results of noisy optimal vector control and filtered
optimal vector control are compared to each other. Nonlinearity of
PMSM and existence of inverter in its control circuit caused that the
system is nonlinear and time-variant. With deriving average model,
the system is changed to nonlinear time-invariant and then the
nonlinear system is converted to linear system by linearization of
model around average values. This model is used to optimize vector
control then two optimal vector controls are compared to each other.
Simulation results show that the performance and robustness to noise
of the control system has been highly improved.
Abstract: The symmetric solution set Σ sym is the set of all solutions to the linear systems Ax = b, where A is symmetric and lies between some given bounds A and A, and b lies between b and b. We present a contractor for Σ sym, which is an iterative method that starts with some initial enclosure of Σ sym (by means of a cartesian product of intervals) and sequentially makes the enclosure tighter. Our contractor is based on polyhedral approximation and solving a series of linear programs. Even though it does not converge to the optimal bounds in general, it may significantly reduce the overestimation. The efficiency is discussed by a number of numerical experiments.
Abstract: The multidelays linear control systems described by
difference differential equations are often studied in modern control
theory. In this paper, the delay-independent stabilization algebraic
criteria and the theorem of delay-independent stabilization for linear
systems with multiple time-delays are established by using the
Lyapunov functional and the Riccati algebra matrix equation in the
matrix theory. An illustrative example and the simulation result, show
that the approach to linear systems with multiple time-delays is
effective.
Abstract: In this paper, we present a preconditioned AOR-type iterative method for solving the linear systems Ax = b, where A is a Z-matrix. And give some comparison theorems to show that the rate of convergence of the preconditioned AOR-type iterative method is faster than the rate of convergence of the AOR-type iterative method.
Abstract: The problem of robust disturbance rejection (RDR) using a proportional state feedback controller is studied for the case of Left Invertible MIMO generalized state space linear systems with nonlinear uncertain structure. Sufficient conditions for the problem to have a solution are established. The set of all proportional feedback controllers solving the problem subject to these conditions is analytically determined.
Abstract: This paper is concerned with the existence of a linear copositive Lyapunov function(LCLF) for a special class of switched positive linear systems(SPLSs) composed of continuousand discrete-time subsystems. Firstly, by using system matrices, we construct a special kind of matrices in appropriate manner. Secondly, our results reveal that the Hurwitz stability of these matrices is equivalent to the existence of a common LCLF for arbitrary finite sets composed of continuous- and discrete-time positive linear timeinvariant( LTI) systems. Finally, a simple example is provided to illustrate the implication of our results.
Abstract: In this article, we aim to discuss the formulation of two explicit group iterative finite difference methods for time-dependent two dimensional Burger-s problem on a variable mesh. For the non-linear problems, the discretization leads to a non-linear system whose Jacobian is a tridiagonal matrix. We discuss the Newton-s explicit group iterative methods for a general Burger-s equation. The proposed explicit group methods are derived from the standard point and rotated point Crank-Nicolson finite difference schemes. Their computational complexity analysis is discussed. Numerical results are given to justify the feasibility of these two proposed iterative methods.
Abstract: This paper proposes a methodology for analysis of
the dynamic behavior of a robotic manipulator in continuous
time. Initially this system (nonlinear system) will be decomposed
into linear submodels and analyzed in the context of the Linear
and Parameter Varying (LPV) Systems. The obtained linear
submodels, which represent the local dynamic behavior of the
robotic manipulator in some operating points were grouped in
a Takagi-Sugeno fuzzy structure. The obtained fuzzy model was
analyzed and validated through analog simulation, as universal
approximator of the robotic manipulator.
Abstract: Genetic algorithms (GAs) have been widely used for
global optimization problems. The GA performance depends highly
on the choice of the search space for each parameter to be optimized.
Often, this choice is a problem-based experience. The search space
being a set of potential solutions may contain the global optimum
and/or other local optimums. A bad choice of this search space
results in poor solutions. In this paper, our approach consists in
extending the search space boundaries during the GA optimization,
only when it is required. This leads to more diversification of GA
population by new solutions that were not available with fixed search
space boundaries. So, these dynamic search spaces can improve the
GA optimization performances. The proposed approach is applied to
power system stabilizer optimization for multimachine power system
(16-generator and 68-bus). The obtained results are evaluated and
compared with those obtained by ordinary GAs. Eigenvalue analysis
and nonlinear system simulation results show the effectiveness of the
proposed approach to damp out the electromechanical oscillation and
enhance the global system stability.