Abstract: This paper presents a longitudinal quasi-linear model for the ADMIRE model. The ADMIRE model is a nonlinear model of aircraft flying in the condition of high angle of attack. So it can-t be considered to be a linear system approximately. In this paper, for getting the longitudinal quasi-linear model of the ADMIRE, a state transformation based on differentiable functions of the nonscheduling states and control inputs is performed, with the goal of removing any nonlinear terms not dependent on the scheduling parameter. Since it needn-t linear approximation and can obtain the exact transformations of the nonlinear states, the above-mentioned approach is thought to be appropriate to establish the mathematical model of ADMIRE. To verify this conclusion, simulation experiments are done. And the result shows that this quasi-linear model is accurate enough.
Abstract: We discuss the convergence property of the minimum residual (MINRES) method for the solution of complex shifted Hermitian system (αI + H)x = f. Our convergence analysis shows that the method has a faster convergence than that for real shifted Hermitian system (Re(α)I + H)x = f under the condition Re(α) + λmin(H) > 0, and a larger imaginary part of the shift α has a better convergence property. Numerical experiments show such convergence properties.
Abstract: This paper studies the problem of exponential
stability of perturbed discrete linear systems with periodic
coefficients. Assuming that the unperturbed system is exponentially
stable we obtain conditions on the perturbations under which the
perturbed system is exponentially stable.
Abstract: In this paper we consider a nonlinear feedback
control called augmented automatic choosing control (AACC)
using the automatic choosing functions of gradient optimization
type 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 minimizing the Hamiltonian
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: An adaptive fuzzy PID controller with gain scheduling is proposed in this paper. The structure of the proposed gain scheduled fuzzy PID (GS_FPID) controller consists of both fuzzy PI-like controller and fuzzy PD-like controller. Both of fuzzy PI-like and PD-like controllers are weighted through adaptive gain scheduling, which are also determined by fuzzy logic inference. A modified genetic algorithm called accumulated genetic algorithm is designed to learn the parameters of fuzzy inference system. In order to learn the number of fuzzy rules required for the TSK model, the fuzzy rules are learned in an accumulated way. In other words, the parameters learned in the previous rules are accumulated and updated along with the parameters in the current rule. It will be shown that the proposed GS_FPID controllers learned by the accumulated GA perform well for not only the regular linear systems but also the higher order and time-delayed systems.
Abstract: We study the semiconvergence of Gauss-Seidel iterative
methods for the least squares solution of minimal norm of rank
deficient linear systems of equations. Necessary and sufficient conditions
for the semiconvergence of the Gauss-Seidel iterative method
are given. We also show that if the linear system of equations is
consistent, then the proposed methods with a zero vector as an initial
guess converge in one iteration. Some numerical results are given to
illustrate the theoretical results.
Abstract: A generalized Dirichlet to Neumann map is
one of the main aspects characterizing a recently introduced
method for analyzing linear elliptic PDEs, through which it
became possible to couple known and unknown components
of the solution on the boundary of the domain without
solving on its interior. For its numerical solution, a well conditioned
quadratically convergent sine-Collocation method
was developed, which yielded a linear system of equations
with the diagonal blocks of its associated coefficient matrix
being point diagonal. This structural property, among others,
initiated interest for the employment of iterative methods for
its solution. In this work we present a conclusive numerical
study for the behavior of classical (Jacobi and Gauss-Seidel)
and Krylov subspace (GMRES and Bi-CGSTAB) iterative
methods when they are applied for the solution of the Dirichlet
to Neumann map associated with the Laplace-s equation
on regular polygons with the same boundary conditions on
all edges.
Abstract: This paper deals with the synthesis of fuzzy state feedback controller of induction motor with optimal performance. First, the Takagi-Sugeno (T-S) fuzzy model is employed to approximate a non linear system in the synchronous d-q frame rotating with electromagnetic field-oriented. Next, a fuzzy controller is designed to stabilise the induction motor and guaranteed a minimum disturbance attenuation level for the closed-loop system. The gains of fuzzy control are obtained by solving a set of Linear Matrix Inequality (LMI). Finally, simulation results are given to demonstrate the controller-s effectiveness.
Abstract: A fully implicit finite-difference method has been proposed for the numerical solutions of one dimensional coupled nonlinear Burgers’ equations on the uniform mesh points. The method forms a system of nonlinear difference equations which is to be solved at each iteration. Newton’s iterative method has been implemented to solve this nonlinear assembled system of equations. The linear system has been solved by Gauss elimination method with partial pivoting algorithm at each iteration of Newton’s method. Three test examples have been carried out to illustrate the accuracy of the method. Computed solutions obtained by proposed scheme have been compared with analytical solutions and those already available in the literature by finding L2 and L∞ errors.
Abstract: In this paper, we give a certain decomposition of the
coefficient matrix of the fully fuzzy linear system (FFLS) to obtain
a simple algorithm for solving these systems. The new algorithm
can solve FFLS in a smaller computing process. We will illustrate
our method by solving some examples.
Abstract: In this paper we consider a nonlinear feedback control
called augmented automatic choosing control (AACC) for nonlinear
systems with constrained input using weighted gradient optimization
automatic choosing functions. 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: Markov games can be effectively used to design
controllers for nonlinear systems. The paper presents two novel
controller design algorithms by incorporating ideas from gametheory
literature that address safety and consistency issues of the
'learned' control strategy. A more widely used approach for
controller design is the H∞ optimal control, which suffers from high
computational demand and at times, may be infeasible. We generate
an optimal control policy for the agent (controller) via a simple
Linear Program enabling the controller to learn about the unknown
environment. The controller is facing an unknown environment and
in our formulation this environment corresponds to the behavior rules
of the noise modeled as the opponent. Proposed approaches aim to
achieve 'safe-consistent' and 'safe-universally consistent' controller
behavior by hybridizing 'min-max', 'fictitious play' and 'cautious
fictitious play' approaches drawn from game theory. We empirically
evaluate the approaches on a simulated Inverted Pendulum swing-up
task and compare its performance against standard Q learning.
Abstract: in this paper, we propose a numerical method
for the approximate solution of fuzzy Fredholm functional
integral equations of the second kind by using an iterative
interpolation. For this purpose, we convert the linear fuzzy
Fredholm integral equations to a crisp linear system of integral
equations. The proposed method is illustrated by some fuzzy
integral equations in numerical examples.
Abstract: This paper is concerned with exponential stability and stabilization of switched linear systems with interval time-varying delays. The time delay is any continuous function belonging to a given interval, in which the lower bound of delay is not restricted to zero. By constructing a suitable augmented Lyapunov-Krasovskii functional combined with Leibniz-Newton-s formula, a switching rule for the exponential stability and stabilization of switched linear systems with interval time-varying delays and new delay-dependent sufficient conditions for the exponential stability and stabilization of the systems are first established in terms of LMIs. Numerical examples are included to illustrate the effectiveness of the results.
Abstract: An optimal mean-square fusion formulas with scalar
and matrix weights are presented. The relationship between them is
established. The fusion formulas are compared on the continuous-time
filtering problem. The basic differential equation for cross-covariance
of the local errors being the key quantity for distributed fusion is
derived. It is shown that the fusion filters are effective for multi-sensor
systems containing different types of sensors. An example
demonstrating the reasonable good accuracy of the proposed filters is
given.
Abstract: In this paper we consider a nonlinear control design for
nonlinear systems by using two-stage formal linearization and twotype
LQ controls. The ordinary LQ control is designed on almost
linear region around the steady state point. On the other region,
another control is derived as follows. This derivation is based on
coordinate transformation twice with respect to linearization functions
which are defined by polynomials. The linearized systems can be
made up by using Taylor expansion considered up to the higher order.
To the resulting formal linear system, the LQ control theory is applied
to obtain another LQ control. Finally these two-type LQ controls
are smoothly united to form a single nonlinear control. Numerical
experiments indicate that this control show remarkable performances
for a nonlinear system.
Abstract: The spectral action balance equation is an equation that
used to simulate short-crested wind-generated waves in shallow water
areas such as coastal regions and inland waters. This equation consists
of two spatial dimensions, wave direction, and wave frequency which
can be solved by finite difference method. When this equation with
dominating convection term are discretized using central differences,
stability problems occur when the grid spacing is chosen too coarse.
In this paper, we introduce the splitting upwind schemes for avoiding
stability problems and prove that it is consistent to the upwind scheme
with same accuracy. The splitting upwind schemes was adopted
to split the wave spectral action balance equation into four onedimensional
problems, which for each small problem obtains the
independently tridiagonal linear systems. For each smaller system
can be solved by direct or iterative methods at the same time which
is very fast when performed by a multi-processor computer.
Abstract: In this paper we propose a robust adaptive fuzzy
controller for a class of nonlinear system with unknown dynamic.
The method is based on type-2 fuzzy logic system to approximate
unknown non-linear function. The design of the on-line adaptive
scheme of the proposed controller is based on Lyapunov technique.
Simulation results are given to illustrate the effectiveness of the
proposed approach.
Abstract: In this paper, we introduce a robust state feedback controller design using Linear Matrix Inequalities (LMIs) and guaranteed cost approach for Takagi-Sugeno fuzzy systems. The purpose on this work is to establish a systematic method to design controllers for a class of uncertain linear and non linear systems. Our approach utilizes a certain type of fuzzy systems that are based on Takagi-Sugeno (T-S) fuzzy models to approximate nonlinear systems. We use a robust control methodology to design controllers. This method not only guarantees stability, but also minimizes an upper bound on a linear quadratic performance measure. A simulation example is presented to show the effectiveness of this method.
Abstract: In this paper, for the understanding of the phytoplankton dynamics in marine ecosystem, a susceptible and an infected class of phytoplankton population is considered in spatiotemporal domain.
Here, the susceptible phytoplankton is growing logistically and the
growth of infected phytoplankton is due to the instantaneous Holling
type-II infection response function. The dynamics are studied in terms of the local and global stabilities for the system and further
explore the possibility of Hopf -bifurcation, taking the half saturation period as (i.e., ) the bifurcation parameter in temporal domain.
It is also observe that the reaction diffusion system exhibits spatiotemporal
chaos and pattern formation in phytoplankton dynamics,
which is particularly important role play for the spatially extended phytoplankton system. Also the effect of the diffusion coefficient
on the spatial system for both one and two dimensional case is obtained. Furthermore, we explore the higher-order stability analysis
of the spatial phytoplankton system for both linear and no-linear system. Finally, few numerical simulations are carried out for pattern
formation.