Design of Nonlinear Observer by Using Augmented Linear System based on Formal Linearization of Polynomial Type
The objective of this study is to propose an observer design for nonlinear systems by using an augmented linear system derived by application of a formal linearization method. A given nonlinear differential equation is linearized by the formal linearization method which is based on Taylor expansion considering up to the higher order terms, and a measurement equation is transformed into an augmented linear one. To this augmented dimensional linear system, a linear estimation theory is applied and a nonlinear observer is derived. As an application of this method, an estimation problem of transient state of electric power systems is studied, and its numerical experiments indicate that this observer design shows remarkable performances for nonlinear systems.
nonlinear system, augmented linear system, nonlinear observer, formal linearization, electric power system.
On-line Identification of Continuous-time Hammerstein Systems via RBF Networks and Immune Algorithm
This paper deals with an on-line identification method
of continuous-time Hammerstein systems by using the radial basis
function (RBF) networks and immune algorithm (IA). An unknown
nonlinear static part to be estimated is approximately represented
by the RBF network. The IA is efficiently combined with the
recursive least-squares (RLS) method. The objective function for the
identification is regarded as the antigen. The candidates of the RBF
parameters such as the centers and widths are coded into binary bit
strings as the antibodies and searched by the IA. On the other hand,
the candidates of both the weighting parameters of the RBF network
and the system parameters of the linear dynamic part are updated
by the RLS method. Simulation results are shown to illustrate the
Continuous-time System, Hammerstein System, OnlineIdentification, Immune Algorithm, RBF network.
Design of Nonlinear Observer by Using Chebyshev Interpolation based on Formal Linearization
This paper discusses a design of nonlinear observer by
a formal linearization method using an application of Chebyshev Interpolation
in order to facilitate processes for synthesizing a nonlinear
observer and to improve the precision of linearization.
A dynamic nonlinear system is linearized with respect to a linearization
function, and a measurement equation is transformed into
an augmented linear one by the formal linearization method which is
based on Chebyshev interpolation. To the linearized system, a linear
estimation theory is applied and a nonlinear observer is derived. To
show effectiveness of the observer design, numerical experiments
are illustrated and they indicate that the design shows remarkable
performances for nonlinear systems.
nonlinear system, nonlinear observer, formal linearization,Chebyshev interpolation.
Hybrid Algorithm for Hammerstein System Identification Using Genetic Algorithm and Particle Swarm Optimization
This paper presents a method of model selection and
identification of Hammerstein systems by hybridization of the genetic
algorithm (GA) and particle swarm optimization (PSO). An unknown
nonlinear static part to be estimated is approximately represented
by an automatic choosing function (ACF) model. The weighting
parameters of the ACF and the system parameters of the linear
dynamic part are estimated by the linear least-squares method. On
the other hand, the adjusting parameters of the ACF model structure
are properly selected by the hybrid algorithm of the GA and PSO,
where the Akaike information criterion is utilized as the evaluation
value function. Simulation results are shown to demonstrate the
effectiveness of the proposed hybrid algorithm.
Hammerstein system, identification, automatic choosing
function model, genetic algorithm, particle swarm optimization.
Design of Extremum Seeking Control with PD Accelerator and its Application to Monod and Williams-Otto Models
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.
Extremum seeking control, Monod model, Williams-
Otto model, PD acceleration term, Optimal operating point.
An Approach to Control Design for Nonlinear Systems via Two-stage Formal Linearization and Two-type LQ Controls
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.
Formal Linearization, LQ Control, Nonlinear Control,Taylor Expansion, Zero Function.
An Augmented Automatic Choosing Control Designed by Extremizing a Combination of Hamiltonian and Lyapunov Functions for Nonlinear Systems with Constrained Input
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.
Augmented Automatic Choosing Control, NonlinearControl, Genetic Algorithm, Hamiltonian, Lyapunovfunction
Gaussian Process Model Identification Using Artificial Bee Colony Algorithm and Its Application to Modeling of Power Systems
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.
Artificial bee colony algorithm, Gaussian process model, identification, nonlinear system, electric power system.
Short-Term Electric Load Forecasting Using Multiple Gaussian Process Models
This paper presents a Gaussian process model-based
short-term electric load forecasting. The Gaussian process model is
a nonparametric model and the output of the model has Gaussian
distribution with mean and variance. The multiple Gaussian process
models as every hour ahead predictors are used to forecast future
electric load demands up to 24 hours ahead in accordance with the
direct forecasting approach. The separable least-squares approach that
combines the linear least-squares method and genetic algorithm is
applied to train these Gaussian process models. Simulation results
are shown to demonstrate the effectiveness of the proposed electric
Direct method, electric load forecasting, Gaussian process model, genetic algorithm, separable least-squares method.