一类非线性系统降维观测器的设计

与线性系统一样，非线性系统状态观测器，按其结构可分为全维观测器和降维观测器。基于对Riccati方程的求解，本文对具有主线性部分，非线性部分满足Lipschitz条件的非线性系统给出了一降维观测器的设计方法，并讨论了该方法的适用性。

Adaptive Nonlinear PID Control and Rule-Based Compensation for Systems with Backlash

The control of dynamic nonlinear systems with unknown backlash was considered. By using an efficient approach to estimate the unknown backlash parameters, a rule? based backlash compensator was presented for canceling the effect of backlash. Adaptive nonlinear PID controller together with rule? based backlash compensator was developed and a satisfactory tracking performance was achieved. Simulation results demonstrated the effectiveness of the proposed method.

Equilibrium Control Theory and Direct Method of Feedback Linearization for Nonlinear Time Varying Systems

Aim To present a simple and effective method for the design of nonlinear and time varying control system. Methods A new concept of dynamic equilibrium of a system and its stability were presented first. It was pointed out that what is controlled directly by the input of a control system is the system's dynamic equilibrium rather than the states. Based on it, a new feedback linearization method for nonlinear system based on the Lyapunov direct method was given. Simulation studies were also carried out. Results The example and simulation show that by use of the method, the controller design becomes very simple and the control effect is quite satisfying. Conclusion The new method unifies the stabilizing problem(regulating problem) with the tracking problem. It is a very simple and effective method for the design of nonlinear and time varying control system.

SEMI ACTIVE VIBRATION CONTROL BASED ON A VIBRATION ABSORBER WITH ADJUSTABLE CLEARANCE

Presented in this paper is a semi active vibration control strategy based on the vibration absorber with adjustable clearance in elastic component. The control law of the clearance for alleviating the vibration of primary system is derived by means of harmonic balancing technique so that the working frequency of the vibration absorber can trace the frequency variation of the harmonic excitation. The efficacy of the strategy is demonstrated by numerical simulations for attenuating the steady state vibration of a SDOF system and a 2 DOF system, which are under the harmonic excitation with slowly varied frequency in a wide range.

Global stabilization for a class of nonlinear time-delay systems using linear output feedback

The stabilization problem via the linear output feedback controller is addressed for a class of nonlinear systems subject to time-delay.The uncertainty of the system satisfies the lower-triangular growth condition and it is affected by time-delay. A linear output feedback controller with a tunable scaling gain is constructed.By selecting an appropriate Lyapunov-Krasovskii functional the scaling gain can be adjusted to render the closed-loop system globally asymptotically stable.The results can also be extended to the non-triangular nonlinear time-delay systems. The proposed control law together with the observer is linear and memoryless in nature and therefore it is easy to implement in practice. Two computer simulations are conducted to illustrate the effectiveness of the proposed theoretical results.

Nonlinear control for a class of hydraulic servo system

The dynamics of hydraulic systems are highly nonlinear and the system may be subjected to non-smooth and discontinuous nonlinearities due to directional change of valve opening, friction, etc. Aside from the nonlinear nature of hydraulic dynamics, hydraulic servo systems also have large extent of model uncertainties. To address these challenging issues, a robust state-feedback controller is designed by employing backstepping design technique such that the system output tracks a given signal arbitrarily well, and all signals in the closed-loop system remain bounded. Moreover, a relevant disturbance attenuation inequality is satisfied by the closed-loop signals. Compared with previously proposed robust controllers, this paper's robust controller based on backstepping recursive design method is easier to design, and is more suitable for implementation.

Unknown Input Extended Kalman Filter and Applications in Nonlinear Fault Diagnosis

Unknown input observer is one of the most famous strategies for robust fault diagnosis of linear systems, but studies on nonlinear cases are not sufficient. On the other hand, the extended Kalman filter （EKF） is wellknown in nonlinear estimation, and its convergence as an observer of nonlinear deterministic system has been derived recently. By combining the EKF and the unknown input Kalman filter, we propose a robust nonlinear estimator called unknown input EKF （UIEKF） and prove its convergence as a nonlinear robust observer under some mild conditions using linear matrix inequality （LMI）. Simulation of a three-tank system “DTS200”, a benchmark in process control, demonstrates the robustness and effectiveness of the UIEKF as an observer for nonlinear systems with uncertainty, and the fault diagnosis based on the UIEKF is found successful.

Chirped Waves for a Generalized (2 + 1)-Dimensional Nonlinear Schrdinger Equation

The exact chirped soliton-like and quasi-periodic wave solutions of （2 ＋ 1）-dimensional generalized nonlinear Schr6dinger equation including linear and nonlinear gain （loss） with variable coefficients are obtained detalledly in this paper. The form and the behavior of solutions are strongly affected by the modulation of both the dispersion coefficient and the nonlinearity coefficient. In addition, self-similar soliton-like waves precisely piloted from our obtained solutions by tailoring the dispersion and linear gain （loss）.

Sliding mode identifier for parameter uncertain nonlinear dynamic systems with nonlinear input

This paper presents a sliding mode (SM) based identifier to deal with the parameter identification problem for a class of parameter uncertain nonlinear dynamic systems with input nonlinearity. A sliding mode controller (SMC) is used to ensure the global reaching condition of the sliding mode for the nonlinear system; an identifier is designed to identify the uncertain parameter of the nonlinear system. A numerical example is studied to show the feasibility of the SM controller and the asymptotical convergence of the identifier.

Adaptive predictive functional control based on Takagi-Sugeno model and its application to pH process

In order to obtain accurate prediction model and compensate for the influence of model mismatch on the control performance of the system and avoid solving nonlinear programming problem,an adaptive fuzzy predictive functional control(AFPFC) scheme for multivariable nonlinear systems was proposed.Firstly,multivariable nonlinear systems were described based on Takagi-Sugeno(T-S) fuzzy models;assuming that the antecedent parameters of T-S models were kept,the consequent parameters were identified on-line by using the weighted recursive least square(WRLS) method.Secondly,the identified T-S models were linearized to be time-varying state space model at each sampling instant.Finally,by using linear predictive control technique the analysis solution of the optimal control law of AFPFC was established.The application results for pH neutralization process show that the absolute error between the identified T-S model output and the process output is smaller than 0.015;the tracking ability of the proposed AFPFC is superior to that of non-AFPFC(NAFPFC) for pH process without disturbances,the overshoot of the effluent pH value of AFPFC with disturbances is decreased by 50% compared with that of NAFPFC;when the process parameters of AFPFC vary with time the integrated absolute error(IAE) performance index still retains to be less than 200 compared with that of NAFPFC.

Nonlinear adaptive switching control for a class of non-affine nonlinear systems

An improved nonlinear adaptive switching control method is presented to relax the assumption on the higher order nonlinear terms of a class of discrete-time non-affine nonlinear systems. The proposed control strategy is composed of a linear adaptive controller, a neural network(NN) based nonlinear adaptive controller and a switching mechanism. An incremental model is derived to represent the considered system and an improved robust adaptive law is chosen to update the parameters of the linear adaptive controller. A new performance criterion of the switching mechanism is designed to select the proper controller. Using this control scheme, all the signals in the system are proved to be bounded. Numerical examples verify the effectiveness of the proposed algorithm.

Nonlinear adaptive optimal control for vehicle handling improvement through steer-by-wire system

A control algorithm for improving vehicle handling was proposed by applying right angle to the steering wheel,based on the nonlinear adaptive optimal control(NAOC).A nonlinear 4-DOF model was initially developed,then it was simplified to a 2-DOF model with reasonable assumptions to design observer and optimal controllers.Then a simplified model was developed for steering system.The numerical simulations were carried out using vehicle parameters for standard maneuvers in dry and wet road conditions.Moreover,the hardware in the loop method was implemented to prove the controller ability in realistic conditions.Simulation results obviously show the effectiveness of NAOC on vehicle handling and reveal that the proposed controller can significantly improve vehicle handling during severe maneuvers.

Pendulation reduction on ship-mounted container crane via T-S fuzzy model

Ship-mounted container cranes are challenging industrial applications of nonlinear pendulum-like systems with oscillating disturbance which can cause them unstable.Since wave-induced ship motion causes the hoisted container to swing during the transfer operation,the swing motion may be dangerously large and the operation must be stopped.In order to reduce payload pendulation of ship-mounted crane,nonlinear dynamics of ship-mounted crane is derived and a control method using T-S fuzzy model is proposed.Simulation results are given to illustrate the validity of the proposed design method and pendulation of ship-mounted crane is reduced significantly.

Influence of the Kerr Effect on the Optical Force Acting on the Dielectric Particle

Basing on the necessary condition for the trapping dielectric particle by the Gaussian beam, the Kerr effect in the tweezers with the nonlinear particle or the nonlinear medium is proposed to concern. The expressions of the optical forces concerned with the Kerr effect, which affects the refractive index of the medium, are presented. The distribution of the optical forces in the trapping region is simulated and discussed. The results show that the stability of the tweezers depends on the nonlinear coefficient of refractive index, and the optical tweezers could be broken down with a critical value of the nonlinear coefficient of refractive index of the surrounding medium, or with a critical value of the laser intensity, duration of laser pulse, and radius of beam waist. Moreover, these results give us the explanation the stability of the optical tweezers used for the trapped object as biological molecule embedded in the fluid, which is sensitive with Kerr effect.

Smoothing Newton-Like Method for the Solution of Nonlinear Systems of Equalities and Inequalities

In this paper,we present a smoothing Newton-like method for solving nonlinear systems of equalities and inequalities.By using the so-called max function,we transfer the inequalities into a system of semismooth equalities.Then a smoothing Newton-like method is proposed for solving the reformulated system,which only needs to solve one system of linear equations and to perform one line search at each iteration. The global and local quadratic convergence are studied under appropriate assumptions. Numerical examples show that the new approach is effective.

Nonlinear Coupled Analysis of a Single Point Mooring System

Coupled effects on a single point mooring(SPM) system subjected to the combined action of wind,waves and current are studied in this paper. Due to the complicatedness of the sea state and the huge size of the vessel,physical experimental study is both time consuming and uneconomical,whereas the numerical study is cost-effective and DNV software provides powerful SESAM software in solving the issues. This paper focuses on the modeling process of the SPM system,catenary equilibrium calculation,static analysis of the vessel in three different scenarios,and dynamic response simulation of the SPM system under environmental excitations. The three scenarios in study are as follows:the SPM is under the combined function of(a) wind,waves and current,(b) wind and waves,(c) current and waves. They are so set that one can compare the contributions of different types of loads in both static and dynamic studies. Numerical study shows that wind and current are the two major factors contributing to the mooring line tension,and surge and sway are the two dominant motions of the moored vessel subjected to environmental excitations.

Remarks on Global Existence for Higher-dimensional Thermoviscoelastic Equations

In this paper, we obtain some global existence results for the higher-dimensionai nonhomogeneous, linear, semilinear and nonlinear thermoviscoelastic systems by using semigroup approach.

Nonlinear analysis of nano-cluster doped fiber

There are prominent nonlinear characteristics that we hope for the semiconductor nano-clusters doped fiber. Refractive index of fiber core can be effectively changed by adulteration. This technology can provide a new method for developing photons components. Because the semiconductor nano-cluster has quantum characteristics, Based on first-order perturba- tion theory and classical theory of fiber, we deduced refractive index expressions of fiber core, which was semiconductor nano-cluster doped fiber. Finally, third-order nonlinear coefficient equation was gained. Using this equation, we calculated SMF-28 fiber nonlinear coefficient. The equation shows that new third-order coefficient was greater.

Chirped Bright and Dark Solitons for NLSE with Localized Dissipation

We report the existence of chirped bright and dark solitons for higher order nonlinear Schrodinger equation in the presence of localized dissipation. The parameter domains are delineated in which these solitons exist. It is found that the chirp associated with each of the soliton pulses is directly proportional to intensity and gets saturated at some finite value as the retarded time approaches its asymptotic value. We further show that the higher order nonlinearities in the system such as self-steepening and self-frequency shift do not influence the amplitude of the soliton pulses significantly but primarily control the strength of the localized dissipation.

Polarization Oblique Projection Based Self-Interference Cancellation against PA Nonlinear Distortion in MIMO Full Duplex System

In MIMO full duplex system,power amplifier(PA) nonlinearity limits the self-interference(SI) cancellation seriously. Most existing methods need to model and estimate the PA nonlinearity in order to reconstruct the SI,however the estimation error caused by the mismatch between the estimated PA model and the actual PA property still impacts the cancellation ability,especially when the transmit power is high. In this paper we propose a polarization oblique projection based self-interference cancellation method which does not need to estimate the PA nonlinearity coefficients. It exploits the polarization state information of the signals which is immune to the PA nonlinearity,and establishes an oblique projection operator to cancel the SI. Numerical results and analysis demonstrate that it can cancel the nonlinear SI effectively. Moreover the signal to interfere plus noise ratio(SINR) and the achievable sum rate do not deteriorate when the transmit power is high. Further,the upper bound of the achievable sum rate can be more than twice that of the half duplex.