基于LMI的不确定时滞非线性系统鲁棒镇定研究

研究了一类不确定时滞非线性系统的鲁棒镇定问题.不确定参数是时变未知有界的,但不一定满足所谓的匹配条件.利用线性矩阵不等式,一些充分条件被获得,保证了相应闭环系统的鲁棒稳定性,并在此基础上得出了相应的状态反馈控制器.最后,通过一个数值例子说明了该方法的有效性.

Robust adaptive dynamic surface control for nonlinear uncertain systems

We propose a new method for robust adaptive backstepping control of nonlinear systems with parametric uncertainties and disturbances in the strict feedback form. The method is called dynamic surface control. Traditional backstepping algorithms require repeated differentiations of the modelled nonlinearities. The addition of n first order low pass filters allows the algorithm to be implemented without differentiating any model nonlinearities, thus ending the complexity arising due to the 'explosion of terms' that makes other methods difficult to implement in practice. The combined robust adaptive backstepping/first order filter system is proved to be semiglobally asymptotically stable for sufficiently fast filters by a singular perturbation approach. The simulation results demonstrate the feasibility and effectiveness of the controller designed by the method.

ROBUST CONTROL OF A CLASS OF NONLINEAR SYSTEM WITH TIME-VARYING PAR AMETRIC UNCERTAINTIES

A class of triangular non li near system with disturbances which has unknown multiplicative time varying par ametric uncertainties in each virtual control is treated by a backstepping techn ique. The controller designed for all admissible uncertainties can guarantee tha t all states of its closed loop system are uniformly bounded. The robust contro ller design algorithm and a sufficient condition of the system stability are giv en. In addition, the closed loop system has an ISS property when the multiplica tive time varying parametric uncertainties are viewed as inputs to the system. Thus, this design provides a way to prevent a destabilizing effect of the multip licative time varying parametric uncertainties. Finally, simulational example i s given and simulational result shows that the controller exhibits effectiveness and excellent robustness.

ROBUST STABILIZATING FOR A OLASS OF UNOERTAIN NONLINEAR INTEROONNECTED SYSTEMS USING VARIABLE STRUCTURE CONTROL

The robust stabilizating control problem for a class of uncertain nonlinear large-scale systems is discussed. Based on the theory of both input/output (I/O) linearization and decentralized variable structure control (VSC),two-level and decentralized variable structure control laws for this kind of systems are presented respectively,which achieve asymptotically stabilization despite the uncertainties and disturbances. At last,sirnulation of the disturbed two-pendulum system is given to illustrate the feasibility of proposed technique.

Adaptive control using interval Type-2 fuzzy logic for uncertain nonlinear systems

A new adaptive Type-2 （T2） fuzzy controller was developed and its potential performance advantage over adaptive Type-1 （T1） fuzzy control was also quantified in computer simulation. Base on the Lyapunov method, the adaptive laws with guaranteed system stability and convergence were developed. The controller updates its parameters online using the laws to control a system and tracks its output command trajectory. The simulation study involving the popular inverted pendulum control problem shows theoretically predicted system stability and good tracking performance. And the comparison simulation experiments subjected to white noige or step disturbance indicate that the T2 controller is better than the T1 controller by 0--18%, depending on the experiment condition and performance measure.

Adaptive Backstepping Sliding Mode Control for Nonlinear Systems with Input Saturation

An adaptive backstepping sliding mode control is proposed for a class of uncertain nonlinear systems with input saturation.A command filtered approach is used to prevent input saturation from destroying the adaptive capabilities of neural networks (NNs).The control law and adaptive updating laws of NNs are derived in the sense of Lyapunov function,so the stability can be guaranteed even under the input saturation.The proposed control law is robust against the disturbance,and it can also eliminate the impact of input saturation.Simulation results indicate that the proposed controller has a good performance.

Robust adaptive control for a class of uncertain non-affine nonlinear systems using neural state feedback compensation

A robust adaptive control is proposed for a class of uncertain nonlinear non-affine SISO systems. In order to approximate the unknown nonlinear function, an affine type neural network(ATNN) and neural state feedback compensation are used, and then to compensate the approximation error and external disturbance, a robust control term is employed. By Lyapunov stability analysis for the closed-loop system, it is proven that tracking errors asymptotically converge to zero. Moreover, an observer is designed to estimate the system states because all the states may not be available for measurements. Furthermore, the adaptation laws of neural networks and the robust controller are given based on the Lyapunov stability theory. Finally, two simulation examples are presented to demonstrate the effectiveness of the proposed control method. Finally, two simulation examples show that the proposed method exhibits strong robustness, fast response and small tracking error, even for the non-affine nonlinear system with external disturbance, which confirms the effectiveness of the proposed approach.

Actuator fault diagnosis of autonomous underwater vehicle based on improved Elman neural network

Autonomous underwater vehicles(AUV) work in a complex marine environment. Its system reliability and autonomous fault diagnosis are particularly important and can provide the basis for underwater vehicles to take corresponding security policy in a failure. Aiming at the characteristics of the underwater vehicle which has uncertain system and modeling difficulty, an improved Elman neural network is introduced which is applied to the underwater vehicle motion modeling. Through designing self-feedback connection with fixed gain in the unit connection as well as increasing the feedback of the output layer node, improved Elman network has faster convergence speed and generalization ability. This method for high-order nonlinear system has stronger identification ability. Firstly, the residual is calculated by comparing the output of the underwater vehicle model(estimation in the motion state) with the actual measured values. Secondly, characteristics of the residual are analyzed on the basis of fault judging criteria. Finally, actuator fault diagnosis of the autonomous underwater vehicle is carried out. The results of the simulation experiment show that the method is effective.

Guaranteed cost sampled-data control for uncertain nonlinear time-varying delay system

The robust guaranteed cost sampled-data control was studied for a class of uncertain nonlinear systems with time-varying delay. The parameter uncertainties are time-varying norm-bounded and appear in both the state and the input control matrices. By applying an input delay approach, the system was transformed into a continuous time-delay system. Attention was focused on the design of a robust guaranteed cost sampled-data control law which guarantees that the closed-loop system is asymptotically stable and the quadratic performance index is less than a certain bound for all admissible uncertainties. By applying Lyapunov stability theory, the theorems were derived to provide sufficient conditions for the existence of robust guaranteed cost sampled-data control law in the form of linear matrix inequalities (LMIs), especially an optimal state-feedback guaranteed cost sampled-data control law which ensures the minimization of the guaranteed cost was given. The effectiveness of the proposed method was illustrated by a simulation example with the asymptotically stable curves of system state under the initial condition of x(0)=[0.679 6 0].

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.

Serret-Frenet frame based on path following control for underactuated unmanned surface vehicles with dynamic uncertainties

The path following problem for an underactuated unmanned surface vehicle(USV) in the Serret-Frenet frame is addressed. The control system takes account of the uncertain influence induced by model perturbation, external disturbance, etc. By introducing the Serret-Frenet frame and global coordinate transformation, the control problem of underactuated system(a nonlinear system with single-input and ternate-output) is transformed into the control problem of actuated system(a single-input and single-output nonlinear system), which simplifies the controller design. A backstepping adaptive sliding mode controller(BADSMC)is proposed based on backstepping design technique, adaptive method and theory of dynamic slide model control(DSMC). Then, it is proven that the state of closed loop system is globally stabilized to the desired configuration with the proposed controller. Simulation results are presented to illustrate the effectiveness of the proposed controller.

Non-fragile delay-dependent H_∞ control of linear time-delay system with uncertainties in state and control input

The problem of designing a non-fragile delay-dependent H∞ state-feedback controller was investigated for a linear time-delay system with uncertainties in state and control input. First, a recently derived integral inequality method and Lyapunov-Krasovskii stability theory were used to derive new delay-dependent bounded real lemmas for a non-fragile state-feedback controller containing additive or multiplicative uncertainties. They ensure that the closed-loop system is internally stable and has a given H∞ disturbance attenuation level. Then, methods of designing a non-fragile H∞ state feedback controller were presented. No parameters need to be tuned and can be easily determined by solving linear matrix inequalities. Finally, the validity of the proposed methods was demonstrated by a numerical example with the asymptotically stable curves of system state and controller output under the initial condition of x(0)=1 0 -1]T and h=0.8 time-delay boundary.

L_1 adaptive controller of nonlinear reference system in presence of unmatched uncertainties

An extension of L_1 adaptive control is proposed for the unmatched uncertain nonlinear system with the nonlinear reference system that defines the performance specifications. The control law adapts fast and tracks the reference system with the guaranteed robustness and transient performance in the presence of unmatched uncertainties. The interval analysis is used to build the quasi-linear parameter-varying model of unmatched nonlinear system, and the robust stability of the proposed controller is addressed by sum of squares programming. The transient performance analysis shows that within the limit of hardware a large adaption gain can improve the asymptotic tracking performance. Simulation results are provided to demonstrate the theoretical findings of the proposed controller.

Robust reliable H_∞ control for a class of uncertain time-delay systems

This paper deals with the problem of robust reliable H∞ control for a class of uncertain nonlinear systems with time-varying delays and actuator failures. The uncertainties in the system are norm-bounded and time-varying. Based on Lyapunov methods, a sufficient condition on quadratic stabilization independent of delay is obtained. With the help of LMIs (linear matrix inequalities) approaches, a linear state feedback controller is designed to quadratically stabilize the given systems with a H∞ performance constraint of disturbance attenuation for all admissible uncertainties and all actuator failures occurred within the prespecified subset. A numerical example is given to demonstrate the effect of the proposed design approach.

ROBUST OBSERVER DESIGN FOR A CLASS OF UNCERTAIN NONLINEAR LARGE SCALE SYSTEMS *

In this paper, a mathematic description of a class of uncertain nonlinear large scale systems based on some practical application is given. A designing method to construct observers for such kind of nonlinear composite systems is developed. The unknown parameters and disturbances are assumed to be neither linear nor matched. A numerical example is used to illustrate the efficiency of our results.

Synchronization of hyperchaotic Rossler system with uncertain parameters via nonlinear control

Based on the Lyapunov stability theory,a new method for synchronization of hyperchaotic Rossler system with uncertain parameters is proposed. By this method, choosing appropriate control law and adaptive update law of uncertain parameters, all the errors of system variable synchronization and of uncertain param- eter track are asymptotically stable. The theoretical analysis and the numerical simulations prove the efffectiveness of the oroDosed method.

ON LIMITATIONS OF THE SAMPLED-DATA FEEDBACK FOR NONPARAMETRIC DYNAMICAL SYSTEMS

In this paper, we study a basic class of first order sampled-data control systems with unknown nonlinear structure and with sampling rate not necessarily fast enough, aiming at understanding the capability and limitations of the sampled-data feedback. We show that if the unknown nonlinear function has a linear growth rate with its 'slope' (denoted by L) being a measure of the 'size' of uncertainty, then the sampling rate should not exceed 1/L multiplied by a constant (≈ 7.53) for the system to be globally stabilizable by the sampled-data feedback. If, however, the unknown nonlinear function has a growth rate faster than linear, and if the system is disturbed by noises modeled as the standard Brownian motion, then an example is given, showing that the corresponding sampled-data system is not stabilizable by the sampled-data feedback in general, no matter how fast the sampling rate is.

A trigonometric interval method for dynamic response analysis of uncertain nonlinear systems

This paper proposes a new non-intrusive trigonometric polynomial approximation interval method for the dynamic response analysis of nonlinear systems with uncertain-but-bounded parameters and/or initial conditions.This method provides tighter solution ranges compared to the existing approximation interval methods.We consider trigonometric approximation polynomials of three types:both cosine and sine functions,the sine function,and the cosine function.Thus,special interval arithmetic for trigonometric function without overestimation can be used to obtain interval results.The interval method using trigonometric approximation polynomials with a cosine functional form exhibits better performance than the existing Taylor interval method and Chebyshev interval method.Finally,two typical numerical examples with nonlinearity are applied to demonstrate the effectiveness of the proposed method.

THE FURTHER RESULT ON GLOBAL PRACTICAL TRACKING FOR HIGH-ORDER UNCERTAIN NONLINEAR SYSTEMS

This paper extends the unknown control coefficients with lower and upper constant bounds to the ones which may take arbitrarily large and /or small values.Since the existing methods are no longer applicable and the technical obstacles caused by the extensions are essential,new control design scheme should be exploited to the global practical tracking.By the approaches of Nussbaum-gain and adding a power integrator,the authors successfully propose the design scheme of the adaptive practical tracking controller for the systems.It is shown that the designed controller guarantees that all the closed-loop system states are bounded and the tracking error becomes prescribed arbitrarily small after a finite time.

ROBUST OUTPUT FEEDBACK STABILIZATION OF NONLINEAR NETWORKED SYSTEMS VIA A FINITE DATA-RATE COMMUNICATION CHANNEL

This paper addresses a robust stabilization problem of a class of uncertain nonlinear systems using output measurements via a finite data-rate communication channel. The authors assumes that there exist an observer and a control law for the systems in the absence of any finite data-rate communi- cation channel. Based on the observer and the control law, the authors constructs an encoder/decoder pair and provides a sufficient condition, including suitable sampling period and data rate, which will guarantee the stability of the closed-loop systems when a finite data-rate communication channel is introduced.