Discrete-time adaptive control of systems with multisegmentpiecewise-linear nonlinearities

Inverse schemes are constructed for multisegment piecewise-linear nonlinearities. Adaptive laws are proposed to update the inverse to cancel the effect of the unknown characteristic of such a nonlinearity which appears at the input of a linear part. Two adaptive control schemes using an adaptive inverse and a linear controller structure are developed: one for the linear part known and the other for the linear part unknown. Different adaptive designs are given based on different a priori nonlinearity knowledge necessary for the construction of an adaptive inverse. The adaptive inverse controllers ensure closed-loop signal boundedness and lead to significant improvements of system tracking performance     

滞环非线性系统的加权自适应控制

本文通过引入一个非线性补偿环节和一个开关量函数,解决了滞环非线性系统的自适应 控制问题,并分别对滞环宽度已知和未知情况,建立了大范围渐近收敛和稳定的加权自适应控 制算法.这种算法具有渐近最优的控制效果,能用于非最小相位系统.仿真结果表明,该算法 具有良好的动态性能.     

Adaptive control of systems with nonsmooth input and outputnonlinearities

Adaptive control schemes are developed for plants with unknown nonsmooth nonlinearities at both the input and output of a linear dynamics. New controller parameterizations with nonlinearity inverses for parameterized nonlinearities are employed. When implemented with true parameters and properly initialized, the inverse controller ensures closed-loop signal boundedness and output tracking. Adaptive laws are designed to update the parameter estimates to implement adaptive inverse controllers for unknown nonlinearities in two cases: the linear part known and the linear part unknown     

Frequency domain identification of Hammerstein models

Discusses Hammerstein model identification in the frequency domain using sampled input-output data. By exploring the fundamental frequency and harmonics generated by the unknown nonlinearity, we propose a frequency domain approach and show its convergence for both the linear and nonlinear subsystems in the presence of noise. No a priori knowledge of the structure of the nonlinearity is required and the linear part can be nonparametric.     

Observer design for systems with multivariable monotone nonlinearities

Globally convergent observers are designed for a class of systems with multivariable nonlinearities. The approach is to represent the observer error system as the feedback interconnection of a linear system and a state-dependent multivariable nonlinearity. We first extend an earlier design (Automatica 37 (12) (2001) 1923) to multivariable nonlinearities, satisfying an analog of the scalar nondecreasing property. Next, we exploit the structure of the nonlinearity to relax the positive real restriction on the linear part of the observer error system. This relaxed design renders the feasibility conditions less restrictive, and widens the applicability of the observer, as illustrated with examples. Finally, output nonlinearities are studied and the design is extended to be adaptive in the presence of unknown parameters.     

Frequency domain identification of Wiener models

This paper proposes a frequency domain algorithm for Wiener model identifications based on exploring the fundamental frequency and harmonics generated by the unknown nonlinearity. The convergence of the algorithm is established in the presence of white noise. No a priori knowledge of the structure of the nonlinearity is required and the linear part can be nonparametric.     

Recursive identification of errors-in-variables Wiener systems

This paper considers the recursive identification of errors-in-variables (EIV) Wiener systems composed of a linear dynamic system followed by a static nonlinearity. Both the system input and output are observed with additive noises being ARMA processes with unknown coefficients. By a stochastic approximation incorporated with the deconvolution kernel functions, the recursive algorithms are proposed for estimating the coefficients of the linear subsystem and for the values of the nonlinear function. All the estimates are proved to converge to the true values with probability one. A simulation example is given to verify the theoretical analysis.     

Decoupling the linear and nonlinear parts in Hammerstein model identification

The main result of this paper is to show that the linear part can be made decoupled from the nonlinear part in Hammerstein model identification. Therefore, identification of the linear part for a Hammerstein model becomes a linear problem and accordingly enjoys the same convergence and consistency results as if the unknown nonlinearity is absent.     

Adaptive neural control for a class of uncertain nonlinear systems with unknown time delay

A neural network (NN)‐based robust adaptive control design scheme is developed for a class of nonlinear systems represented by input–output models with an unknown nonlinear function and unknown time delay. By approximating on‐line the unknown nonlinear functions with a three‐layer feedforward NN, the proposed approach does not require the unknown parameters to satisfy the linear dependence condition. The control law is delay independent and possible controller singularity problem is avoided. It is proved that with the proposed neural control law, all the signals in the closed‐loop system are semiglobally bounded in the presence of unknown time delay and unknown nonlinearity. A simulation example is presented to demonstrate the method. Copyright © 2008 John Wiley & Sons, Ltd.     

A Kiefer‐Wolfowitz Algorithm Based Iterative Learning Control for Hammerstein‐Wiener Systems

The iterative learning control (ILC) is considered for the Hammerstein‐Wiener (HW) system, which is a cascading system consisting of a static nonlinearity followed by a linear stochastic system and then a static nonlinearity. Except the structure, the system is unknown, but the system output is observed with additive noise. Both the linear and nonlinear parts of the system may be time‐varying. The optimal control sequence under the tracking performance is first characterized, which, is however, unavailable since the system is unknown. By using the observations on system output the ILC is generated by a Kiefer‐Wolfowitz (KW) algorithm with randomized differences, which aims at minimizing the tracking error. It is proved that ILC converges to the optimal one with probability one and the resulting tracking error tends to its minimal value. Copyright © 2011 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society     

Practical time-varying formation tracking for high-order nonlinear multi-agent systems based on the distributed extended state observer

Practical time-varying formation tracking analysis and design problems for high-order nonlinear multi-agent systems are investigated, where the time-varying formation tracking error is controlled within an arbitrarily small bound. The states of followers form a predefined time-varying formation while tracking the state of the leader with unknown control input. Besides, the dynamics of each agent has heterogeneous nonlinearity and disturbance. First, a distributed extended state observer is constructed to estimate the follower's nonlinearity and disturbance, and the leader's unknown control input simultaneously. A protocol based on the distributed extended state observer is proposed. Second, sufficient conditions for the multi-agent systems to achieve the practical time-varying formation tracking under the protocol are presented by using the Lyapunov stability theory. Third, an approach is derived to design the proposed protocol by solving a linear matrix inequality. Finally, numerical simulation results are given to illustrate the effectiveness of the theoretical results.     

Neural network-based robust adaptive control of nonlinear systems with unmodeled dynamics

A neural network-based robust adaptive control design scheme is developed for a class of nonlinear systems represented by input–output models with an unknown nonlinear function and unmodeled dynamics. By on-line approximating the unknown nonlinear functions and unmodeled dynamics by radial basis function (RBF) networks, the proposed approach does not require the unknown parameters to satisfy the linear dependence condition. It is proved that with the proposed control law, the closed-loop system is stable and the tracking error converges to zero in the presence of unmodeled dynamics and unknown nonlinearity. A simulation example is presented to demonstrate the method.     

Markov chain approach to identifying Wiener systems

Identification of the Wiener system composed of an infinite impulse response (IIR) linear subsystem followed by a static nonlinearity is considered.The recursive estimates for unknown coefficients of the linear subsystem and for the values of the nonlinear function at any fixed points are given by the stochastic approx-imation algorithms with expanding truncations (SAAWET).With the help of properties of the Markov chain connected with the linear subsystem,all estimates derived in the paper are proved to be strongly consistent.In comparison with the existing results on the topic,the method presented in the paper simplifies the convergence analysis and requires weaker conditions.A numerical example is given,and the simulation results are consistent with the theoretical analysis.     

Operator-Based Robust Nonlinear Free Vibration Control of a Flexible Plate With Unknown Input Nonlinearity

In this paper,a robust nonlinear free vibration control design using an operator based robust right coprime factorization approach is considered for a flexible plate with unknown input nonlinearity.With considering the effect of unknown input nonlinearity from the piezoelectric actuator,operator based controllers are designed to guarantee the robust stability of the nonlinear free vibration control system.Simultaneously,for ensuring the desired tracking performance and reducing the effect of unknown input nonlinearity,operator based tracking compensator and estimation structure are given,respectively.Finally,both simulation and experimental results are shown to verify the effectiveness of the proposed control scheme.     

Adaptive robust control of uncertain nonlinear systems with nonlinear delayed state perturbations

The problem of robust stabilization of uncertain nonlinear dynamical systems with multiple time delays is considered. In the paper, the upper bound of the nonlinearity and uncertainty, including delayed states, is assumed to be a linear function of some parameters which are still assumed to be unknown. Here, we do not require that the nonlinear terms including delayed states are linear norm-bounded in the states. An improved adaptation law with σ-modification is employed to estimate the unknown parameters, and a class of memoryless adaptive robust state feedback controllers is proposed. It is also shown that the proposed adaptive robust controllers can guarantee the uniform asymptotic stability of uncertain nonlinear time-delay systems. Finally, as a numerical example, an uncertain time-delay ecosystem with two competing species is given to demonstrate the validity of the results.     

基于广义线性模型的变参数广义卡尔曼滤波

给出了连续系统的一种广义线性模型,不仅适用于已知系统,而且适用于未知系统,无论系统是线性还是非线性的。该模型系数服从确定的变化规律而无需在线辨识或预先计算,因而实时性好。定义了基于这种模型的变参数广义卡尔曼滤波。并给出其递推计算公式,可对未知系统实现实时滤波估计,且满足均方误差最小。该系统能方便、快捷、准确地实现未来多个时刻状态群的实时预报,以便提早掌握系统未来的运动趋势,提高系统的控制性能和对机动目标拦截的制导精度。算例仿真表明,结果是令人满意的。     

Incorporating anti-windup gain in improving stability of actuator constrained linear multiple state delays systems

This paper proposes the design of anti-windup compensator gain for improving stability of actuator input constrained linear multiple state delays systems. The system state delays are classified into mixed delay-dependent/delay-independent analysis and described by delay-differential equations. The real scalar delays are assumed to be fixed and unknown, but with known coefficient matrices. It is shown that the closed-loop system containing the controller plus the anti-windup gain can be modeled as a linear system with dead-zone nonlinearity. The formulation of anti-windup compensator gain is based on convex optimization using linear matrix inequalities (LMI) that ensure closed-loop asymptotic stability of the system while accounting upper-bound delays. The devised LMIs based on Lyapunov-Krasovskii functionals prove significantly less conservative in giving higher upper bounds delays in the formulation of anti-windup gain besides ensuring closed-loop asymptotic stability.     

Identification of block-oriented systems in the presence of nonparametric input nonlinearities of switch and backlash types

The problem of identifying Hammerstein-like systems containing dynamic nonlinearities, of the switch or backlash types, is considered. Interestingly, the nonlinearity borders are nonparametric borders (i.e. of unknown structure) and so are allowed to be noninvertible and cross each other. A semi-parametric identification approach is developed to estimate the linear subsystem parameters and m points on both nonlinearity borders. It relies on two main experiments designed so that during each one, the focus is on one lateral border exciting m specific points. Doing so, the initial nonparametric identification problem is decomposed into two simpler problems involving static parametric nonlinearities. The new problems are dealt with independently using least squares type estimators. It is formally shown that the experiments generate persistently exciting signals ensuring the consistency of all involved parameter estimators.     

Adaptive tracking control of MIMO nonlinear nonminimum phase system with unknown input nonlinearity

This paper proposes a nonlinear adaptive control for output tracking of multi‐input multi‐output nonlinear nonminimum phase system with input nonlinearity. The parameters of the input nonlinearity are assumed to be unknown. This problem is challenging, not only because of the unstable internal dynamics of nonminimum phase system, but also the existence of the unknown input nonlinearity. The partially linearized model of the original system is obtained through input/output linearization, and a states tracking model is constructed based on the computed ideal internal dynamics. A nonlinear adaptive controller, which can guarantee the bounded of output tracking error in the existence of unknown input nonlinearity, is proposed. Finally, a numerical simulation on vertical takeoff and landing aircraft is given to show the effectiveness of the proposed control methods.     

一种多输入单输出Hammerstein系统的集成辨识方法

针对多输入单输出(MISO)Hammerstein系统提出了一种稳态与动态辨识相结合的集成辨识方法.该方法利用稳态信息获取稳态模型的强一致性估计,并通过稳态模型以神经网络获得其非线性逼近函数,再利用动态信息辨识获取多输入单输出(MISO)Hammerstein系统的线性子系统未知参数的一致性估计.仿真结果表明了该方法的有效性和实用性.