Robust adaptive regulation without persistent excitation

A globally convergent adaptive regulator for minimum or nonminimum phase systems subject to bounded disturbances is presented. The control strategy is designed for a particular input-output representation obtained from the state-space representation of the system. The leading coefficient of the novel representation is the product of the observability and controllability matrices of the system. The controller scheme uses a least-squares identification algorithm with a dead zone. The dead zone is chosen to obtain convergence properties on the estimates and on the covariance matrix as well. This allows the definition of modified estimates which secure well-conditioned matrices in the adaptive control law. Explicit bounds on the plant output are given     

An improved adaptive control for robust adaptation

An adaptive control law consisting of an integral and proportional adaptation is suggested. It is shown that the addition of the proportional adaptation term to the control law improves the performance of the adaptive system. Although this is done in the context of a first-order system, it is believed that this may also be the case for higher-order systems. The scalar case is only discussed. Simulation results are presented to complement the theoretical developments     

A new robust adaptive control algorithm for linear time-varying plants

Robustness is an important property of a control system. Robust adaptive control has been an active research area for more than a decade. Since it was shown that un-modelled dynamics or even a small bounded disturbance can cause most adaptive control algorithms to go unstable, various modifications of the adaptive control algorithms have been developed to counteract instability and improve robustness with respect to unmodelled dynamics and bounded disturbances. However, we know that most of the modified approaches to achieve robustness require knowledge of either the parameter of bounding function on the unmodelled dynamics, or the upper bound on the disturbances, or the bound on the norm of unknown matching controller/plant parameters, and such knowledge can hardly be obtained in practice. A new indirect adaptive control algorithm for linear time-varying plants is proposed to achieve robustness to a class of unmodelled dynamics, bounded disturbances and plant parameter time variations. A modified relative dead zone technique is used, so that knowledge of the parameters of the upper bounding function on the unmodelled dynamics and the disturbances is not required. The stability analysis and the robust performance of adoptively controlled time-varying systems are provided for the new scheme. A simulation example is given to show the effectiveness of the proposed algorithm.     

Design of a robust adaptive control law for robotic manipulators

In this article, a robust adaptive control scheme for robotic manipulators is designed based on the concept of performance index and Lyapunov's second method. Compensators are selected for a given feedback system by using a quadratic performance index. Then the stability of the system is proven based on Lyapunov's method, where a Lyapunov function and its time-derivative are derived from the selected compensators. In the process of stabilization, stability bounds are obtained for disturbances, control gains, adaptation gains, and desired trajectories, in the presence of feedback delay due to digital computation and first-order hold in the control loop. © 1994 John Wiley & Sons, Inc.     

基于复合自适应律的直线电机自适应鲁棒控制

自适应鲁棒控制(ARC)能克服参数不确定性与扰动对系统的影响, 具有良好的输出跟踪性能. 然而常规ARC的参数估计值难以逼近真值. 为实现高性能的控制与准确的参数估计, 本文提出了基于复合自适应律的自适应鲁棒控制(CAARC). 该方法同时采用了输出误差与参数估计误差的相关信息构造自适应律, 具有比常规ARC更好的参数估计效果. 本文在理论上证明了CAARC的闭环稳定性与参数估计误差的收敛性, 并通过分析表明CAARC具有比常规ARC更好的输出跟踪性能, 最后通过仿真验证了该方法的有效性.     

Robust adaptive control of discrete-time systems using persistent excitation

An important result in the robust adaptive control of continuous-time systems, using the persistent excitation of the reference input, was recently given by Narendra and Annaswamy (1986, IEEE Trans. Aut. Control, AC-31, 306–315). According to this result, the global boundedness of all the signals in the adaptive system can be assured if the degree of persistent excitation of the reference input is larger than an appropriate bound on the external disturbance. The main theorem in Narendra and Annaswamy (1986) is proved for a class of plants characterized by the property that the reference model used in the adaptive controller could be chosen to be strictly positive real, a condition which involves constraints on the relative degree of the plant. This paper presents a generalization of the above result to plants of arbitrary relative degree. Together with the work reported in the earlier paper, it demonstrates that the boundedness of all the signals in an adaptive system in the presence of bounded disturbances and arbitrary initial conditions can be assured by increasing the degree of persistent excitation of the reference input.     

A robust model reference adaptive control without strictly positive real condition

This paper considers the model reference adaptive control problem for the system (1) with unmodelled dynamics m n dominated by a small constant k multiplied by a quantity dependent on the input, output and noise. Using bounded external excitation and randomly varying truncation techniques, we give design method of a model reference adaptive controller which is similar to that in Meyn and Brown (1992). It is shown that the closed-loop system is globally stable, the estimation error for parameter contained in the modelled part is of order k, and the closed-loop system under the model reference adaptive control law is suboptimal in the sense of lim sup 1/n n (A m (z) y i+1 - B m (z)z* i - C m (z) w i+1 ) 2 h O( k 2 ) + n 2 b 1 2 while the SPR condition usually used in other papers is replaced by a stability condition.     

On the usefulness of persistent excitation in ARX adaptive tracking

The usefulness of persistent excitation is well known in the control community. Using a persistently excited adaptive tracking control, we show that it is possible to avoid the strong controllability assumption recently proposed by the authors for multivariate ARX models. We establish the almost sure convergence for both least squares and weighted least squares estimators of the unknown parameters. A central limit theorem and a law of iterated logarithm are also provided. This asymptotical analysis is related to the Schur complement of a suitable limiting matrix.     

Improved robust backstepping adaptive control for nonlinear discrete-time systems without overparameterization

This paper reports a robust backstepping adaptive controller for output tracking of nonlinear discrete-time systems. The result improves the previous one in Zhang, Wen, and Soh [(2001). Robust adaptive control for nonlinear discrete-time systems without overparameterization. Automatica, 37, 551-558] by removing the lower bound constraints on the system nonlinearities.     

非持续激励条件下系统辨识递推最小二乘最小范数算法

系统辨识中广泛应用的最小二乘算法需要输入向量序列满足持续激励性条件(PE条件); 但在大多情况下这是难以满足的. 本文提出了一种不依赖于PE条件的递推最小二乘、最小范数辨识算法. 首先分析了最小二乘算法解空间的结构, 并运用罚函数方法, 将参数辨识问题转化为无约束优化问题. 然后, 提出了将步长、罚因子等过程控制参数统一的迭代－递推形式的辨识算法, 证明了算法在给定的控制参数约束下收敛于唯一的最小二乘、最小范数解向量. 仿真实验表明在非PE条件下算法的有效性.     

基于参数估计误差的鲁棒自适应律设计及验证

针对传统自适应控制系统设计的自适应律参数收敛慢进而影响控制系统瞬态性能的问题,研究一类新的基于参数估计误差修正的鲁棒自适应律设计.首先引入滤波操作给出参数估计误差的提取方法,构建出含参数估计误差修正项的自适应律,进而将该自适应律用于控制器设计和分析中,可同时实现控制误差和参数估计误差指数收敛.对比分析了几类传统自适应律和所提出自适应律的收敛性和鲁棒性,并给出了保证参数收敛所需持续激励条件的一种直观、简便的在线判别方法.数值仿真及基于自制三自由度直升机系统俯仰轴实验结果表明,基于参数误差修正的自适应律及控制器可得到优于传统自适应方法的跟踪控制和参数估计性能.     

附加控制输入反演自适应滑模鲁棒励磁控制

为了提高一类非匹配不确定非线性系统的渐近稳定鲁棒控制能力,简化传统反演自适应变结构控制计算,通过引入变结构附加控制输入量,降低子系统虚拟函数反演设计难度,克服传统反演自适应$L_{2     

A family of robust adaptive excitation controllers for synchronous generators with steam valve via Hamiltonian function method

Using the Hamiltonian function method,this paper proposes a family of robust adaptive excitation controllers for synchronous generators with steam valve control.First,a parameterization method of robus...     

一种新型自适应RBF神经网络滑模制导律

针对导弹拦截问题,提出一种自适应RBF神经网络滑模制导律．首先根据准平行接近原理和变结构控制理论设计滑模面,然后将滑模面作为RBF神经网络的输入变量,输出量即为导弹的加速度．为了使得导弹系统能够到达滑模面,采用自适应算法实时在线调整RBF神经网络的连接权值．该导引律将目标机动视为干扰量,在拦截过程中不需要测量目标加速度,因此该导引律对目标机动具有较强的鲁棒性．在执行上,只用到了视线角速率,因而实现简单．仿真结果表明,所提出的导引律和比例导引相比在脱靶量、拦截时间等方面有了很大的提高．     

一种基于鲁棒自适应观测器的故障区分方法

设计了一种鲁棒自适应观测器,通过其输出残差对传感器故障信息敏感性很高,而对系统故障信息敏感性很低的特点,实现了故障区分.设计了一套故障区分控制系统和检测策略,用以区分两类故障,以免发生误判现象.举例说明了该策略的可行性和有效性.     

A robust direct adaptive controller

This paper proposes a new direct adaptive control algorithm which is robust with respect to additive and multiplicative plant unmodeled dynamics. The algorithm is designed based on the reduced-order plant, which is assumed to be minimum phase and of known order and relative degree, but is analyzed with respect to the overall plant which, due to the unmodeled dynamics, may be nonminimum phase and of unknown order and relative degree. It is shown that if the unmodeled dynamics are sufficiently small in the low-frequency range, then the algorithm guarantees boundedness of all signals in the adaptive loop and "small" residual tracking errors for any bounded initial conditions. In the absence of unmodeled dynamics, the residual tracking error is shown to be zero.     

A robust stochastic adaptive controller

The adaptive tracking problem is considered for discrete-time stochastic systems consisting of a modeled part being a stable ARMAX process and unmodeled dynamics dominated by a small constant ϵ multiplied by a quantity independent of ϵ but tending to infinity as the past input, output, and noise grow. The adaptive control law proposed is switched at stopping times and is disturbed by a sequence of random vectors bounded by an arbitrary small but fixed constant σ. It is shown that the closed-loop system is globally stable, the estimation errors for parameters contained in the modeled part of the order ϵ, and the tracking error differs from the minimum tracking error for systems without unmodeled dynamics by value of O(ϵ² )+O(σ²)     

A robust stabilizing law for switched linear systems

In this paper, we address some robustness issues for a class of switched linear systems with non-linear perturbations. We illustrate through an example that the well-known state-space-partition-based switching law may lead to chattering in the event that the systems undergo perturbations. To overcome this, we propose a state-feedback switching law with a non-zero level set. We prove that this switching law can prevent the system from chattering. In addition, this switching law makes the perturbed systems bounded with bounded perturbations, and practically convergent with convergent perturbations. We also propose an observer-based switching law to steer the switched system stable with nice robustness performances.     

A globally convergent adaptive pole placement algorithm without a persistency of excitation requirement

This paper presents an indirect adaptive control scheme for deterministic plants which are not necessarily minimum phase. Global convergence is established for the scheme in the sense that the closed-loop poles are asymptotically assigned for the given data sequence and the system input and output remain bounded for all time. A key feature of the scheme is that no persistency of excitation condition is required. The algorithm uses recursive least squares with variable forgetting factor, normalized regression vectors, and a matrix gain with constant trace.     

A robust adaptive controller for Hammerstein nonlinear systems

Hammerstein nonlinear systems have appeared useful in modeling nonlinear processes encountered in engineering practice. Control algorithms may lead to unsatisfactory performance if the parametric model does not agree with the plant. To this end, this paper proposes a new robust adaptive control approach for discrete-time Hammerstein nonlinear systems which are more close to some industrial plants. The adaptive control law and recursive parameter estimation are updated by introducing the estimate of the model error as a feedback. Theoretical results show that parameter estimation convergence and closed-loop system stability can be guaranteed under mild conditions. Simulation examples including a continuous stirred tank reactor (CSTR) system are given to show the effectiveness of the obtained results.