Robust adaptive control of proper systems

To date, all the adaptive control algorithms have been proposed only for strictly proper systems. In this paper, a scheme is proposed to design an adaptive controller for proper systems. To study the robustness of the adaptive controller, both additive and multiplicative types of unmodeled dynamics are considered and can also be allowed to be proper, or even improper. Global bounded input bounded output stability is established. The achievement of a small in the mean tracking error and perfect tracking/rejection of deterministic trajectories/disturbances in the absence of system unmodeled dynamics are discussed. The results are also verified by simulation studies     

Decentralized robust adaptive control of nonlinear systems withunmodeled dynamics

The authors present a decentralized robust adaptive output feedback control scheme for a class of large-scale nonlinear systems of the output feedback canonical form with unmodeled dynamics. A modified dynamic signal is introduced for each subsystem to dominate the unmodeled dynamics and an adaptive nonlinear damping is used to counter the effects of the interconnections. It is shown that under certain assumptions, the proposed decentralized adaptive control scheme guarantees that all the signals in the closed-loop system are bounded in the presence of unmodeled dynamics, high-order interconnections and bounded disturbances. Furthermore, by choosing the design constants appropriately, the tracking error can be made arbitrarily small regardless of the interconnections, disturbances, and unmodeled dynamics in the system. An illustration example demonstrates the effectiveness of the proposed scheme     

Robust adaptive control of nonlinear systems represented by input-output models

A robust adaptive control scheme is proposed for a class of nonlinear systems represented by input-output models with unmodeled dynamics. The scheme does not require the unknown parameters to satisfy the linear dependence condition and parameter estimation is not needed. With the proposed control scheme, all the variables in the closed-loop system are bounded in the presence of unmodeled dynamics and bounded disturbances. Moreover, the mean-square tracking error can be made arbitrarily small by choosing some design parameters appropriately.     

Robust pole placement direct adaptive control

A pole-placement direct adaptive control for not necessarily minimum-phase plants is presented, which is robust with respect to unmodeled dynamics and bounded disturbances. The robustness is achieved by using both a normalized least-squares algorithm with dead zone and appropriate nonlinear feedback. The resulting closed-loop system is shown to be globally stable subject to standard assumptions     

Robust direct adaptive controllers with a new normalizationtechnique

This note presents a robust direct adaptive control scheme with a new normalization technique and its stability analysis in the presence of unmodeled dynamics and/or bounded disturbances. Following input-output stability theory, L₂ and L_∞ stability of the system is studied using the sector stability and passivity theorems and conditions for global stability are derived. It is also shown that robustness of the adaptive control system can be improved when relative dead zone and the novel normalization technique are incorporated into the scheme     

Robustness of continuous-time adaptive control algorithms in the presence of unmodeled dynamics

This paper examines the robustness properties of existing adaptive control algorithms to unmodeled plant high-frequency dynamics and unmeasurable output disturbances. It is demonstrated thai there exist two infinite-gain operators in the nonlinear dynamic system which determines the time-evolution of output and parameter errors. The pragmatic implication of the existence of such infinite-gain operators is that 1) sinusoidal reference inputs at specific frequencies and/or 2) sinusoidal output disturbances at any frequency (including dc), can cause the loop gain to increase without bound, thereby exciting the unmodeled high-frequency dynamics, and yielding an unstable control system. Hence, it is concluded that existing adaptive control algorithms as they are presented in the literature referenced in this paper, cannot be used with confidence in practical designs where the plant contains unmodeled dynamics because instability is likely to result. Further understanding is required to ascertain how the currently implemented adaptive systems differ from the theoretical systems studied here and how further theoretical development can improve the robustness of adaptive controllers.     

Robust adaptive observer for nonlinear systems with unmodeled dynamics

Unmodeled dynamics exist in almost all applications of observers due to the impossibility of using exact and detailed models. It is highly desired that the observers can dominate the effects of unmodeled dynamics independently to prevent the state estimations from diverging and to get the precise estimations. Based on adaptive nonlinear damping, this paper presents a robust adaptive observer for multiple-input multiple-output nonlinear systems with unknown parameters, uncertain nonlinearities, disturbances and unmodeled dynamics. The observer only has one adaptive parameter no matter how high the order of the system is and how many unknown parameters there are. With the proposed observer, neither estimating the unknown parameters or solving linear matrix inequalities is needed. It is shown that the state estimation error is uniformly bounded and can be made arbitrarily small.     

Robust adaptive quasi-sliding mode controller for discrete-time systems

In this paper, a discrete robust quasi-sliding mode adaptive controller is presented for the system with model uncertainties, unmodeled dynamics and bounded disturbances. The proposed method is adaptive control in conjunction with a sliding mode based controller design. The bounded motion of the state around the sliding surface and the stability of the global system in the sense that all signals remain bounded are guaranteed. In the proposed adaptive algorithms, the dead-zone method is employed even though the upper and lower bounds of the disturbances are unknown. Simulation results have shown the effectiveness of the proposed algorithms.     

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.     

随机系统最小二乘辨识的稳健性收敛性及适应控制

基于估计随机系统已建模部分未知参数的推广最小二乘算法,递推地定义了跟踪随机参考信号的适应控制器。我们证明了闭环系统稳定;当未建模动态特性在平均意义下有界时,估计误差随未建模 动态特性的衰减而减少且跟踪误差以一个微小的量偏离其最小值;当未建模动态特性在平均意义下趋于零时,可同时获得估计的强一致性及适应跟踪的渐近最优性。     

全系数自适应控制方法的鲁棒性

研究全系数自适应控制方法对未建模动态、参数慢时变、非线性和有界干扰的鲁捧 稳定性,证明了在有未建模动态及扰动的情况下,采用经投影修正的梯度算法估计标称对象. 黄金分割自适应控制器仍能稳定标称对象.对含乘性不确定性的线性慢时变对象及具有渐消 记忆的非线性慢时变对象,分别给出了自适应控制系统鲁棒稳定的充分条件.     

Robust adaptive output stabilization using dynamic normalizing signal

For a class of nonlinear systems with dynamic uncertainties, robust adaptive stabilization problem is considered in this paper. Firstly, by introducing an observer, an augmented system is obtained. Based on the system, we construct an exp-ISpS Lyapunov function for the unmodeled dynamics, prove that the unmodeled dynamics is exp-ISpS, and then obtain a dynamic normalizing signal to counteract the dynamic disturbances. By the backstepping technique, an adaptive controller is given, it is proved that all the signals in the adaptive control system are globally uniformly ultimately bounded, and the output can be regulated to the origin with any prescribed accuracy. A simulation example further demonstrates the efficiency of the control scheme.     

船舶航向的鲁棒自适应控制器的设计和仿真

针对带参数不确定性,未知有界扰动及未建模动态的船舶航向跟踪控制问题,本文介绍了一种鲁棒自适应算法。此算法能保证系统的全局稳定,使闭环系统的所有变量一致有界。并通过仿真对两种算法进行比较,可以看出,依照本文算法设计的控制器具有很好的鲁棒性。     

Robust adaptive output stabilization using dynamic normalizing signal

For a class of nonlinear systems with dynamic uncertainties, robust adaptive stabilization problem is considered in this paper. Firstly, by introducing an observer, an augmented system is obtained. Based on the system, we construct an exp-ISpS Lyapunov function for the unmodeled dynamics, prove that the unmodeled dynamics is exp-ISpS, and then obtain a dynamic normalizing signal to counteract the dynamic disturbances. By the backstepping technique, an adaptive controller is given, it is proved that all the signals in the adaptive control system are globally uniformly ultimately bounded, and the output can be regulated to the origin with any prescribed accuracy. A simulation example further demonstrates the efficiency of the control scheme.     

大纯滞后系统的自适应补偿控制

针对工业过程中普遍存在的纯滞后对象的控制问题,提出了一种带误差补偿环节的模型参考自适应控制方法。仿真结果表明,这种自适应控制器对于一类大纯滞后系统的控制具有比较好的控制效果,且结构简单,有一定的鲁棒性。     

鲁棒稳定的Clarke-Gawthrop改进型自校正控制器

本文提出了一种修改的Ｃｌａｒｋｅ－Ｇａｗｔｈｒｏｐ自校正控制器，并且证明了控制器对未建模动态和有界扰动的钱棒稳定性，控制器结合了Ｃｌａｒｋｅ－Ｇａｗｔｈｒｏｐ二次标函数，并通过引入模型误差反馈进行了修改，参数辨识采用了带有相对死区的修正最小二乘算法，鲁棒稳定性结果既没有要求系统参数太多的先验知识，没有使用关于自适应信号的任何假设条件     

Adaptive fuzzy backstepping output feedback control for strict feedback nonlinear systems with unknown sign of high-frequency gain

In this paper, an adaptive fuzzy robust output feedback control approach is proposed for a class of SISO nonlinear strict-feedback systems with unknown sign of high-frequency gain and the unmeasured states. The nonlinear systems addressed in this paper are assumed to possess the unmodeled dynamics, dynamical disturbances and unknown nonlinear functions, where the unknown nonlinear functions are not linearly parameterized, and no prior knowledge of their bounds is available. In the recursive designing, fuzzy logic systems are used to approximate the unknown nonlinear functions, K-filters are designed to estimate the unmeasured states, and a dynamical signal and Nussbaum gain functions are introduced to handle the unmodeled dynamics and the unknown sign of the high-frequency gain, respectively. Based on Lyapunov function method, a stable adaptive fuzzy output feedback control scheme is developed. It is mathematically proved that the proposed adaptive fuzzy control approach can guarantee that all the signals of the closed-loop system are uniformly ultimately bounded, the output converges to a small neighborhood of the origin. The effectiveness of the proposed approach is illustrated by the simulation examples.     

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.     

具有动态不确定性的自适应动态面控制

针对一类具有未建模动态的纯反馈非线性系统,提出一种自适应动态面控制方法。利用神经网络逼近未知连续函数,通过引入一种动态信号克服未建模动态。与现有结果相比,提出的设计方案简化了对未建模动态的处理过程,取消了神经网络逼近误差有界的假设。理论分析证明了该自适应控制方法能够保证闭环系统是半全局一致终结有界的,仿真结果验证了该方案的有效性。     

A new adaptive law for robust adaptation without persistent excitation

A new adaptive law motivated by the work of loannou and Kokotovic (1983) is proposed for the robust adaptive control of plants with unknown parameters. In this adaptive law the output error plays a dual role in the adjustment of the control parameter vector. The advantages of using the adaptive law over others proposed in the literature are discussed. In the ideal case the adaptive system has bounded solutions; in addition, the origin of the error equations is exponentially stable when the reference input is persistently exciting and has a sufficiently large amplitude. The adaptive system is also shown to be robust under bounded external disturbances. Finally, it is shown that, by suitably modifying the adaptive law, the overall system can be made robust in the presence of a class of unmodeled dynamics of the plant. Simulation results are presented throughout the paper to complement the theoretical developments.