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     

Robust continuous-time adaptive control by parameter projection

The problem of adaptive control of a continuous-time plant of arbitrary relative degree, in the presence of bounded disturbances as well as unmodeled dynamics, is addressed. The adaptation considered is the usual gradient update law with parameter projection, the latter being the only robustness enhancement modification employed. It is shown that if the unmodeled dynamics, which consists of multiplicative as well as additive system uncertainty, is small enough, then all the signals in the closed-loop system are bounded. This shows that extra modifications are not necessary for robustness with respect to bounded disturbances and small unmodeled dynamics. In the nominal case, where unmodeled dynamics and disturbances are absent, the asymptotic error in tracking a given reference signal is zero. Moreover, the performance of the adaptive controller is also robust     

Robustness of unmodified stochastic adaptive control algorithms

Originally, adaptive control theory was developed for the ideal system models, i.e., linear system models under the assumption that relative degree and upper bounds on the order of the systems are known. In the early 1980s, adaptive control algorithms designed for such ideal system models were strongly attacked by many researchers due to “lack of robustness” in the presence of unmodeled dynamics and external disturbances. The purpose of the present paper is to relax existing constant pressure on the adaptive control algorithms originally designed for the ideal system models. It is shown that such adaptive control algorithms are globally stable and robust with respect to unmodeled dynamics and external disturbances without any modifications, such as iσ-modification, ϵ₁-modification, relative dead-zone, projection of the parameter estimates, etc. Global stability of the unmodified algorithms is established by requiring the reference signal to be persistently exciting     

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.     

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     

一个基于神经网络模型的鲁棒自适应控制算法

对于具有不确定因素的离散非线性动态系统,通过校正神经网络预报器的输出,运用加权 预报控制性能指标和网络辨识器模型局部线性化的思想,提出了一个间接鲁棒自适应神经网 络控制算法,仿真研究证实了该控制策略的鲁棒性和有效性.     

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.     

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.     

A robust indirect adaptive regulation algorithm withself-excitation capability

A robust version of the adaptive control algorithm established by G. Kreisselmeier (1989) is presented. If the conventional dead-zone adaptive law is used in the adaptive system, it is troublesome that the size of the unmodeled dynamics, denoted by ∈, must be within the chosen dead-zone size for robustness. In this robust version, by introducing a positive design parameter, the robust stability can be achieved without this constraint. It is also shown that the plant output and control input will converge asymptotically within a certain bound. Moreover, in the ideal case, the plant output and control input will converge to zero under some condition     

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。     

Rohrs' Example Revisited: On the Robustness of Adaptive Iterative Learning Control

Adaptive feedback based methods in iterative learning control (ILC) have garnered much interest from researchers for some time now. Much as in adaptive feedback control, most of these methods use Lyapunov functions and positive real transfer functions to prove convergence and boundedness of system signals updated through iterative estimations. While Rohrs et al. have motivated further research on the design of robust adaptive feedback controllers by demonstrating in the early 1980's that the algorithms of the time were not robust in the presence of unmodeled dynamics, the topic of robustness has not been studied much in the adaptive iterative learning control (AILC) literature. Inspired by Rohrs' counterexample, we use a model reference AILC scheme to show the lack of robustness to unmodeled dynamics in AILC. We rigorously define the concept of stability in ILC via space concepts, and demonstrate the existence of unstable learning operators. We put forth linear systems arguments to explain how conditions leading to instability can occur, and support heuristic arguments with simulation examples. Our findings indicate that the shortcomings of AILC in terms of robustness are no different than those of adaptive feedback, with the robustness issue more severe in certain cases, and further research is necessary to design robust AILC schemes.     

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.     

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.     

Direct adaptive fuzzy backstepping robust control for single input and single output uncertain nonlinear systems using small-gain approach

In this paper, a direct adaptive fuzzy robust control approach is proposed for single input and single output (SISO) strict-feedback nonlinear systems with nonlinear uncertainties, unmodeled dynamics and dynamical disturbances. No prior knowledge of the boundary of the nonlinear uncertainties is required. Fuzzy logic systems are used to approximate the intermediate stabilizing functions, and a stable direct adaptive fuzzy backstepping robust control approach is developed by combining the backstepping technique with the fuzzy adaptive control theory. The stability of the closed-loop system and the convergence of the system output are proved based on the small-gain theorem. Simulation studies are conducted to illustrate the effectiveness of the proposed approach.     

基于矩阵分解的多变量鲁棒自适应反推控制

针对含有输入未建模动态的一类MIMO系统,在高频增益矩阵的顺序主子式的符号已知的前提下,给出了多变量自适应反推控制器的设计.严格地证明了对一类未建模动态,闭环适应系统的所有信号都是全局一致有界的,且输出渐近收敛于零.     

Stability and robustness analysis of MIMO MRAC using Kp = L 2 D 2 S 2 factorization

For a class of MIMO systems with input and output unmodeled dynamics, bounded disturbances and any relative degree, using the idea of K_p = L ₂ D ₂ S ₂ factorization, the design and analysis of robust direct model reference adaptive control are further investigated in this article. By establishing the L_p and L _2δ relationship properties between the input and output, multivariable swapping lemmas and relating all the signals in the closed-loop system with the normalizing signal, stability and robustness of adaptive system are analyzed rigorously. Compared with the existing results, the proof procedure is more compact and simple. A simulation example verifies the effectiveness of the control scheme.     

Fuzzy adaptive backstepping robust control for SISO nonlinear system with dynamic uncertainties

In this paper, a fuzzy adaptive backstepping design procedure is proposed for a class of nonlinear systems with three types of uncertainties: (i) nonlinear uncertainties; (ii) unmodeled dynamics and (iii) dynamic disturbances. The fuzzy logic systems are used to approximate the nonlinear uncertainties, nonlinear damping terms are used to counteract the dynamic disturbances and fuzzy approximation errors, and a dynamic signal is introduced to dominate the unmodeled dynamics. The derived fuzzy adaptive control approach guarantees the global boundedness property for all the signals and states, and at the same time, steers the output to a small neighborhood of the origin. Simulation studies are included to illustrate the effectiveness of the proposed approach.     

Robustness of an adaptive predictive controller

In this correspondence, robustness properties of an adaptive predictive controller are presented. The algorithm is obtained via a receding horizon control strategy by minimizing a quadratic performance index under the constraint that the output matches the reference over a suitable number of terminal steps. Both the nonadaptive and an adaptive version of the algorithm are examined in the case of unmodeled plant dynamics     

Robust adaptive fuzzy backstepping output feedback tracking control for nonlinear system with dynamic uncertainties

In this paper, an adaptive fuzzy output feedback control approach based on backstepping design is proposed for a class of SISO strict feedback nonlinear systems with unmeasured states, nonlinear uncertainties, unmodeled dynamics, and dynamical disturbances. Fuzzy logic systems are employed to approximate the nonlinear uncertainties, and an adaptive fuzzy state observer is designed for the states estimation. By combining backstepping technique with the fuzzy adaptive control approach, a stable adaptive fuzzy...     

On the design of stabilizing controllers for singularly perturbedsystems

The robustness of output feedback control designs for singularly perturbed systems based on the reduced systems is discussed. A frequency-domain approach is presented to determine the conditions for the stability of linear time-invariant systems subject to neglected high-frequency dynamics. In contrast with the qualitative analyses for robust stability that have appeared in the literature, this approach gives an explicit, computable bound on unmodeled dynamics which does not destabilize the systems. Stability conditions for various feedback control schemes are presented. It is noted that the approach, extended to systems with mixed singular-regular perturbations, can be used to derive the robust stability condition