Accommodation of unknown actuator faults using output feedback‐based adaptive robust control

In this paper, we solve the problem of output tracking for linear uncertain systems in the presence of unknown actuator failures using discontinuous projection‐based output feedback adaptive robust control (ARC). The faulty actuators are characterized as unknown inputs stuck at unknown values experiencing bounded disturbance and actuators losing effectiveness at unknown instants of time. Many existing techniques to solve this problem use model reference adaptive control (MRAC), which may not be well suited for handling various disturbances and modeling errors inherent to any realistic system model. Robust control‐based fault‐tolerant schemes have guaranteed transient performance and are capable of dealing with modeling errors to certain degrees. But, the steady‐state tracking accuracy of robust controllers, e.g. sliding mode controller, is limited. In comparison, the backstepping‐based output feedback adaptive robust fault‐tolerant control (ARFTC) strategy presented here can effectively deal with such uncertainties and overcome the drawbacks of individual adaptive and robust controls. Comparative simulation studies are performed on a linearized Boeing 747 model, which shows the effectiveness of the proposed scheme. Copyright © 2011 John Wiley & Sons, Ltd.     

Online data‐driven composite adaptive backstepping control with exact differentiators

This paper presents an online data‐driven composite adaptive backstepping control for a class of parametric strict‐feedback nonlinear systems with mismatched uncertainties, where both tracking errors and prediction errors are utilized to update parametric estimates. Hybrid exact differentiators are applied to obtain the derivatives of virtual control inputs such that the complexity problem of integrator backstepping can be avoided. Closed‐loop tracking error equations are integrated in a moving‐time window to generate prediction errors such that online recorded data can be utilized to improve parameter adaptation. Semiglobal asymptotic stability of the closed‐loop system is rigorously established by the time‐scales separation and Lyapunov synthesis. The proposed composite adaptation can not only avoid the application of identification models and linear filters resulting in a simpler control structure, but also suppress parametric uncertainties and external perturbations via the time‐interval integral. Simulation results have demonstrated that the proposed approach possesses superior control performances under both noise‐free and noisy‐measurement environments. Copyright © 2015 John Wiley & Sons, Ltd.     

Unifying adaptive control with the nonlinear PI methodology: Designs for unknown strict‐feedback nonlinear systems with nonsmooth actuator nonlinearities

In this paper, we extend the nonlinear PI control methodology within an adaptive control framework. An adaptive nonlinear PI controller is proposed for output tracking of strict‐feedback nonlinear systems with nonsmooth actuator nonlinearities and unknown control directions. The current approach relaxes the standard assumption of known bounds for the associated system nonlinearities made in earlier nonlinear PI schemes. New theoretical boundedness results have been proved that enable the successful combination of backstepping and linear parametric approximators with the nonlinear PI approach and ensure semiglobal approximate tracking of the output to some reference trajectory. Following recent extensions of the nonlinear PI method to strict‐feedback systems, the intermediate virtual control laws are derived through suitable integral equations. Simulation results are also presented in this paper that verify our theoretical analysis.     

Precision motion control of a small launching platform with disturbance compensation using neural networks

A kind of launching platform driven by two permanent magnet synchronous motors which is used to launch kinetic load to hit the target always faces strong parameter uncertainties and strong external disturbance such as the air current impulsion which would degrade their tracking accuracy greatly. In this paper, a practical method which combines adaptive robust control with neural network‐based disturbance observer is proposed for high‐accuracy motion control of the launching platform. The proposed controller not only accounts for the parametric uncertainties but also takes the external disturbances into account. Adaptive control is designed to compensate the former, while neural network‐based disturbance observer is designed to compensate the latter respectively and both of them are integrated together via a feedforward cancellation technique. A new kind of parametric adaptation and weight adaptation strategy is designed by using the linear combination of the system's tracking error and the weight estimation error as a driving signal for parametric adaptation and disturbance approximation. The stability of the novel control scheme is analyzed via a Lyapunov method and this method presents a prescribed output tracking performance in the presence of both parameter uncertainties and unmodeled nonlinearities. Extensive comparative simulation and experimental results are obtained to verify the high‐performance of the proposed control strategy. Copyright © 2016 John Wiley & Sons, Ltd.     

Adaptive prescribed performance control for hydraulic system with disturbance compensation

In this article, an adaptive prescribed performance controller is developed for hydraulic system with uncertainties. An extraordinary feature is that better prescribed performance control can be achieved by compensating the uncertainties including parameter uncertainties and disturbances. For this reason, the transformation of system output error is realized by a prescribed performance function, which is employed to constrain the boundary of tracking error and convergence rate, then the tracking error of the original system with a priori prescribed performance can be realized by stabilizing the transformed system. Adaptive control is employed to solve the system parametric uncertainties; extended state observers are built to estimate the multiple disturbances. Based on the backstepping method, they are integrated into the design of the novel controller to guarantee prescribed tracking error performance. The stability analysis of the proposed controller is carried out via the Lyapunov theory. Finally, experimental results indicate good performance of the proposed algorithm.     

Adaptive output feedback actuator failure compensation for a class of non‐linear systems

An adaptive compensation control scheme using output feedback is designed and analysed for a class of non‐linear systems with state‐dependent non‐linearities in the presence of unknown actuator failures. For a linearly parameterized model of actuator failures with unknown failure values, time instants and pattern, a robust backstepping‐based adaptive non‐linear controller is employed to handle the system failure, parameter and dynamics uncertainties. Robust adaptive parameter update laws are derived to ensure closed‐loop signal boundedness and small tracking errors, in general, and asymptotic regulation, in particular. An application to controlling the angle of attack of a non‐linear hypersonic aircraft dynamic model in the presence of elevator segment failures is studied and simulation results show that the developed adaptive control scheme has desired actuator failure compensation performance. Copyright © 2004 John Wiley & Sons, Ltd.     

Robust adaptive control for non‐linear systems in generalized output‐feedback canonical form

Design of global robust adaptive output‐feedback dynamic compensators for stabilization and tracking of a class of systems that are globally diffeomorphic into systems in generalized output‐feedback canonical form is investigated. This form includes as special cases the standard output‐feedback canonical form and various other forms considered previously in the literature. Output‐dependent non‐linearities are allowed to enter both additively and multiplicatively. The system is allowed to contain unknown parameters multiplying output‐dependent non‐linearities and, also, unknown non‐linearities satisfying certain bounds. Under the assumption that a constant matrix can be found to achieve a certain property, it is shown that a reduced‐order observer and a backstepping controller can be designed to achieve practical stabilization of the tracking error. If this assumption is not satisfied, it is shown that the control objective can be achieved by introducing additional dynamics in the observer. Sufficient conditions under which asymptotic tracking and stabilization can be achieved are also given. This represents the first robust adaptive output‐feedback tracking results for this class of systems. Copyright © 2003 John Wiley & Sons, Ltd.     

Adaptive robust control of a class of nonlinear systems in semi‐strict feedback form with non‐uniformly detectable unmeasured internal states

This paper proposes a novel control method for a special class of nonlinear systems in semi‐strict feedback form. The main characteristic of this class of systems is that the unmeasured internal states are non‐uniformly detectable, which means that no observer for these states can be designed to make the observation error exponentially converge to zero. In view of this, a projection‐based adaptive robust control law is developed in this paper for this kind of system. This method uses a projection‐type adaptation algorithm for the estimation of both the unknown parameters and the internal states. Robust feedback term is synthesized to make the system robust to uncertain nonlinearities and disturbances. Although the estimation error for both the unknown parameters and the internal states may not converge to zero, the tracking error of the closed‐loop system is proved to converge to zero asymptotically if the system has only parametric uncertainties. Furthermore, it is theoretically proved that all the signals are bounded, and the control algorithm is robust to bounded disturbances and uncertain nonlinearities with guaranteed output tracking transient performance and steady‐state accuracy in general. The class of system considered here has wide engineering applications, and a practical example—control of mechanical systems with dynamic friction—is used as a case study. Simulation results are obtained to demonstrate the applicability of the proposed control methodology. Copyright © 2010 John Wiley & Sons, Ltd.     

Output‐feedback adaptive tracking control of stochastic nonlinear systems using multi‐dimensional Taylor network

In this paper, an adaptive multi‐dimensional Taylor network (MTN) control scheme based on the backstepping and dynamic surface control (DSC) is developed to solve the tracking control problem for the stochastic nonlinear system with immeasurable states. The MTNs are used to approximate the unknown nonlinearities, and then based on the multivariable analog of circle criterion, an observer is first introduced to estimate the immeasurable states. By combining the adaptive backstepping technique and the DSC technique, an adaptive MTN output‐feedback backstepping DSC approach is developed. It is shown that the proposed controller ensures that all signals of the closed‐loop system are remain bounded in probability, and the tracking error converges to an arbitrarily small neighborhood around the origin in the sense of probability. Finally, the effectiveness of the design approach is illustrated by simulation results.     

Adaptive motion/force tracking control of holonomic constrained mechanical systems: a unified viewpoint

This paper proposes a robust adaptive motion/force tracking controller for holonomic constrained mechanical systems with parametric uncertainties and disturbances. First, two types of well‐known holonomic systems are reformulated as a unified control model. Based on the unified control model, an adaptive scheme is then developed in the presence of pure parametric uncertainty. The proposed controller guarantees asymptotic motion and force tracking without the need of extra conditions. Next, when considering external disturbances, control gains are designed by solving a linear matrix inequality (LMI) problem to achieve prescribed robust performance criterion. Indeed, arbitrary disturbance/parametric error attenuation with respect to both motion and force errors along with control input penalty are ensured in the L₂‐gain sense. Finally, applications are carried out on a two‐link constrained robot and two planar robots transporting a common object. Numerical simulation results show the expected performances. Copyright © 2006 John Wiley & Sons, Ltd.     

Adaptive robust dynamic surface control with composite adaptation laws

This paper focuses on an adaptive robust dynamic surface control (ARDSC) with composite adaptation laws (CAL) for a class of uncertain nonlinear systems in semi‐strict feedback form. A simple and effective controller has been obtained by introducing dynamic surface control (DSC) technique and designing novel adaptation laws. First, the ‘explosion of terms’ problem caused by backstepping method in the traditional adaptive robust control (ARC) is avoided. Meanwhile, through a new proof philosophy the asymptotical output tracking that the ARC possesses is theoretically preserved. Second, when persistent excitation (PE) condition satisfies, true parameter estimates could be acquired via designing CALs which integrate the information of estimation errors. Finally, simulation results are presented to illustrate the effectiveness of the proposed method. Copyright © 2010 John Wiley & Sons, Ltd.     

Adaptive backstepping repetitive learning control design for nonlinear discrete‐time systems with periodic uncertainties

This paper addresses a tracking problem for uncertain nonlinear discrete‐time systems in which the uncertainties, including parametric uncertainty and external disturbance, are periodic with known periodicity. Repetitive learning control (RLC) is an effective tool to deal with periodic unknown components. By using the backstepping procedures, an adaptive RLC law with periodic parameter estimation is designed. The overparameterization problem is overcome by postponing the parameter estimation to the last backstepping step, which could not be easily solved in robust adaptive control. It is shown that the proposed adaptive RLC law without overparameterization can guarantee the perfect tracking and boundedness of the states of the whole closed‐loop systems in presence of periodic uncertainties. In addition, the effectiveness of the developed controller is demonstrated by an implementation example on a single‐link flexible‐joint robot. Copyright © 2014 John Wiley & Sons, Ltd.     

Rejection of unknown periodic disturbances for continuous‐time MIMO systems with dynamic uncertainties

Rejection of unknown periodic disturbances in multi‐channel systems has several industrial applications that include aerospace, consumer electronics, and many other industries. This paper presents a design and analysis of an output‐feedback robust adaptive controller for multi‐input multi‐output continuous‐time systems in the presence of modeling errors and broadband output noise. The trade‐off between robust stability and performance improvement as well as practical design considerations for performance improvements are presented. It is demonstrated that proper shaping of the open‐loop plant singular values as well as over‐parameterizing the controller parametric model can significantly improve performance. Numerical simulations are performed to demonstrate the effectiveness of the proposed scheme. Copyright © 2016 John Wiley & Sons, Ltd.     

多关节机器人的反演自适应模糊滑模控制

针对二关节机器人轨迹跟踪问题,设计了一种新的反演自适应模糊滑模控制器.该方法设计了反演滑模控制器和自适应模糊控制器,通过设计合适的自适应律,采用模糊控制器在线估计不确定性上界值,实现了对建模误差和干扰的自动跟踪,削弱了抖振.利用李亚普诺夫定理证明了系统的稳定性.仿真结果表明该方法的有效性.     

电液伺服系统的神经网络在线自学习自适应控制

针对电流伺服系统的复杂非线性和不确定性特性,提出了一种基于神经网络的在线自学习自适应控制策略,引入的神经网络模型可跟踪学习系统的时为动力学,控制器的设计依赖于系统的先验知识,控制参数的调整是基于被控过程的测量信息利用反馈误差学习算法实现的,该系统已应用大于型电液伺服结构试验机的控制,显示了优良的控制品质。     

An adaptive robust observer for velocity estimation in an electro‐hydraulic system

This paper proposes the design of an observer to estimate the velocity of an electro‐hydraulic system by using pressure measurements only. The difficulties involved in the design of an observer for such a system include the highly nonlinear system dynamics, severe parametric uncertainties such as large variation of inertial load and unmatched model uncertainties. In order to address these issues, a nonlinear model‐based adaptive robust observer is designed to estimate the velocity. The contributions of the proposed work is twofold. First, it introduces a novel coordinate transformation to reconstruct the velocity estimate. And second, from a structural viewpoint, the design has two important features: (i) an underlying robust filter structure, which can attenuate the effect of uncertain nonlinearities such as friction and disturbances on the velocity estimation, and (ii) an adaptation mechanism to reduce the extent of parametric uncertainties. Experimental results on the swing motion control of an electro‐hydraulic robot arm demonstrate the effectiveness of the proposed observer. Copyright © 2012 John Wiley & Sons, Ltd.     

Learning‐based iterative modular adaptive control for nonlinear systems

In this paper, we study the problem of adaptive trajectory tracking control for a class of nonlinear systems with structured parametric uncertainties. We propose to use an iterative modular approach: we first design a robust nonlinear state feedback that renders the closed‐loop input‐to‐state stable (ISS). Here, the input is considered to be the estimation error of the uncertain parameters, and the state is considered to be the closed‐loop output tracking error. Next, we propose an iterative adaptive algorithm, where we augment this robust ISS controller with an iterative data‐driven learning algorithm to estimate online the parametric uncertainties of the model. We implement this method with two different learning approaches. The first one is a data‐driven multiparametric extremum seeking method, which guarantees local convergence results, and the second is a Bayesian optimization‐based method called Gaussian Process Upper Confidence Bound, which guarantees global results in a compact search set. The combination of the ISS feedback and the data‐driven learning algorithms gives a learning‐based modular indirect adaptive controller. We show the efficiency of this approach on a two‐link robot manipulator numerical example.     

Adaptive neural dynamic surface control of MIMO stochastic nonlinear systems with unknown control directions

In this paper, an adaptive neural output‐feedback control approach is considered for a class of uncertain multi‐input and multi‐output (MIMO) stochastic nonlinear systems with unknown control directions. Neural networks (NNs) are applied to approximate unknown nonlinearities, and K‐filter observer is designed to estimate unavailable system's states. Due to utilization of Nussbaum gain function technique in the proposed approach, the singularity problem and requirement to prior knowledge about signs of high‐frequency gains are removed, simultaneously. Razumikhin functional method is employed to deal with unknown state time‐varying delays, so that the offered control approach is free of common assumptions on derivative of time‐varying delays. Also, an adaptive neural dynamic surface control is developed; hence, explosion of complexity in conventional backstepping method is eliminated, effectively. The boundedness of all the resulting closed‐loop signals is guaranteed in probability; meanwhile, convergence of the tracking errors to adjustable compact set in the sense of mean quartic value is also proved. Finally, simulation results are shown to verify and clarify efficiency of the offered approach. Copyright © 2016 John Wiley & Sons, Ltd.     

Adaptive robust control of nonlinear systems with dynamic uncertainties

In this paper, the discontinuous projection‐based adaptive robust control (ARC) approach is extended to a class of nonlinear systems subjected to parametric uncertainties as well as all three types of nonlinear uncertainties—uncertainties could be state‐dependent, time‐dependent, and/or dynamic. Departing from the existing robust adaptive control approach, the proposed approach differentiates between dynamic uncertainties with and without known structural information. Specifically, adaptive robust observers are constructed to eliminate the effect of dynamic uncertainties with known structural information for an improved steady‐state output tracking performance—asymptotic output tracking is achieved when the system is subjected to parametric uncertainties and dynamic uncertainties with known structural information only. In addition, dynamic normalization signals are introduced to construct ARC laws to deal with other uncertainties including dynamic uncertainties without known structural information not only for global stability but also for a guaranteed robust performance in general. Copyright © 2008 John Wiley & Sons, Ltd.     

Decentralized adaptive multi‐dimensional Taylor network tracking control for a class of large‐scale stochastic nonlinear systems

This paper investigates the problem of adaptive multi‐dimensional Taylor network (MTN) decentralized tracking control for large‐scale stochastic nonlinear systems. Minimizing the influence of randomness and complex nonlinearity, which increases computational complexity, and improving the controller's real‐time performance for the stochastic nonlinear system are of great significance. With combining adaptive backstepping with dynamic surface control, a decentralized adaptive MTN tracking control approach is developed. In the controller design, MTNs are used to approximate nonlinearities, the backstepping technique is employed to construct the decentralized adaptive MTN controller, and the dynamic surface control technique is adopted to avoid the “explosion of computational complexity” in the backstepping design. It is proven that all the signals in the closed‐loop system remain bounded in probability, and the tracking errors converge to a small residual set around the origin in the sense of a mean quartic value. As the MTN contains only addition and multiplication, the proposed control method is more simplified and of good real‐time performance, compared with the existing control methods for large‐scale stochastic nonlinear systems. Finally, a numerical example is presented to illustrate the effectiveness of the proposed design approach, and simulation results demonstrate that the method presented in this paper has good real‐time performance and control quality, and the dynamic performance of the closed‐loop system is satisfactory.