Neural network–based direct adaptive robust control of unknown MIMO nonlinear systems using state observer

This paper focuses on the problem of adaptive robust tracking control for a class of uncertain multiple-input and multiple-output (MIMO) nonlinear system. Unlike most previous research studies, model dynamics, disturbances, and state variables are unknown in this paper. A novel observer-based direct adaptive neuro-sliding mode control approach is proposed of which the only required knowledge is the system output. By incorporating the Adaptive Linear Neuron (ADALINE) neural network (NN) into the conventional sliding mode observer, the proposed observer has favorable performance. In the controller, a radial basis function (RBF) NN is constructed to approximate the unknown equivalent control laws and the estimation of the sliding surface is applied as the input. A gain-adaptation sliding mode term is designed to enhance the robustness of the control system. Besides, the free parameters of the ADALINE NN and the RBFNN are updated online by adaptive laws to obtain optimal approximation performance. Finally, the comparative simulations are given to show the effectiveness and merits of proposed scheme.     

Adaptive prescribed performance control of nonlinear systems with unknown dead zone

An alternative adaptive control with prescribed performance is proposed to address the output tracking of nonlinear systems with a nonlinear dead zone input. An appropriate function that characterizes the convergence rate, maximum overshoot, and steady‐state error is adopted and incorporated into an output error transformation, and thus the stabilization of the transformed system is sufficient to achieve original tracking control with prescribed performance. The nonlinear dead zone is represented as a time‐varying system and Nussbaum‐type functions are utilized to deal with the unknown control gain dynamics. A novel high‐order neural network with a scalar adaptive weight is developed to approximate unknown nonlinearities, thus the computational costs can be diminished dramatically. Some restrictive assumptions on the system dynamics and the dead‐zone are circumvented. Simulations are included to validate the effectiveness of the proposed scheme. Copyright © 2012 John Wiley & Sons, Ltd.     

Robust output tracking of uncertain nonlinear time‐delay systems with unknown dead‐zone inputs via control schemes with a simple structure

The adaptive robust output tracking control problem is considered for a class of uncertain nonlinear time‐delay systems with completely unknown dead‐zone inputs. A new design method is proposed so that some adaptive robust output tracking control schemes with a rather simple structure can be constructed. It is not necessary to know the nonlinear upper bound functions of uncertain nonlinearities. In fact, the constructed output tracking control schemes are structurally linear in the state and have a self‐tuning control gain function that is updated by an adaptation law. In this paper, the dead‐zone input is nonsymmetric, and its information is assumed to be completely unknown. In addition, a numerical example is given to describe the design procedure of the presented method, and the simulations of this numerical example are implemented to demonstrate the validity of the theoretical results.     

Robust scheme of an indirect MRACS system taking into account the presence of deterministic disturbances

This paper presents a method for the design of an indirect model reference adaptive control (MRAC) system for a plant with deterministic disturbances, robust to modeling errors due to unmodeled dynamics and observation noise. In the proposed method, the structure of the controller is determined on the basis of the internal model principle to reject the deterministic disturbance, and its parameters are adjusted by using the estimated plant parameters. Robustness to the modeling errors is ensured by the use of the adaptive law with a dead zone and a fixed compensator of integral type. The adaptive law prevents the adjustable parameters from drifting and the fixed compensator improves the control performance degraded by the use of the dead zone. Stability of the MRAC system is analyzed using the concept of the ??_2δ norm and the Bellman–Gronwall lemma, based on the properties guaranteed by the adaptive law. Effectiveness of the proposed method is demonstrated by the simulation carried out for a plant with second‐order nominal part and a step disturbance. © 2004 Wiley Periodicals, Inc. Electr Eng Jpn, 146(4): 65–75, 2004; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/eej.10190     

A new robust model reference control with improved performance for a class of multivariable unknown plants

Motivated by recent works on parametrization of multivariable plants for model reference adaptive control (MRAC), a new robust model reference control (MRC) scheme for a class of multivariable unknown plants is presented. The salient feature of this control scheme is the improved performance of the output-tracking property, which is hardly attainable by the traditional MRAC schemes. The controller here is devised using the concept of variable structure design which prevails in the robust control context. It is shown by a Lyapunov approach that without any persistent excitation the global stability of the overall system is achieved and the tracking errors will converge to a residual set. The size of that set can be directly related to the size of unmodelled dynamics and output disturbances explicitly as long as a set of control parameters is chosen properly (large).     

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.     

Adaptive fault‐tolerant attitude tracking control for spacecraft formation with unknown inertia

In this paper, an adaptive fault‐tolerant attitude coordinated tracking problem for spacecraft formation is investigated under a directed communication topology containing a spanning tree with the leader as the root, where inertia matrices and external disturbances are unknown time‐varying. With no prior knowledge of faults and inertia, an adaptive approach is proposed to reject the influence of disturbances and uncertainties. Meanwhile, combining with a consensus algorithm and graph theory, an adaptive fault‐tolerant attitude synchronization tracking control law is presented to regulate the attitude to a common time‐varying reference state. Aiming at optimizing the control law, a dynamic adjustment function is introduced to adjust the control gain according to the attitude tracking error. The effectiveness of the proposed control approach is demonstrated through simulation results.     

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.     

一类非线性系统的自组织模糊神经网络控制

针对一类MIMO不确定非线性有干扰且控制增益符号未知的系统进行跟踪控制的问题,提出了一种在线自组织模糊神经网络的改进算法,用以克服参数选择困难的问题,并基于该算法给出了一种自适应鲁棒控制方法。首先基于主导输入的概念将MIMO系统分解为多个SISO系统构成的系统,然后结合自组织模糊神经网络在线对系统中的未知函数进行逼近,对网络结构和参数实现在线调节,再利用Nussbaum函数来克服控制增益符号未知,并且引入鲁棒项及复合误差的估计来补偿复合误差。最后基于Lyapunov稳定性理论证明了整个闭环系统半全局一致最终有界。理论和仿真结果表明提出方法的有效性。     

Robust adaptive steering control for unmanned surface vehicle with unknown control direction and input saturation

A robust adaptive steering control method is proposed to solve the control problem of the unmanned surface vehicle (USV) with uncertainties, unknown control direction, and input saturation. In the controller design process, the adaptive fuzzy system is incorporated into dynamic surface control (DSC) to approximate the uncertainty term induced by external environmental disturbances and model parameters. Then, the Nussbaum function is used to eliminate the requirement for a priori knowledge of the control direction. Besides, to handle the input saturation, the adaptive fuzzy DSC is extended by a second‐order nonlinear filter and antisaturation auxiliary function to compensate for the magnitude and rate saturation of the rudder. All signals of the closed‐loop system are proven to be uniformly ultimately bounded (UUB) by Lyapunov theorem and the Lemma of Nussbaum gain, and the course error can converge to a small neighborhood of zero through choosing design parameters appropriately. Finally, simulation results and comprehensive comparisons are shown for the USV course system, which is demonstrative of the proposed controller's effectiveness and robustness.     

Robust adaptive active fault‐tolerant control of UAH with unknown disturbances and actuator faults

This paper proposes a robust active fault‐tolerant control (AFTC) approach for medium‐scale unmanned autonomous helicopter (UAH) with rotor flapping dynamics in the presence of unknown external disturbances and actuator faults. The robust items are adopted to improve the disturbance rejection capability of the UAH system. The adaptive fault observers are developed to estimate the fault parameters and the fault detection (FD) algorithms are presented to detect the actuator faults in different loops. In order to obtain satisfactory trajectory tracking performance, a backstepping‐based robust AFTC scheme is designed for the simplified 6‐degree‐of‐freedom (DOF) UAH nonlinear dynamics model and the global stability of the closed‐loop system is proved by using the Lyapunov method. Several groups of numerical simulation results are carried out to verify the effectiveness of the developed method.     

Design of disturbance observer based on adaptive-neural control for large-scale time-delay systems in the presence of actuator fault and unknown dead zone

This article presents an adaptive neural compensation scheme for a class of large-scale time delay nonlinear systems in the presence of unknown dead zone, external disturbances, and actuator faults. In this article, the quadratic Lyapunov–Krasovskii functionals are introduced to tackle the system delays. The unknown functions of the system are estimated by using radial basis function neural networks. Furthermore, a disturbance observer is developed to approximate the external disturbances. The proposed adaptive neural compensation control method is constructed by utilizing a backstepping technique. The boundedness of all the closed-loop signals is guaranteed via Lyapunov analysis and the tracking errors are proved to converge to a small neighborhood of the origin. Simulation results are provided to illustrate the effectiveness of the proposed control approach.     

Neural network‐based adaptive attitude tracking control for flexible spacecraft with unknown high‐frequency gain

Adaptive control design using neural networks (a) is investigated for attitude tracking and vibration stabilization of a flexible spacecraft, which is operated at highly nonlinear dynamic regimes. The spacecraft considered consists of a rigid body and two flexible appendages, and it is assumed that the system parameters are unknown and the truncated model of the spacecraft has finite but arbitrary dimension as well, for the purpose of design. Based on this nonlinear model, the derivation of an adaptive control law using neural networks (NNs) is treated, when the dynamics of unstructured and state‐dependent nonlinear function are completely unknown. A radial basis function network that is used here for synthesizing the controller and adaptive mechanisms is derived for adjusting the parameters of the network and estimating the unknown parameters. In this derivation, the Nussbaum gain technique is also employed to relax the sign assumption for the high‐frequency gain for the neural adaptive control. Moreover, systematic design procedure is developed for the synthesis of adaptive NN tracking control with L₂ ‐gain performance. The resulting closed‐loop system is proven to be globally stable by Lyapunov's theory and the effect of the external disturbances and elastic vibrations on the tracking error can be attenuated to the prescribed level by appropriately choosing the design parameters. Numerical simulations are performed to show that attitude tracking control and vibration suppression are accomplished in spite of the presence of disturbance torque/parameter uncertainty. Copyright © 2009 John Wiley & Sons, Ltd.     

Robust pole placement indirect adaptive control

The problem of designing a robustly stable pole placement indirect adaptive controller in the presence of output disturbances and unmodelled dynamics is addressed. The key features of such a design are the following. (1) The unknown parameters are estimated by a normalized least-squares algorithm with a dead zone to provide the stability robustness with respect to bounded disturbances and ‘small’ unmodelled dynamics. (2) The estimated model controllability is ensured by modifying the control law over a finite time. The modification involved consists of adding an internal impulse excitation and ‘freezing’ the controller parameters.     

Robust output tracking of uncertain nonlinear systems with completely unknown dead‐zone input: A self‐tuning design approach

The main purpose of this paper is to propose a direct and simple approach, called a self‐tuning design approach, to dealing with any nonsymmetric dead‐zone input nonlinearity where its information is completely unknown. In order to describe the approach, the output tracking problem is considered for a class of uncertain nonlinear systems with any nonsymmetric dead‐zone input. First, a dead‐zone input is represented as a time‐varying input‐dependent function such that the considered dynamical system with dead‐zone input can be transfered into an uncertain nonlinear dynamical system subject to a linear input with time‐varying input coefficient. Then, by making use of the self‐tuning design approach, a class of adaptive robust output tracking control schemes with a rather simple structure is synthesized. Thus, the proposed direct and simple self‐tuning design approach can be easily understood by the engineering designers, and the resulting simple adaptive robust control schemes can be well implemented in most practical engineering control problems. By combining the proposed self‐tuning design approach with other control methods, one may expect to obtain a number of interesting results for a rather large class of uncertain nonlinear dynamical systems with dead‐zone in the actuators. Finally,the simulations of some numerical examples are provided to demonstrate the validity of the theoretical results. Copyright © 2016 John Wiley & Sons, Ltd.     

A combined backstepping and dynamic surface control to adaptive fuzzy state‐feedback control

This paper studies an adaptive fuzzy dynamic surface control for a class of nonlinear systems with fuzzy dead zone, unmodeled dynamics, dynamical disturbances, and unknown control gain functions. The unknown system functions are approximated by the Takagi‐Sugeno–type fuzzy logic systems. There are 3 main features for the presented systematic design scheme. First, by adopting an integrated method, a novel adaptive fuzzy controller is constructed for the nonlinear system with fuzzy dead zone. Second, only 3 online learning parameters need to be tuned, which significantly reduces the computation burden. Third, the possible controller singularity problem in some of the existing adaptive control methods with feedback linearization techniques can be avoided. On the basis of the backstepping technique and dynamic surface control, all the signals of the closed‐loop system are guaranteed to be semiglobally uniformly ultimately bounded. Finally, 2 simulation examples are provided to illustrate the effectiveness of the proposed scheme.     

Adaptive recurrent Chebyshev neural network control for PM synchronous motor servo‐drive electric scooter with V‐belt continuously variable transmission

Because of unknown nonlinearity and time‐varying characteristics of electric scooter with V‐belt continuously variable transmission (CVT) driven by permanent magnet synchronous motor (PMSM), its accurate dynamic model is difficult to establish for the design of the linear controller in whole system. In order to conquer this difficulty and raise robustness, an adaptive recurrent Chebyshev neural network (NN) control system is proposed to control for PMSM servo‐drive electric scooter with V‐belt CVT under lumped nonlinear external disturbances in this study. The adaptive recurrent Chebyshev NN control system consists of a recurrent Chebyshev NN control and a compensated control with estimation law. In addition, the online parameters tuning methodology of the recurrent Chebyshev NN and the estimation law of the compensated controller can be derived by using the Lyapunov stability theorem. Moreover, the two optimal learning rates of the recurrent Chebyshev NN based on a discrete‐type Lyapunov function are proposed to guarantee the convergence of tracking error. Finally, comparative studies are demonstrated by experimental results in order to show the effectiveness of the proposed control scheme. Copyright © 2014 John Wiley & Sons, Ltd.     

Adaptive homo‐backstepping tracking control for strict‐feedback systems in presence of unknown dead‐zones

An adaptive homo‐backstepping control for nonlinear strict‐feedback systems subjected to unknown actuator dead‐zone and disturbance is investigated. A sliding‐mode‐based integral filter is constructed and used to approximate the desired feedback control in the backstepping‐like recursive design technique. Subsequently, the problem of “explosion of complexity” is solved by obviating the analytic derivatives deduction for virtual control in the conventional backstepping technology. The actuator dead‐zone dynamic is modeled as the combination of a line and a disturbance‐like term, which makes the controller design simpler. The interconnected control module and filter module in the resulting closed‐loop system satisfy the input‐to‐state practically stability‐modularity condition, provided that the small‐gain theorem is exploited to ensure the stability of closed‐loop system. The proposed approach cannot only mitigate the effect of dead‐zone but also solve the problem of explosion of complexity in the previous literature. Numerical simulations performed on a manipulator with a brushed DC motor are introduced to illustrate the effectiveness of underlying control scheme.     

Neural‐hybrid control of systems with sandwiched dead‐zones

The control of systems that have sandwiched nonsmooth nonlinearities, such as a dead‐zone sandwiched between two dynamic blocks, is addressed. An adaptive inverse control scheme using a hybrid controller structure and a neural network based inverse compensator, is proposed for such systems with unknown sandwiched dead‐zone. This neural‐hybrid controller consists of an inner loop discrete‐time feedback structure incorporated with an adaptive inverse using a neural network for the unknown dead‐zone, and an outer‐loop continuous‐time feedback control law for achieving desired output tracking. The dead‐zone compensator consists of two neural networks, one used as an estimator of the sandwiched dead‐zone function and the other for the compensation itself. The compensator neural network has neurons that can approximate jump functions such as a dead‐zone inverse. The weights of the two neural networks are tuned using a modified gradient algorithm. Simulation results are given to illustrate the performance of the proposed neural‐hybrid controller. Copyright © 2002 John Wiley & Sons, Ltd.     

Adaptive fuzzy finite-time consensus tracking for multiple Euler-Lagrange systems with unknown control directions

In this paper, the problem of adaptive fuzzy finite-time consensus tracking control for multiple Euler-Lagrange systems (ELSs) with uncertain dynamics and unknown control directions (UCDs) is investigated. The computational complexity problem in conventional backstepping is avoided by using finite-time command filter (FTCF), and the error in the filtering process is eliminated through error compensation signals. The fuzzy logic system combined with the adaptive control technique is applied to approximate and estimate the unknown nonlinear dynamics of ELS. The Nussbaum function-based continuous and nonsmooth input control torque is established to eliminate the influence of UCDs, and the proposed control scheme can guarantee the consensus tracking errors converge to the desired neighborhood of the origin within a finite time. Numerical simulation is used to test the effectiveness of the given algorithm.