Adaptive neural finite-time output-feedback tracking control for nonlinear stochastic nonstrict-feedback systems with input saturation

In this paper, an observer-based adaptive neural output-feedback control scheme is developed for a class of nonlinear stochastic nonstrict-feedback systems with input saturation in finite-time interval. The mean value theorem and the property of the smooth function are applied to cope with the difficulties caused by the existence of input saturation. According to the universal approximation capability of the radial basis function neural network, it will be utilized to compensate the unknown nonlinear functions. Based on the state observer, the finite-time Lyapunov stability theorem, we propose an adaptive neural output-feedback control scheme for nonlinear stochastic systems in nonstrict-feedback form. The developed controller guarantees that the system output signal can track the given reference signal trajectory, and all closed-loop signals are semi-globally finite-time stability in probability. The observer errors and the tracking error can converge to a small neighborhood of the origin. Finally, simulation results demonstrate the effectiveness of the developed control scheme.     

Adaptive neural control for nonstrict‐feedback stochastic nonlinear time‐delay systems with input and output constraints

This paper investigates an adaptive neural tracking control for a class of nonstrict‐feedback stochastic nonlinear time‐delay systems with input saturation and output constraint. First, the Gaussian error function is used to represent a continuous differentiable asymmetric saturation model. Second, the appropriate Lyapunov‐Krasovskii functional and the property of hyperbolic tangent functions are used to compensate the time‐delay effects, the neural network is used to approximate the unknown nonlinearities, and a barrier Lyapunov function is designed to ensure that the output parameters are restricted. At last, based on Lyapunov stability theory, a robust adaptive neural control method is proposed, and the designed controller decreases the number of learning parameters and thus reduces the computational burden. It is shown that the designed neural controller can ensure that all the signals in the closed‐loop system are 4‐Moment (or 2 Moment) semi‐globally uniformly ultimately bounded and the tracking error converges to a small neighborhood of the origin. Two examples are given to further verify the effectiveness of the proposed approach.     

Tracking control for nonlinear time-delay multiagent systems with input saturation

In this paper, the tracking control problem for a class of nonlinear time-delay multiagent systems with input saturation is considered. The nonlinear dynamics are dominated by strict-feedback form and satisfy Lipschitz conditions with constant gains. First, it indicated that the tracking control problem is equivalent to a general bound problem of high-dimensional multivariable systems. Second, an ingenious state transformation is utilized to change the bound problem into the parameter design problem. Third, by the static gain control technique and the hyperbolic tangent function, both state feedback and output feedback controllers are built such that all signals of the closed-loop systems are globally bounded, and the tracking errors between the followers and the leader can converge to a small neighborhood around the origin by appropriately selecting parameters. Finally, an example is shown to verify the feasibility of our results.     

Adaptive multi-dimensional Taylor network funnel control of a class of nonlinear systems with asymmetric input saturation

In view of the result and performance of control are affected by the existence of input constraints and requirements, adaptive multi-dimensional Taylor network (MTN) funnel control problem is studied for a class of nonlinear systems with asymmetric input saturation in this paper. Firstly, the effect of asymmetric input saturation can overcome by introducing the Gaussian error function, namely, the asymmetric saturation model is represented as a simple linear model with a bounded disturbance. Secondly, MTNs are employed to approximate the unknown functions in the controller design. Then, an adaptive MTN tracking controller is developed by blends the idea of funnel control into backstepping, which can guarantee that the tracking error always meets the given prescribed performance regarding the transient and steady state responses as well as the output of system tracks the give continuous reference signal. Finally, the effectiveness of the proposed control is demonstrated using two examples.     

Adaptive dynamic surface control of stochastic nonstrict-feedback constrained nonlinear systems with input and state unmodeled dynamics

In this paper, the issue of adaptive neural control is discussed for a class of stochastic nonstrict-feedback constrained nonlinear systems with input and state unmodeled dynamics. A dynamic signal produced by the first-order auxiliary system is employed to deal with the dynamical uncertain terms. Radial basis function neural networks are used to reconstruct unknown nonlinear continuous functions. With the help of the mean value theorem and Young's inequality, only one learning parameter is adjusted online at recursive each step. Using the hyperbolic tangent function as nonlinear mapping, the output constrained stochastic nonstrict-feedback system in the presence of unmodeled dynamics is transformed into a novel unconstrained stochastic nonstrict-feedback system. Based on dynamic surface control technology and the property of Gaussian function, adaptive neural control is developed for the transformed stochastic nonstrict-feedback system. The output abides by stochastic constraints in probability. By the Lyapunov method, all signals of the closed-loop control system are proved to be semi-global uniform ultimate bounded (SGUUB) in probability. The obtained theoretical findings are verified by two numerical examples.     

Saturated observer-based adaptive neural network leader-following control of N tractors with n-trailers with a guaranteed performance

This article addresses the leader-following neural network adaptive observer-based control of N tractors connected to n trailers with the prescribed performance specifications. To propose the controller, a change of coordinates and a nonlinear error transformation are used to transform the constrained error dynamics to a new second-order Euler-Lagrange unconstrained error dynamics which inherits all structural properties of ith vehicle dynamic model. By combining a projection-type neural network and an adaptive robust technique, a novel leader-following saturated output-feedback controller is proposed to force that ith vehicle tracks a virtual leader trajectory with the prescribed transient and steady-state characteristics while reducing the actuator saturation risk and compensating all unknown dynamic model parameters, external disturbances, unmolded dynamics, and NN approximation errors. A saturated velocity observer is heuristically proposed to obviate the requirement for the velocity measurements of ith vehicle without any unwanted peaking. A Lyapunov-based stability analysis is utilized to prove that all the tracking and state observation errors are semi-globally uniformly ultimately bounded (SGUUB) and they converge to small bounds including the origin with a prescribed performance. At the end, computer simulations will be shown to validate the efficacy of the proposed controller in practice.     

Prescribed performance adaptive fuzzy control for nonstrict-feedback nonlinear systems with dead zone outputs

This paper presents an adaptive fuzzy control scheme for a class of nonstrict-feedback nonlinear systems with dead zone outputs and prescribed performance. By utilizing the monotonically increasing property of system bounding functions and the Nussbaum function, the design difficulties caused by the nonstrict-feedback structure and dead zone output are overcome. Combining backstepping technique with prescribed performance algorithm, a feasible adaptive fuzzy controller is designed to guarantee the boundedness of all signals of the closed-loop system and the prescribed tracking performance of the system. Finally, simulation results are depicted to illustrate the effectiveness of the proposed control approach.     

Neural networks-based adaptive finite-time prescribed performance fault-tolerant control of switched nonlinear systems

In this article, the adaptive finite-time fault-tolerant control problem is considered for a class of switched nonlinear systems in nonstrict-feedback form with actuator fault. The problem of finite-time fault-tolerant control is solved by introducing a finite-time performance function. Meanwhile, the completely unknown nonlinear functions exist in the switched system are identified by the neural networks. Based on the common Lyapunov function method with adaptive backstepping technique, the finite-time fault-tolerant controller is designed. The proposed control strategy can guarantee that the tracking error converges to a prescribed zone at a finite-time and all system variables remain semiglobally practical finite-time stable. Numerical examples are offered to verify the feasibility of the theoretical result.     

Adaptive saturation compensation for strict-feedback systems with unknown control coefficient and input saturation

This work presents an adaptive saturation compensation scheme for the strict-feedback uncertain systems with unknown control coefficient and input saturation. An adaptive saturation dynamic filter that does not require the a priori information of the completely unknown control coefficient is incorporated to correct position errors online to reduce the saturation effect. A Nussbaum-type function is employed to handle the unknown control coefficient and avoid the control singularity. The adaptive command-filtered backstepping is employed to derive the adaptive controller. The repeated differential operations of stabilizing functions required in the traditional backstepping are obviated due to command filters. It is analyzed that the designed adaptive controller achieves the system output tracking and the closed-loop uniform ultimate stability. A simulation example is provided to validate the 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.     

高超声速飞行器预设性能反演鲁棒控制

针对吸气式高超声速飞行器的飞行控制问题,提出一种新的预设性能模糊反演控制设计方法。通过构造一种新的预设性能函数,在初始误差正负未知的情况下,可以保证跟踪误差能够按照预定的收敛速度、超调量及稳态误差收敛至任意小的区域,同时实现了对跟踪误差稳态性能和瞬态性能的约束。为提高控制系统的鲁棒性,在反演控制的设计框架下,引入模糊控制器逼近动力学模型中的不确定项。为避免传统反演方法中存在的"微分膨胀"问题,引入滑模微分器对虚拟控制量的导数进行精确估计。最后,通过不同初始误差下的轨迹仿真验证所设计控制系统的有效性。     

Finite-time adaptive fuzzy control for a class of output constrained nonlinear systems with dead-zone

The article investigates the finite-time adaptive fuzzy control for a class of nonlinear systems with output constraint and input dead-zone. First, by skillfully combining the barrier Lyapunov function, backstepping design method, and finite-time control theory, a novel adaptive state-feedback tracking controller is constructed, and the output constraint of the nonlinear system is not violated. Second, the fuzzy logic system is used to approximate unknown function in the nonlinear system. Third, the finite-time command filter is introduced to avoid the problem of “complexity explosion” caused by repeated differentiations of the virtual control signal in conventional backstepping control schemes. Meanwhile, a new saturation function is added in the compensating signal for filter error to improve control accuracy. Finally, based on Lyapunov stability analysis, all the signals of the closed-loop are proved to be semi-globally uniformly ultimately bounded, and the tracking error converges to a small neighborhood region of the origin in a finite time. A simulation example is presented to demonstrate the effectiveness for the proposed control scheme.     

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.     

Fuzzy adaptive control of a class of nonlinear systems with unmodeled dynamics

This paper investigates the tracking control problem for a class of pure‐feedback systems with unmodeled dynamics. The useful properties of the fuzzy basis functions and membership are explored to be used for stability analysis, and an alternative Lyapunov function depending on both control input and system state is utilized. Then, an adaptive fuzzy controller is designed to ensure that the tracking error is within a small adjustable neighborhood of the origin, where some conventional assumptions imposed on the unmodeled dynamics have been relaxed. Finally, simulation results are given to validate the theoretical results.     

Adaptive fixed-time minimal learning force/position control of uncertain manipulators subject to input saturation

This article solves the fixed-time force/position control problem for constrained manipulators in the presence of input saturation and uncertain dynamics. Under the fixed-time stability theory, a novel fixed-time auxiliary dynamic system (ADS) is first presented to compensate for the effects of input saturation nonlinearity. System uncertainties are estimated by using radial basis function neural networks (RBF NNs) and only need to tune one neural parameter online. In addition, with a fixed-time sliding mode surface and the proposed fixed-time ADS, a novel fixed-time adaptive neural force/position controller is designed which can not only ensure the fixed-time stability of the position tracking error but also enable the manipulator to track the desired force trajectory. By using the Lyapunov method, the boundedness of all signals in the closed-loop system is proved. Finally, the effectiveness of the proposed method is demonstrated by comparative simulation works.     

Neural adaptive robust output feedback control of wheeled mobile robots with saturating actuators

This paper addresses the output feedback tracking control problem of electrically driven wheeled mobile robots subjected to actuator constraints. The main drawback of previously proposed controllers is the actuator saturation problem, which degrades the transient performance of the closed‐loop control system. In order to alleviate this problem, a saturated tracking controller has been proposed using the hyperbolic tangent function. A new nonlinear observer is introduced in order to leave out the velocity sensors in the robot system to decrease the cost and weight of the system for practical applications. A dynamic surface control strategy is effectively used to reduce the design complexity when considering actuator dynamics. In addition, neural network approximation capabilities and adaptive robust techniques are also adopted to improve the tracking performance in the presence of uncertain nonlinearities and unknown parameters. Semi‐global stability of the closed‐loop system is presented using direct Lyapunov method. Simulation results are provided to illustrate the effectiveness of the proposed control system for a differential drive mobile robot in practice. Copyright © 2014 John Wiley & Sons, Ltd.     

基于PCH模型的有源电力滤波器滑动耗散阻尼限幅自适应L2增益控制

基于有源电力滤波器(APF)的端口受控哈密顿系统(PCH)平均化模型,提出了一种采用滑动耗散阻尼限幅的自适应L2增益控制新方法.该方法基于APF的能量耗散特性和能量平衡原理,建立了APFPCH平均化模型和误差系统PCH平均化模型.在此基础上设计了自适应L2增益控制方法,在确保误差系统稳定的同时有效抑制了参数摄动和外界干扰对控制效果的影响.针对误差系统的欠驱动性质和准确估计直流电容参考电压波动量的困难,分别采用间接控制以及大电容条件下忽略直流电容参考电压波动量的方法,简化了控制方法的执行过程;此外,该方法还分析了APF内层控制过调制现象产生的原因.针对跟踪精度和干扰抑制的要求与APF内层控制过调制约束条件间的矛盾,通过以滑动耗散阻尼限幅控制代替固定耗散阻尼控制,在满足内层控制约束条件下确保跟踪精度和补偿效果.仿真实验验证了本文所提方法的正确性和有效性.     

基于改进滑模趋近律和非线性干扰观测器的PMSM位置跟踪

针对永磁同步电机（PMSM）在实际运行过程中会受到参数摄动和外界不确定干扰等非线性因素影响,导致电机控制性能下降,位置跟踪精度降低。提出将滑模控制（SMC）与反演控制(Backsteeping Control)结合设计非线性控制器,对反演滑模控制中的趋近律做出改进,提出一种基于指数趋近律的双幂次趋近律,并利用非线性干扰观测器（NDOB）观测和估计干扰,对其进行补偿。最后利用Matlab/Simulink进行仿真,结果显示：该方法在一定程度上提高了电机位置控制精度,减小了位置跟踪误差,同时增强了系统抗干扰能力。     

A gain‐scheduled control algorithm for input constrained systems to track time‐varying references using controller state resets

In this paper, we propose a control law for a discrete‐time linear system with actuator saturation to track time‐varying reference signals. The proposed control law consists of a feedback controller and a target recalculation mechanism. The feedback controller includes an integrator to achieve zero steady‐state error in the case where the reference signal is constant. The feedback gains of the controller are parameterized by a single scheduling parameter. In the proposed control algorithm, when the tracking error is large, a modified reference signal is computed by the target recalculation mechanism so that feasibility of the algorithm and stability of the control system are guaranteed at all times. At this stage, the controller state is modified online so that the tracking control performance is improved. Further, when the tracking error becomes small, the scheduling parameter and the controller state are updated simultaneously so that the tracking control performance is improved. The problems of determining the scheduling parameter, the controller state, and the modified reference signal are reduced to convex optimization problems with linear matrix inequality constraints. The effectiveness of the proposed control method is shown through an experiment. © 2016 Institute of Electrical Engineers of Japan. Published by John Wiley & Sons, Inc.     

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.