Backstepping control for periodically time-varying systems using high-order neural network and Fourier series expansion

An adaptive backstepping tracking scheme is developed for a class of strict-feedback systems with unknown periodically time-varying parameters and unknown control gain functions. High-order neural network (HONN) and Fourier series expansion (FSE) are combined into a new function approximator to model each uncertain term in the system. The dynamic surface control (DSC) approach is used to solve the problem of ‘explosion of complexity’ in the backstepping design procedure. Nussbaum gain function (NGF) is employed to deal with the unknown control gain functions. The uniform boundedness of all closed-loop signals is guaranteed. The tracking error is proved to converge to a small residual set around the origin. Two simulation examples are provided to demonstrate the effectiveness of the control scheme designed in this paper.     

Robust preview control for a class of uncertain discrete-time systems with time-varying delay

This paper proposes a concept of robust preview tracking control for uncertain discrete-time systems with time-varying delay. Firstly, a model transformation is employed for an uncertain discrete system with time-varying delay. Then, the auxiliary variables related to the system state and input are introduced to derive an augmented error system that includes future information on the reference signal. This leads to the tracking problem being transformed into a regulator problem. Finally, for the augmented error system, a sufficient condition of asymptotic stability is derived and the preview controller design method is proposed based on the scaled small gain theorem and linear matrix inequality (LMI) technique. The method proposed in this paper not only solves the difficulty problem of applying the difference operator to the time-varying matrices but also simplifies the structure of the augmented error system. The numerical simulation example also illustrates the effectiveness of the results presented in the paper.     

输入受限无人帆船自适应航向跟踪控制

针对带有输入受限且存在未知控制系数约束情形下,考虑了具有未知模型和风、浪等外界干扰的无人船航向跟踪控制问题,提出一种受限控制输入约束下的跟踪控制方法。该方法运用RBF神经网络对未知模型进行在线逼近,利用Nussbaum自适应增益技术解决未知控制系数问题。根据滑模控制理论,设计具有指数趋近律的鲁棒控制项,保证所得误差闭环系统快速响应且最终趋向0。为弱化传统滑模控制产生的抖振问题,将符号函数替换成饱和函数使控制输入变得平滑。引入一种误差辅助系统,构建了帮助误差闭环系统输入退出饱和机制。通过李雅普诺夫稳定性理论,给出了跟踪控制方法的稳定性数学分析过程,证明误差闭环跟踪控制系统的所有信号最终一致有界性。最后通过仿真结果验证了所得理论的有效性。     

Containment control of networked autonomous underwater vehicles: A predictor-based neural DSC design

This paper investigates the containment control problem of networked autonomous underwater vehicles in the presence of model uncertainty and unknown ocean disturbances. A predictor-based neural dynamic surface control design method is presented to develop the distributed adaptive containment controllers, under which the trajectories of follower vehicles nearly converge to the dynamic convex hull spanned by multiple reference trajectories over a directed network. Prediction errors, rather than tracking errors, are used to update the neural adaptation laws, which are independent of the tracking error dynamics, resulting in two time-scales to govern the entire system. The stability property of the closed-loop network is established via Lyapunov analysis, and transient property is quantified in terms of L₂ norms of the derivatives of neural weights, which are shown to be smaller than the classical neural dynamic surface control approach. Comparative studies are given to show the substantial improvements of the proposed new method.     

Robust finite-time consensus control for multi-agent systems with disturbances and unknown velocities

In this paper, we investigated the finite-time consensus tracking problem for multi-agent systems with external bounded disturbances and input bounded disturbances and unknown velocities. Based on the Lyapunov finite-time theorem, a novel finite-time consensus control is constructed by using the backstepping method. For unknown velocities, the high-gain observer is used to estimate the velocity information. It is proved that the consensus can be achieved in finite time. The consensus shows fast response and strong robustness to various disturbances. Finally, the effectiveness of the results is illustrated by numerical simulations.     

自主式水下机器人自适应区域跟踪控制

研究自主式水下机器人的区域跟踪控制问题,提出一种基于PD神经滑模的自适应区域跟踪控制方法。针对自主式水下机器人自适应控制器中仅在线调整网络权值的径向基函数神经网络存在收敛性能差的问题,给出同时对径向基函数神经网络权值、径向基函数中心与方差进行自适应调整的方法,使径向基函数神经网络无须离线选取径向基函数中心与方差,即可进行在线自适应学习。考虑到控制器中滑模控制项易引起系统抖振的问题,提出一种基于指数函数的滑模切换增益调节方法,使滑模切换增益能够依据跟踪误差实时调节以降低系统抖振。基于Lyapunov理论对所提自适应区域跟踪控制方法的稳定性进行分析。通过自主式水下机器人的仿真试验与水池试验验证所提方法的有效性。     

Decentralized adaptive neural prescribed performance control for high-order stochastic switched nonlinear interconnected systems with unknown system dynamics

In this paper, the problem of decentralized adaptive neural backstepping control is investigated for high-order stochastic nonlinear systems with unknown interconnected nonlinearity and prescribed performance under arbitrary switchings. For the control of high-order nonlinear interconnected systems, it is assumed that unknown system dynamics and arbitrary switching signals are unknown. First, by utilizing the prescribed performance control (PPC), the prescribed tracking control performance can be ensured, while the requirement for the initial error is removed. Second, at each recursive step, only one adaptive parameter is constructed to overcome the over-parameterization, and RBF neural networks are employed to tackle the difficulties caused by completely unknown system dynamics. At last, based on the common Lyapunov stability method, the decentralized adaptive neural control method is proposed, which decreases the number of learning parameters. It is shown that the designed common controller can ensure that all the signals in the closed-loop system are semi-globally uniformly ultimately bounded (SGUUB), and the prescribed tracking control performance is guaranteed under arbitrary switchings. The simulation results are presented to further illustrate the effectiveness of the proposed control scheme.     

Modeling and output tracking of transverse flux permanent magnet machines using high gain observer and RBF neural network

This paper deals with modeling and adaptive output tracking of a transverse flux permanent magnet machine as a nonlinear system with unknown nonlinearities by utilizing high gain observer and radial basis function networks. The proposed model is developed based on computing the permeance between rotor and stator using quasiflux tubes. Based on this model, the techniques of feedback linearization and H_∞ control are used to design an adaptive control law for compensating the unknown nonlinear parts, such as the effect of cogging torque, as a disturbance is decreased onto the rotor angle and angular velocity tracking performances. Finally, the capability of the proposed method in tracking both the angle and the angular velocity is shown in the simulation results.     

Adaptive control of uncertain continuously stirred tank reactors with unknown actuator nonlinearities

Adaptive nonlinear control is investigated for continuously stirred tank reactor (CSTR) systems using neural networks. The CSTR plant under study belongs to a class of nonaffine nonlinear systems, and contains an unknown parameter that enters the model nonlinearly. Using adaptive backstepping and neural network (NN) approximation techniques, an alternative adaptive NN controller is developed that achieves asymptotic output tracking control. A novel integral-type Lyapunov function, which includes both system states and control input as its arguments, is constructed to solve the difficulty associated with the nonaffine control problem. Numerical simulation is performed to show the feasibility of the proposed approach for chemical process control.     

Command filter based adaptive control of asymmetric output-constrained switched stochastic nonlinear systems

In this paper, adaptive tracking control problem is investigated for a class of switched stochastic nonlinear systems with an asymmetric output constraint. By introducing a nonlinear mapping (NM), the asymmetric output-constrained switched stochastic system is first transformed into a new system without any constraint, which achieves the equivalent control objective. The command filter technique is employed to handle the “explosion of complexity” in traditional backstepping design, and neural networks (NNs) are directly utilized to cope with the completely unknown nonlinear functions and stochastic disturbances existing in systems. At last, on the basis of stochastic Lyapunov function method, an adaptive neural controller is developed for the considered system. It is shown that the designed adaptive controller can guarantee that all the signals remain semi-globally uniformly ultimately bounded (SGUUB), while the output constraint is satisfied and the desired signal can be tracked with a small domain of the origin. Simulation results are offered to illustrate the feasibility of the newly designed control scheme.     

Robust tracking and distributed synchronization control of a multi-motor servomechanism with H-infinity performance

The multi-motor servomechanism (MMS) is a multi-variable, high coupling and nonlinear system, which makes the controller design challenging. In this paper, an adaptive robust H-infinity control scheme is proposed to achieve both the load tracking and multi-motor synchronization of MMS. This control scheme consists of two parts: a robust tracking controller and a distributed synchronization controller. The robust tracking controller is constructed by incorporating a neural network (NN) K-filter observer into the dynamic surface control, while the distributed synchronization controller is designed by combining the mean deviation coupling control strategy with the distributed technique. The proposed control scheme has several merits: 1) by using the mean deviation coupling synchronization control strategy, the tracking controller and the synchronization controller can be designed individually without any coupling problem; 2) the immeasurable states and unknown nonlinearities are handled by a NN K-filter observer, where the number of NN weights is largely reduced by using the minimal learning parameter technique; 3) the H-infinity performances of tracking error and synchronization error are guaranteed by introducing a robust term into the tracking controller and the synchronization controller, respectively. The stabilities of the tracking and synchronization control systems are analyzed by the Lyapunov theory. Simulation and experimental results based on a four-motor servomechanism are conducted to demonstrate the effectiveness of the proposed method.     

Novel prescribed performance neural control of a flexible air-breathing hypersonic vehicle with unknown initial errors

A novel prescribed performance neural controller with unknown initial errors is addressed for the longitudinal dynamic model of a flexible air-breathing hypersonic vehicle (FAHV) subject to parametric uncertainties. Different from traditional prescribed performance control (PPC) requiring that the initial errors have to be known accurately, this paper investigates the tracking control without accurate initial errors via exploiting a new performance function. A combined neural back-stepping and minimal learning parameter (MLP) technology is employed for exploring a prescribed performance controller that provides robust tracking of velocity and altitude reference trajectories. The highlight is that the transient performance of velocity and altitude tracking errors is satisfactory and the computational load of neural approximation is low. Finally, numerical simulation results from a nonlinear FAHV model demonstrate the efficacy of the proposed strategy.     

Identification and adaptive neural network control of a DC motor system with dead-zone characteristics

In this paper, an adaptive control approach based on the neural networks is presented to control a DC motor system with dead-zone characteristics (DZC), where two neural networks are proposed to formulate the traditional identification and control approaches. First, a Wiener-type neural network (WNN) is proposed to identify the motor DZC, which formulates the Wiener model with a linear dynamic block in cascade with a nonlinear static gain. Second, a feedforward neural network is proposed to formulate the traditional PID controller, termed as PID-type neural network (PIDNN), which is then used to control and compensate for the DZC. In this way, the DC motor system with DZC is identified by the WNN identifier, which provides model information to the PIDNN controller in order to make it adaptive. Back-propagation algorithms are used to train both neural networks. Also, stability and convergence analysis are conducted using the Lyapunov theorem. Finally, experiments on the DC motor system demonstrated accurate identification and good compensation for dead-zone with improved control performance over the conventional PID control.     

Adaptive iterative learning control of a class of nonlinear time-delay systems with unknown backlash-like hysteresis input and control direction

This paper presents an adaptive iterative learning control scheme for a class of nonlinear systems with unknown time-varying delays and control direction preceded by unknown nonlinear backlash-like hysteresis. Boundary layer function is introduced to construct an auxiliary error variable, which relaxes the identical initial condition assumption of iterative learning control. For the controller design, integral Lyapunov function candidate is used, which avoids the possible singularity problem by introducing hyperbolic tangent funciton. After compensating for uncertainties with time-varying delays by combining appropriate Lyapunov-Krasovskii function with Young's inequality, an adaptive iterative learning control scheme is designed through neural approximation technique and Nussbaum function method. On the basis of the hyperbolic tangent function's characteristics, the system output is proved to converge to a small neighborhood of the desired trajectory by constructing Lyapunov-like composite energy function (CEF) in two cases, while keeping all the closed-loop signals bounded. Finally, a simulation example is presented to verify the effectiveness of the proposed approach.     

Development of an adaptive radial basis function neural network estimator-based continuous sliding mode control for uncertain nonlinear systems

In this paper an adaptive neural network (NN)-based nonlinear controller is proposed for trajectory tracking of uncertain nonlinear systems. The adopted control algorithm combines a continuous second-order sliding mode control (CSOSMC), the radial basis function neural network (RBFNN) and the adaptive control methodology. First, a second-order sliding mode control scheme (SOSMC), which is published recently in literature for linear uncertain systems, is extended for nonlinear uncertain systems. Second, an adaptive radial basis function neural network estimator-based continuous second order sliding mode control algorithm (CSOSMC-ANNE) is adopted. In CSOSMC-ANNE control methodology, a radial basis function neural network with adaptive parameters is exploited to approximate the unknown system parameters and improve performance against perturbations. Also, the discontinuous switching control of SOSMC is supplanted with a smooth continuous control action to completely eliminate the chattering phenomenon. The convergence and global stability of the closed-loop system are proved using Lyapunov stability method. Numerical computer simulations, with dynamical model of the nonlinear inverted pendulum system, are presented to demonstrate the effectiveness and advantages of the presented control scheme.     

Learning from adaptive neural network output feedback control of a unicycle-type mobile robot

This paper studies learning from adaptive neural network (NN) output feedback control of nonholonomic unicycle-type mobile robots. The major difficulties are caused by the unknown robot system dynamics and the unmeasurable states. To overcome these difficulties, a new adaptive control scheme is proposed including designing a new adaptive NN output feedback controller and two high-gain observers. It is shown that the stability of the closed-loop robot system and the convergence of tracking errors are guaranteed. The unknown robot system dynamics can be approximated by radial basis function NNs. When repeating same or similar control tasks, the learned knowledge can be recalled and reused to achieve guaranteed stability and better control performance, thereby avoiding the tremendous repeated training process of NNs.     

Lattice distortions in GaN on sapphire using the CBED–HOLZ technique

The convergent beam electron diffraction (CBED) methodology was developed to investigate the lattice distortions in wurtzite gallium nitride (GaN) from a single zone-axis pattern. The methodology enabled quantitative measurements of lattice distortions (α, β, γ and c) in transmission electron microscope (TEM) specimens of a GaN film grown on (0, 0, 0, 1) sapphire by metal-organic vapour-phase epitaxy. The CBED patterns were obtained at different distances from the GaN/sapphire interface. The results show that GaN is triclinic above the interface with an increased lattice parameter c. At 0.85 μm from the interface, α=90°, β=8905° and γ=11966°. The GaN lattice relaxes steadily back to hexagonal further away from the sapphire substrate. The GaN distortions are mainly confined to the initial stages of growth involving the growth and the coalescence of 3D GaN islands.     

Finite-time sliding surface constrained control for a robot manipulator with an unknown deadzone and disturbance

This paper presents finite-time sliding mode control (FSMC) with predefined constraints for the tracking error and sliding surface in order to obtain robust positioning of a robot manipulator with input nonlinearity due to an unknown deadzone and external disturbance. An assumed model feedforward FSMC was designed to avoid tedious identification procedures for the manipulator parameters and to obtain a fast response time. Two constraint switching control functions based on the tracking error and finite-time sliding surface were added to the FSMC to guarantee the predefined tracking performance despite the presence of an unknown deadzone and disturbance. The tracking error due to the deadzone and disturbance can be suppressed within the predefined error boundary simply by tuning the gain value of the constraint switching function and without the addition of an extra compensator. Therefore, the designed constraint controller has a simpler structure than conventional transformed error constraint methods and the sliding surface constraint scheme can also indirectly guarantee the tracking error constraint while being more stable than the tracking error constraint control. A simulation and experiment were performed on an articulated robot manipulator to validate the proposed control schemes.     

Receding horizon online optimization for torque control of gasoline engines

This paper proposes a model-based nonlinear receding horizon optimal control scheme for the engine torque tracking problem. The controller design directly employs the nonlinear model exploited based on mean-value modeling principle of engine systems without any linearizing reformation, and the online optimization is achieved by applying the Continuation/GMRES (generalized minimum residual) approach. Several receding horizon control schemes are designed to investigate the effects of the integral action and integral gain selection. Simulation analyses and experimental validations are implemented to demonstrate the real-time optimization performance and control effects of the proposed torque tracking controllers.