Robust model predictive control for switched linear systems

Developed is a robust model predictive control scheme for a class of discrete-time switched linear systems. The system is described in linear fractional transformation form in the presence of model uncertainty and induced norm bounded disturbances. The objective is to minimize the upper bound of an infinite horizon cost function subject to a terminal inequality. A Lyapunov function analysis for the switched system shows guaranteed closed-loop stability. Taking into account the switching structure of the system, the predictive control design problem along with sufficient conditions for the existence of a solution is expressed in terms of Riccati–Metzler inequalities. Then, these inequalities are turned into a linear matrix inequality feasibility problem. Three cases are analyzed to demonstrate the performance and effectiveness of the proposed robust model predictive controller for switched discrete-time linear systems.     

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.     

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.     

Temporally local recurrent radial basis function network for modeling and adaptive control of nonlinear systems

In this paper, a novel temporally local recurrent radial basis function network for modeling and adaptive control of nonlinear systems is proposed. The proposed structure consists of recurrent hidden neurons having weighted self-feedback loops and a weighted linear feed-through from the input layer directly to the output layer neuron(s). The dynamic back-propagation algorithm is developed and used for updating the parameters of the proposed structure. To improve the performance of learning algorithm, discrete Lyapunov stability method is used to develop an adaptive learning rate scheme. This scheme ensures the faster convergence of the parameters and maintains the stability of the system. A total of 5 complex nonlinear systems are used to test and compare the performance of the proposed network with other neural network structures. The disturbance rejection tests are also carried out to check whether the proposed scheme is able to handle the external disturbance/noise signals effects or not. The obtained results show the efficacy of the proposed method.     

Robust integral of neural network and precision motion control of electrical–optical gyro-stabilized platform with unknown input dead-zones

Parametric uncertainty associated with unmodeled disturbance always exist in physical electrical–optical gyro-stabilized platform systems, and poses great challenges to the controller design. Moreover, the existence of actuator deadzone nonlinearity makes the situation more complicated. By constructing a smooth dead-zone inverse, the control law consisting of the robust integral of a neural network (NN) output plus sign of the tracking error feedback is proposed, in which adaptive law is synthesized to handle parametric uncertainty and RISE robust term to attenuate unmodeled disturbance. In order to reduce the measure noise, a desired compensation method is utilized in controller design, in which the model compensation term depends on the reference signal only. By mainly activating an auxiliary robust control component for pulling back the transient escaped from the neural active region, a multi-switching robust neuro adaptive controller in the neural approximation domain, which can achieve globally uniformly ultimately bounded (GUUB) tracking stability of servo systems recently. An asymptotic tracking performance in the presence of unknown dead-zone, parametric uncertainties and various disturbances, which is vital for high accuracy tracking, is achieved by the proposed robust adaptive backstepping controller. Extensively comparative experimental results are obtained to verify the effectiveness of the proposed control strategy.     

机械臂反演非奇异终端的神经滑模控制

为了解决具有外部干扰以及建模误差的多关节机械臂的轨迹跟踪问题,提出了一种机械臂反演非奇异终端的神经滑模控制方法。采用非奇异终端的滑模面,基于反演方法以及滑模控制的原理,设计了反演滑模控制器。针对由于外部干扰以及建模误差引起的反演滑模控制系统中不确定的因素上界,设计了径向基(radial basis function,简称RBF)神经网络的自适应律,对不确定因素上界进行了在线估计,并对控制系统的稳定性使用了Lyapunov定理进行证明。仿真分析结果表明,所提出的方法不仅可以减少系统中存在的抖振现象,而且具有较好的轨迹跟踪性能和较强的鲁棒性。     

Perturbed dynamics of discrete-time switched nonlinear systems with delays and uncertainties

This paper addresses the dynamics of a class of discrete-time switched nonlinear systems with time-varying delays and uncertainties and subject to perturbations. It is assumed that the nominal switched nonlinear system is robustly uniformly exponentially stable. It is revealed that there exists a maximal Lipschitz constant, if perturbation satisfies a Lipschitz condition with any Lipschitz constant less than the maximum, then the perturbed system can preserve the stability property of the nominal system. In situations where the perturbations are known, it is proved that there exists an upper bound of coefficient such that the perturbed system remains exponentially stable provided that the perturbation is scaled by any coefficient bounded by the upper bound. A numerical example is provided to illustrate the proposed theoretical results.     

自由漂浮空间机械臂基于神经网络的鲁棒自适应控制

考虑数学模型难以精确获得及带外部干扰情况下,针对自由漂浮空间机械臂的轨迹跟踪控制问题,提出一种基于神经网络的自适应鲁棒控制策略。基于Lyapunov稳定性理论设计理想控制器,进而推出系统的不确定模型。利用神经网络的学习能力逼近系统不确定模型,从而避免保守上界的估计。利用线性化技术并结合Lyapunov函数,设计包括权值及隐层参数在内的在线自适应学习律及鲁棒控制器,加快了误差收敛速度及控制精度,并消除了高阶逼近误差及扰动,保证了系统的一致最终有界,仿真比较表明了该控制策略的有效性。     

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.     

Robust adaptive sliding mode control for uncertain systems with unknown time-varying delay input

This article focuses on robust adaptive sliding mode control law for uncertain discrete systems with unknown time-varying delay input, where the uncertainty is assumed unknown. The main results of this paper are divided into three phases. In the first phase, we propose a new sliding surface is derived within the Linear Matrix Inequalities (LMIs). In the second phase, using the new sliding surface, the novel Robust Sliding Mode Control (RSMC) is proposed where the upper bound of uncertainty is supposed known. Finally, the novel approach of Robust Adaptive Sliding ModeControl (RASMC) has been defined for this type of systems, where the upper limit of uncertainty which is assumed unknown. In this new approach, we have estimate the upper limit of uncertainties and we have determined the control law based on a sliding surface that will converge to zero. This novel control laws are been validated in simulation on an uncertain numerical system with good results and comparative study. This efficiency is emphasized through the application of the new controls on the two physical systems which are the process trainer PT326 and hydraulic system two tanks.     

具有状态约束的机械臂切换自适应控制

为了解决具有状态约束的机械臂的控制问题,本文针对一类具有全状态约束和状态不完全可测的切换严格反馈非线性系统进行研究,通过引入状态观测器、自适应神经网络和动态表面控制技术,设计了一种基于径向基函数(RBF)神经网络的自适应输出反馈控制方法。利用Lyapunov方法和平均驻留时间理论(ADT)保证了闭环系统所有信号是半全局一致最终有界的(SGUUB),通过数值例子仿真验证了所提方法的有效性。最后将该方法应用于带电机驱动的机械臂并进行仿真实验,仿真结果表明,机械臂轨迹跟踪误差很小,有着良好的控制精度,同时也表明所提出的控制算法能够应用于实际工程模型。     

单神经元自适应PID控制在SRD中的应用

介绍了一种基于单神经元自适应控制算法及其在开关磁阻电动机调速中的应用;通过仿真这种算法在开关磁阻电动机调速中的应用,给出了基于这种算法的控制策略和控制程序的流程。     

Adaptive nonsingular fast terminal sliding-mode control for the tracking problem of uncertain dynamical systems

In this paper, robust and adaptive nonsingular fast terminal sliding-mode (NFTSM) control schemes for the trajectory tracking problem are proposed with known or unknown upper bound of the system uncertainty and external disturbances. The developed controllers take the advantage of the NFTSM theory to ensure fast convergence rate, singularity avoidance, and robustness against uncertainties and external disturbances. First, a robust NFTSM controller is proposed which guarantees that sliding surface and equilibrium point can be reached in a short finite-time from any initial state. Then, in order to cope with the unknown upper bound of the system uncertainty which may be occurring in practical applications, a new adaptive NFTSM algorithm is developed. One feature of the proposed control law is their adaptation techniques where the prior knowledge of parameters uncertainty and disturbances is not needed. However, the adaptive tuning law can estimate the upper bound of these uncertainties using only position and velocity measurements. Moreover, the proposed controller eliminates the chattering effect without losing the robustness property and the precision. Stability analysis is performed using the Lyapunov stability theory, and simulation studies are conducted to verify the effectiveness of the developed control schemes.     

Adaptive NN output-feedback stabilization for a class of stochastic nonlinear strict-feedback systems

In this paper, the adaptive neural network output-feedback stabilization problem is investigated for a class of stochastic nonlinear strict-feedback systems. The nonlinear terms, which only depend on the system output, are assumed to be completely unknown, and only an NN is employed to compensate for all unknown upper bounding functions, so that the designed controller is more simple than the existing results. It is shown that, based on the backstepping method and the technique of nonlinear observer design, the closed-loop system can be proved to be asymptotically stable in probability. The simulation results demonstrate the effectiveness of the proposed control scheme.     

柔顺并联机器人动力学及轨迹跟踪

以含有开槽型柔顺关节的并联机器人为研究对象,对其动力学及轨迹跟踪问题进行研究。根据柔顺关节特性,建立系统分析模型,应用拉格朗日方法建立系统动力学方程。为补偿系统具有的不确定性,分别设计趋近律上界滑模控制策略和径向基函数(Radial basis function,RBF)神经网络趋近律滑模控制策略,基于Lyapunov理论证明了系统的全局稳定性。应用S型速度规划曲线,分别给出直线轨迹和圆轨迹的运动规划算法。仿真结果表明,系统模型及控制策略能够有效实现柔顺关节并联机器人的轨迹跟踪。     

基于神经网络的通用模型自适应控制

应用复合正交神经网络来实现过程的自适应逆控制方法,和通用模型控制器策略相结合,提出了一种基于神经网络的通用模型自适应控制方法,将非线性过程模型应用逆系统的方法可以在控制算法中直接嵌入过程模型,从而保证通用模型控制策略的可实现性.另一方面,在自适应逆控制中采用复合正交神经网络具有算法简单、学习收敛速度快等优点,可以克服常用的BP和RBF神经网络一些缺点.基于神经网络的通用模型自适应控制方法中的参考轨迹是一条典型的二阶曲线,该控制器参数具有明显的物理意义,参数整定方便.仿真验证了该控制策略的有效性.     

基于径向基神经网络的直线超声电机位置控制

针对直线超声电机的精密位置控制,提出了一种基于径向基神经网络的自适应控制机制。鉴于直线超声电机工作原理,其运行状态必然受到摩擦、强非线性和时变等不确定性因素的干扰,为了对这些不确定性因素进行有效的逼近,采用了径向基神经网络。为了提高控制机制的自适应能力,首先利用来自试验数据的训练样本按正交最小二乘算法确定径向基神经网络的隐层单元的个数和相关参数,再按递推最小二乘法在线调整隐层与输出层之间的权重。试验结果表明,基于径向基神经网络的自适应控制器的性能不仅优于传统的PID控制和误差反向传播神经网络控制,而且具有很好的抗干扰能力。     

热轧立辊电液伺服系统的自适应模糊控制

以热轧立辊为研究背景,针对其液压伺服系统存在的非线性、参数不确定性以及负载干扰等特点,基于模糊基函数网络提出一种自适应控制方法.首先将非线性系统线性化并将其作为已知系统,利用这部分已知的动态特性设计反馈控制使标称系统稳定.然后利用模糊基函数网络仅学习非线性系统不确定性的上界,将输出作为补偿控制器的参数,并在Lyapunov稳定意义下构造自适应控制器,该自适应控制器不仅确保了闭环系统的鲁棒性而且加快了跟踪误差的收敛速度.将该控制器应用于某热轧立辊电液位置伺服系统中进行仿真研究,结果表明,该控制器优于传统的PID控制器,可以取得较好的控制效果.     

GA-BASED PID NEURAL NETWORK CONTROL FOR MAGNETIC BEARING SYSTEMS

In order to overcome the system non-linearity and uncertainty inherent in magnetic bear-ing systems,a GA(genetic algorithm)-based PID neural network controller is designed and trained to emulate the operation of a complete system (magnetic bearing,controller,and power amplifiers). The feasibility of using a neural network to control nonlinear magnetic bearing systems with un-known dynamics is demonstrated. The key concept of the control scheme is to use GA to evaluate the candidate solutions (chromosomes),increase the generalization ability of PID neural network and avoid suffering from the local minima problem in network learning due to the use of gradient descent learning method. The simulation results show that the proposed architecture provides well robust performance and better reinforcement learning capability in controlling magnetic bearing systems.     

神经网络滑模控制在位置伺服系统的应用

针对直流无刷电机伺服系统参数摄动、非线性以及其他不确定因素等问题,提出一种神经网络滑模变结构控制方案。利用一个三层RBF神经网络和滑模变结构控制器实现了无刷电机伺服系统位置的精确控制。该方案综合径向基神经网络和滑模变结构算法的优点,对系统参数变化和外部扰动具有很强的鲁棒性,是一种较理想的智能控制策略。仿真结果表明控制器具有良好的动静态品质,工程实现简单,具有广阔的应用前景。