Discretization of nonlinear non-affine time delay systems based on second-order hold

When calculating the sampled-date representation of nonlinear systems second-order hold(SOH) assumption can be applied to improving the precision of the discretization results. This paper proposes a discretization method based on Taylor series and the SOH assumption for the nonlinear systems with the time delayed non-affine input. The mathematical structure of the proposed discretization method is explored. This proposed discretization method can provide a precise and finite dimensional discretization model for the nonlinear time-delayed non-affine system by keeping the truncation order of the Taylor series. The performance of the proposed discretization method is evaluated by doing the simulation using a nonlinear system with the time-delayed non-affine input.Different input signals, time-delay values and sampling periods are considered in the simulation to investigate the proposed method.The simulation results demonstrate that the proposed method is practical and easy for time-delayed nonlinear non-affine systems.The comparison between SOH assumption with first-order hold(FOH) and zero-order hold(ZOH) assumptions is given to show the advantages of the proposed method.     

Controller design for nonlinear systems with time delay using model algorithm control (MAC)

This paper presents a digital model algorithm control (MAC) for nonlinear time-delayed systems. The MAC controller is designed based on the sampled-data representation of the dynamic system. A new discretization method using the Taylor series and zero order hold assumption is proposed to discretize the continuous nonlinear time-delayed system. The proposed discretization method can provide accurate time discretization results and convert the discrete-time system into a general nonlinear system, so that the MAC method can be employed. Several simulations are conducted to verify the performance of the proposed method.     

Predictor-based control for an uncertain Euler–Lagrange system with input delay

Controlling a nonlinear system with actuator delay is a challenging problem because of the need to develop some form of prediction of the nonlinear dynamics. Developing a predictor-based controller for an uncertain system is especially challenging. In this paper, tracking controllers are developed for an Euler–Lagrange system with time-delayed actuation, parametric uncertainty, and additive bounded disturbances. The developed controllers represent the first input delayed controllers developed for uncertain nonlinear systems that use a predictor to compensate for the delay. The results are obtained through the development of a novel predictor-like method to address the time delay in the control input. Lyapunov–Krasovskii functionals are used within a Lyapunov-based stability analysis to prove semi-globally uniformly ultimately bounded tracking. Experimental results illustrate the performance and robustness of the developed control methods.     

受限的非仿射非线性系统的自适应控制

针对受限的非仿射非线性系统,结合自抗扰思想提出了非仿射系统的扩张状态观测器(ESO)设计,从而将辅助系统设计技巧拓展到了非仿射系统,然后利用反演和指令滤波器设计了自适应控制器,为受限的不确定非仿射系统提供了新的设计思路.为了补偿受限带来的影响,引入了辅助系统,它的状态被用来补偿跟踪误差.指令滤波器用来处理虚拟控制受限问题,同时获得虚拟控制导数的估计,避免了backstepping中对它的繁琐计算,扩张状态观测器被用来估计系统的未知非仿射非线性项和外部干扰.利用输入状态稳定性(ISS)分析了闭环系统的全局一致有界稳定性.最后仿真结果验证了该设计方案的有效性.     

Adaptive tracking control for non-affine nonlinear systems with non-affine function possibly being discontinuous

A novel adaptive control scheme is presented for a class of non-affine nonlinear systems with non-affine nonlinear function possibly being discontinuous. A discontinuous condition for non-affine nonlinear systems is present to guarantee the controllability of system. The non-affine nonlinear function is modelled appropriately by using piecewise functions. Based on Lyapunov analysis method, the basic idea of invariant set theory is constructively introduced to prove the boundedness of all the signals in the closed-loop system. Finally, simulation example is provided to demonstrate the effectiveness of the proposed approach.     

一类纯反馈非线性系统的简化自适应神经网络动态面控制

针对一类完全非仿射纯反馈非线性系统,提出一种简化的自适应神经网络动态面控制方法.基于隐函数定理和中值定理将未知非仿射输入函数进行分解,使其含有显式的控制输入;利用简化的神经网络逼近未知非线性函数,对于阶SISO纯反馈系统,仅一个参数需要更新;动态面控制可消除反推设计中由于对虚拟控制反复求导而导致的复杂性问题.通过Lyapunov稳定性定理证明了闭环系统的半全局稳定性,数值仿真验证了方法的有效性.     

Time discretization of nonlinear time-delay system using matrix exponential method

A time discretization method for nonlinear time-delay systems is proposed in this paper. The proposed method is based on the matrix exponential method and includes the automatic correction of rounding errors. It is robust to ill-conditioned problems and suitable for any nonlinear system. In the proposed algorithm, each sampling time interval is divided into two subintervals to be considered separately according to the time delay and the sampling period. The performance of the proposed discretization procedure is evaluated by two case studies.     

非仿射纯反馈非线性系统的自抗扰控制

针对一类具有外部扰动的不确定非仿射纯反馈非线性系统,结合反演和自抗扰技术,提出了一种新的控制设计方案,该方案中反演设计的每一步引入了自抗扰设计,同时采用微分器和扩展状态观测器分别估计虚拟控制的导数和系统的未知部分.与现有设计方法不同,它不是直接利用逼近定理来构建理想的控制器.该方案设计过程简单,并且通过输入状态稳定性分析证明了系统状态能渐近收敛到原点的任意小邻域内.仿真结果证实了该方法的有效性.     

Decentralised stabilisation for nonlinear time delay interconnected systems using static output feedback

In this paper, time delay interconnected systems are considered where the nominal isolated subsystems are fully nonlinear. The interconnections and the matched and mismatched disturbances are nonlinear and time-delayed. A decentralised static output feedback control strategy is proposed to stabilise the resulting interconnected system uniformly asymptotically. A novel approach is proposed to deal with the interconnections by introducing artificial interconnections, such that accessible information is fully exploited in the control design to reduce conservatism. Simulation results show the effectiveness of the proposed approach.     

Two‐stage stability control for strict‐feedback systems with input delays and input nonlinear uncertainties

In this paper, a two‐stage control procedure is proposed for stabilization of a class of strict‐feedback systems with unknown constant time delays and nonlinear uncertainties in the input. A nominal controller is first designed to compensate input time delays without considering input nonlinear uncertainties. Extended from backstepping algorithm, input delay compensation is realized by means of predicted states that are computed through integration of cascaded system dynamics, making the nominal closed‐loop system asymptotically stable. Based on the nominal controller presented for the input delay system, a multi‐timescale system is subsequently developed to estimate the unknown input nonlinearity and make the estimate approach the nominal control input as fast as possible. It is proved that the proposed control scheme can make states of the strict‐feedback systems converge to zero and all the signals of the closed‐loop systems are guaranteed to be bounded in the presence of input time delays and nonlinear uncertainties. Simulation verification is carried out to illuminate the effectiveness of the proposed control approach.     

Design of large-scale time-delayed systems with dead-zone input via variable structure control

To deal with time delay in the interconnection and dead-zone nonlinearity in the input, a new decentralized variable structure control (DVSC) law is proposed for a class of uncertain large-scale system (LSS) in this paper. The developed DVSC for the interconnected systems is realized independently through the delay terms. The applied control effort of the DVSC law is always out of the dead-band to eliminate the effects arisen from the dead-zone nonlinearity in the input function. In the sliding mode, it can be seen that the invariance condition also holds. It is worth noting that the traditional large-scale time-delayed system is only a special case in this work. Illustrative examples are given to verify the validity of the developed controller.     

Delay‐range‐dependent control of nonlinear time‐delay systems under input saturation

This paper describes a delay‐range‐dependent local state feedback controller synthesis approach providing estimation of the region of stability for nonlinear time‐delay systems under input saturation. By employing a Lyapunov–Krasovskii functional, properties of nonlinear functions, local sector condition and Jensen's inequality, a sufficient condition is derived for stabilization of nonlinear systems with interval delays varying within a range. Novel solutions to the delay‐range‐dependent and delay‐dependent stabilization problems for linear and nonlinear time‐delay systems, respectively, subject to input saturation are derived as specific scenarios of the proposed control strategy. Also, a delay‐rate‐independent condition for control of nonlinear systems in the presence of input saturation with unknown delay‐derivative bound information is established. And further, a robust state feedback controller synthesis scheme ensuring L₂ gain reduction from disturbance to output is devised to address the problem of the stabilization of input‐constrained nonlinear time‐delay systems with varying interval lags. The proposed design conditions can be solved using linear matrix inequality tools in connection with conventional cone complementary linearization algorithms. Simulation results for an unstable nonlinear time‐delay network and a large‐scale chemical reactor under input saturation and varying interval time‐delays are analyzed to demonstrate the effectiveness of the proposed methodology. Copyright © 2015 John Wiley & Sons, Ltd.     

Neural Network Based Adaptive Tracking Control for a Class of Pure Feedback Nonlinear Systems With Input Saturation

In this paper, an adaptive neural networks (NNs) tracking controller is proposed for a class of single-input/singleoutput (SISO) non-affine pure-feedback non-linear systems with input saturation. In the proposed approach, the original input saturated nonlinear system is augmented by a low pass filter. Then, new system states are introduced to implement states transformation of the augmented model. The resulting new model in affine Brunovsky form permits direct and simpler controller design by avoiding back-stepping technique and its complexity growing as done in existing methods in the literature. In controller design of the proposed approach, a state observer, based on the strictly positive real (SPR) theory, is introduced and designed to estimate the new system states, and only two neural networks are used to approximate the uncertain nonlinearities and compensate for the saturation nonlinearity of actuator. The proposed approach can not only provide a simple and effective way for construction of the controller in adaptive neural networks control of non-affine systems with input saturation, but also guarantee the tracking performance and the boundedness of all the signals in the closed-loop system. The stability of the control system is investigated by using the Lyapunov theory. Simulation examples are presented to show the effectiveness of the proposed controller.      

Global robust tracking control of non-affine nonlinear systems with application to yaw control of UAV helicopter

In this paper, a novel robust nonlinear tracking control scheme is proposed for the yaw channel of an unmanned-aerial-vehicle helicopter that is non-affine in the control input. By a novel dynamic modeling technique, the non-affine nonlinear systems are approximated to facilitate the desired control design. In the controller design procedure, the terminal sliding model control method is introduced to deal with the unknown uncertainties/disturbances. Moreover, filter and disturbance estimator are combined to further reduce the chattering. A systematic procedure is developed and related theoretical and practical issues are discussed. The proposed nonlinear tracking control scheme can guarantee the asymptotic output tracking of the closed-loop control systems in spite of unknown uncertainties/disturbances. Finally, the simulation results on the dynamic model of a real helicopter-on-arm are provided to demonstrate the effectiveness of the proposed new control techniques.     

Prescribed performance distributed consensus control for nonlinear multi-agent systems with unknown dead-zone input

In this paper, the problem of prescribed performance distributed output consensus for higher-order non-affine nonlinear multi-agent systems with unknown dead-zone input is investigated. Fuzzy logical systems are utilised to identify the unknown nonlinearities. By introducing prescribed performance, the transient and steady performance of synchronisation errors are guaranteed. Based on Lyapunov stability theory and the dynamic surface control technique, a new distributed consensus algorithm for non-affine nonlinear multi-agent systems is proposed, which ensures cooperatively uniformly ultimately boundedness of all signals in the closed-loop systems and enables the output of each follower to synchronise with the leader within predefined bounded error. Finally, simulation examples are provided to demonstrate the effectiveness of the proposed control scheme.     

时滞正反馈控制下汽车悬架系统的多目标优化

兼顾时滞正反馈控制下汽车悬架系统的隔振效果和控制力输入,提出设计变量的多目标优化策略。建立时滞正反馈控制下1/4汽车悬架系统的力学模型;分析系统的稳定性,得到反馈增益系数和时滞两参数平面上的稳定性分区图;以反馈增益系数和时滞为设计变量,将车身加速度与控制力幅值的线性加权组合为优化目标,通过粒子群优化算法得到设计变量的最优值。研究结果表明,与无时滞正反馈控制下汽车悬架系统相比,最优时滞正反馈控制下汽车悬架系统的隔振效果显著提升,控制力幅值大幅下降。     

RBFN-based decentralized adaptive control of a class of large-scale non-affine nonlinear systems

For a class of large-scale decentralized nonlinear systems with strong interconnections, a radial basis function neural network (RBFN) adaptive control scheme is proposed. The system is composed of a class of non-affine nonlinear subsystems, which are implicit function and smooth with respect to control input. Based on implicit function theorem, inverse function theorem and the design idea of pseudo-control, a novel control algorithm is proposed. Two neural networks are used to approximate unknown nonlinearities in the subsystem and unknown interconnection function, respectively. The stability is proved rigidly. The result of simulation validates the effectiveness of the proposed scheme.     

基于遗传算法的非线性系统时变时滞的在线估计方法

针对系统输入带有纯时滞的一类非线性系统,选择有限点的的输出误差的平方和构成适应度函数,采用十进制编码技术,提出一种基于遗传算法的非线性系统时变时滞的在线估计方法,该方法具有一定的抗噪声能力。仿真实验结果验证了所提出方法的有效性。     

非仿射非线性多智能体系统迭代学习一致跟踪

为了解决非仿射非线性多智能体系统在给定时间区间上一致性完全跟踪问题,基于迭代学习控制方法设计一种分布式一致性跟踪控制算法.首先,由引入的虚拟领导者与所有跟随者组成多智能体系统的通信拓扑,其中虚拟领导者的作用是提供期望轨迹.然后,在只有部分跟随者能够获得领导者信息的条件下,利用每个跟随者及其邻居的跟踪误差构造每个跟随者的迭代学习一致性跟踪控制器.同时采用中值定理将非仿射非线性多智能体系统转化仿射形式,并基于压缩映射方法证明所提算法的收敛性,给出算法的收敛条件.理论分析表明,在智能体的非线性函数未知情况下,利用所提算法可以使非仿射非线性多智能体系统在给定时间区间上随迭代次数增加逐次实现一致性完全跟踪.最后,通过仿真算例进一步验证所提算法的有效性.