Reduced-order observer-based output feedback control of nonlinear time-delay systems with prescribed performance

This paper studies the problem of output feedback control for a class of nonlinear time-delay systems with prescribed performance. The system is in the form of triangular structure with unmodelled dynamics. First, we introduce a reduced-order observer to provide the estimate of the unmeasured states. Then, by setting a new condition with the performance function, we design the state transformation with prescribed performance control. By employing backstepping method, we construct the output feedback controller. It is proved that the resulting closed-loop system is asymptotically stable and both transient and steady-state performance of the output are preserved with the changing supply function idea. Finally, a simulation example is conducted to show the effectiveness of the main results.     

不确定LTI-SISO系统的降阶时滞观测器控制

提出了降阶时滞观测器, 利用时滞来观测系统的不确定性和受到的外部干扰, 实现了不确定系统的鲁棒控制. 降阶时滞观测器控制系统中参考模型的阶数由系统的相对阶数决定, 而与系统阶数无关, 简化了控制器的设计, 有利于根据性能指标的要求获得合适的参考模型. 对于相对阶低于系统阶的一般对象, 通过引入低通滤波器也能实现降阶时滞滤波器控制. 大量的仿真结果表明, 降阶时滞观测器能够很好地抑制系统的不确定性和受到的外部干扰, 是一种性能优良的鲁棒控制方法.     

降阶的鲁棒分散自适应反推控制

针对一类含有未建模动态的关联系统,考虑了降阶的鲁棒分散自适应反推控制问题.首先通过一系列坐标变换,将原系统重新参数化,然后引入降阶观测器,得到一个误差系统.基于该系统,给出了一种降阶自适应反推控制器的设计方案.证明了自适应控制系统的所有信号全局一致有界,调节误差渐近收敛到零.控制器阶次的降低使得本文的设计方案更具应用价值.     

Reduced-order observer-based decentralised control of non-linear interconnected systems

The output feedback-based asymptotic stabilisation problem for a class of non-linear interconnected systems is considered, where the non-linear interconnections between subsystems satisfy quadratic constraints. A novel decentralised dynamic output feedback control strategy involving local projection operator-based reduced-order observers is proposed. This decentralised controller is characterised by the separation property. Two easily verifiable conditions that guarantee the asymptotic stability of the closed-loop system driven by the proposed decentralised controller are given. The effectiveness of the developed decentralised control strategy is illustrated with a numerical example and simulations.     

非线性时滞系统基于降阶观测器的反步镇定控制

针对一类状态未知的非线性严格反馈时滞系统, 本文提出了一种基于静态增益函数的输出反馈控制方案. 首先构造了降阶观测器以估计非线性系统的未知状态. 然后在Backstepping设计的每一步定义了具有控制增益函数 的新型Lyapunov-Krasovskii泛函以补偿未知时变时滞, 定义新的选择不唯一的连续控制增益函数以补偿非匹配项 以及Lyapunov-Krasovskii泛函补偿时滞时产生的非负项. 提出了一种无记忆输出反馈控制方案. 理论分析表明: 该 控制方案消除了未知时滞的影响, 保证了闭环系统所有信号的有界性, 并使系统实现渐近稳定. 最后仿真结果验证 了此控制方案的有效性.     

Reduced-order observer-based finite-time control for one-sided Lipschitz nonlinear switched singular systems

The reduced-order observer-based finite-time control problem for one-sided Lipschitz nonlinear switched singular systems is addressed in this paper. First, the design method of the reduced-order observer is given via state transformation. Then, based on the average dwell time (ADT) approach, some new sufficient conditions for regularity, impulse-freeness, have a unique solution and finite-time boundedness (FTB) of the dynamic augmented systems are obtained by exploring the reduced-order observer-based controller. Further, the lower finite-time bound can be obtained by using singular value decomposition method. And the state feedback gain and the observer gain are computed by solving linear matrix inequalities (LMIs). Finally, the validity of the obtained method is illustrated by means of a numerical example and a DC motor system.     

Extended state observer-based motion synchronisation control for hybrid actuation system of large civil aircraft

Hybrid actuation system with dissimilar redundant actuators, which is composed of a hydraulic actuator (HA) and an electro-hydrostatic actuator (EHA), has been applied on modern civil aircraft to improve the reliability. However, the force fighting problem arises due to different dynamic performances between HA and EHA. This paper proposes an extended state observer (ESO)-based motion synchronisation control method. To cope with the problem of unavailability of the state signals, the well-designed ESO is utilised to observe the HA and EHA state variables which are unmeasured. In particular, the extended state of ESO can estimate the lumped effect of the unknown external disturbances acting on the control surface, the nonlinear dynamics, uncertainties, and the coupling term between HA and EHA. Based on the observed states of ESO, motion synchronisation controllers are presented to make HA and EHA to simultaneously track the desired motion trajectories, which are generated by a trajectory generator. Additionally, the unknown disturbances and the coupling terms can be compensated by using the extended state of the proposed ESO. Finally, comparative simulation results indicate that the proposed ESO-based motion synchronisation controller can achieve great force fighting reduction between HA and EHA.     

Passivity and robust synchronisation of switched interval coupled neural networks with time delay

This paper is concerned with passivity and robust synchronisation of switched coupled neural networks with uncertain parameters. First, the mathematical model of switched coupled neural networks with interval uncertain parameters is established, which consists of L modes and switches from one mode to another according to the switching rule. Second, by employing passivity theory and linear matrix inequality techniques, delay-independent and delay-dependent conditions are derived to guarantee the passivity of switched interval coupled neural networks. Moreover, based on the proposed passivity results, global synchronisation criteria can be obtained for switched coupled neural networks with or without uncertain parameters. Finally, an illustrative example is provided to demonstrate the effectiveness of the obtained results.     

Impulsive observer-based consensus control for multi-agent systems with time delay

The paper deals with the distributed consensus problem of a class of general linear multi-agent systems with time delay. Assuming that the state of the multi-agent system cannot be measured and the output of the multi-agent system is measured discontinuously, a novel impulsive observer is constructed. Based on the impulsive observer, a distributed consensus protocol is proposed for the multi-agent system with a directed communication topology. In view of the hybrid characteristic of the multi-agent system with the impulsive observer, a novel type of piecewise Lyapunov functional which can overcome the jump phenomena at impulsive times is introduced. Based on this, some sufficient conditions in terms of linear matrix inequalities are presented such that the consensus of the multi-agent system can be achieved with an exponential convergence rate. A numerical example under two cases is given to show the effectiveness of the theoretical results.     

Reduced-order observer-based control design for nonlinear stochastic systems

In this paper, we investigate the stabilization control design problem of nonlinear stochastic SISO systems in strict-feedback form. By introducing a novel reduced-order observer, an output-feedback-based control is constructively designed, which renders the closed-loop system asymptotically stable in the large when the nonlinearities and stochastic disturbance equal zero at the equilibrium point of the open-loop system, and bounded in probability, otherwise. Besides, the obtained controller preserves the equilibrium point of the open-loop nonlinear system.     

Extended-state-observer-based adaptive control for synchronisation of multi-agent systems with unknown nonlinearities

This paper studies the problem of synchronisation to a desired trajectory for non-linear multi-agent systems. By introducing extended state observer approach, decentralised adaptive controllers are designed for distributed systems which have non-identical unknown non-linear dynamics. The non-identical unknown non-linear dynamics allows for a tracked command dynamics which is also non-linear and unknown. State variables of agents can be obtained only in the case where leader agent and the network communication topology for multi-agent systems is strongly connected digraph network structures. A Lyapunov-function-based approach is given to show that the tracking error is ultimately bounded. Some simulation results are given to demonstrate the effectiveness of the developed techniques in this paper.     

Looper and tension control in hot rolling mills: A survey

Looper and tension control is important in hot strip mills because they affect the strip quality as well as strip threading. Moreover, the most difficult challenge in controller design and control performance arises from the interaction between looper angle and strip tension. Disturbances from several sources cause a deterioration in control performance, and thus a major role of the control algorithm is effective disturbance rejection. Many authors have proposed and applied a variety of control schemes to this control problem, but nevertheless, the increasingly strict market demand for strip quality requires further improvements in this control area. Hence, this paper critically surveys the strengths and weaknesses of several existing academic and industrial approaches and explores the potential for development in this area.     

Cluster synchronisation of coupled delay reaction-diffusion systems

This paper considers the cluster synchronisation of coupled delay reaction-diffusion systems (DRDSs). First, in light of the technique of matrix representation, we turn the cluster synchronisation of coupled DRDSs into the asymptotical stability of a transformed system. Based on this transformation and by virtue of the Lyapunov-Krasovskii functional method, we provide the sufficient conditions that ensure the cluster synchronisation for DRDSs with constant delay. The effects of spatial domain on the cluster synchronisation is shown by these sufficient conditions. Then, we deal with time-varying delay systems with reaction-diffusion term. The criterion of cluster synchronisation is presented and a brief proof is given. Finally, numerical examples are carried out to show the effectiveness of our results.     

Reduced-order observer-based output feedback regulation for a class of nonlinear systems with iISS inverse dynamics

Global asymptotic regulation via output feedback based on a reduced-order observer is considered for a class of nonlinear systems with integral input-to-state stable (iISS) inverse dynamics. The contributions are that: (1) we further consider the conditions on changing supply rates in iISS systems, and discuss the necessity of some conditions by constructing a counter-example; (2) For a more general class of nonlinear systems with iISS inverse dynamics, a reduced-order observer is introduced, and by the combined approach of backstepping and changing iISS supply rates, an output feedback controller is given to drive the output of system to the origin asymptotically and maintain other closed-loop signals bounded.     

基于观测器的受扰非线性系统近似最优跟踪控制

研究一类受扰非线性系统的最优输出跟踪控制问题.给出了有限时域最优输出跟踪控制律的近似设计算法.首先将求解受扰非线性系统最优跟踪控制问题转换为求解状态向量与伴随向量耦合的非线性两点边值问题,然后利用逐次逼近方法构造序列将其转化为求解两个解耦的线性微分方程序列问题.通过迭代求解伴随向量的序列,可得到由解析的线性前馈-反馈控制部分和伴随向量的极限形式的非线性补偿部分组成的最优输出跟踪控制律.利用参考输入降维观测器和扰动降维观测器,解决了前馈控制的物理可实现问题.最后仿真结果表明了该方法的有效性.     

冷带轧机厚控系统自适应鲁棒输出反馈动态控制器设计

冷带轧机厚控系统可被认为是一个受外界干扰的线性不确定时滞系统.本文首先设计了标称系统下的鲁棒输出反馈动态控制器,以改善闭环系统的动静态性能;其次,在系统不需要满足不确定性匹配条件的情况下,将参数和外部扰动不确定性综合考虑.应用Lyapunov稳定性理论设计了系统不确定性上界参数的自适应估计器和系统的自适应控制器,保证了闭环系统的渐近稳定性,减小了设计的保守性;两者结合实现了板带出口厚度的有效控制.最后通过一个仿真实例说明本文所提出的自适应鲁棒控制器的有效性.     

Uncertainty observer-based robust tracking control for high-order nonlinear systems using forwarding technique

Based on uncertainty observers, we develop a robust tracking control approach for high-order nonlinear systems subject to uncertainties satisfying mismatched condition. In this study, by combining with forwarding technique, uncertainty observers are designed to estimate uncertainties including parameter perturbations and external disturbances in a bottom-up way; at the same time, the convergence rate of estimate error of uncertainty observers is analysed in detail. The insensitivity to uncertainties for each manifold, no need of a prior knowledge on the bound of the uncertainty and the feasibility of practical implementation are three advantages of the proposed scheme. Moreover, approximate error of uncertainty observer can be made sufficiently small by tuning the parameters. The design procedures are elaborated and the boundedness of all trajectories of the closed-loop systems is guaranteed. Two examples are illustrated, highlighting the superiority of the proposed methodology via comparison with other control strategies.     

Observer-based multivariable flatness control of a cold rolling mill

The synthesis methodology developed by Kimura (1985) based on the design theory of output regulators essentially due to Wonham (1974) has been applied successfully to the flatness control system for a 6-high cold rolling mill. The system has the following remarkable features.

1. (1) The structure of the controller is simple. This makes it easy to tune the control system.

2. (2) The controller copes well with the detection time delay, and thus high performance is obtained even at a low rolling speed.

3. (3) The flatness error caused by the rolling force variation in mill acceleration and deceleration time would be kept to a minimum by the function to adjust roll bending force using the signal of rolling force.

不确定LTI- SISO系统的低通滤波降阶时滞观测器控制

提出一种低通滤波降价时滞观测器,避免了常规时滞观测器控制中由于时滞状态微分近似引起的控制信号颤振。参考模型的选取只与系统的相对阶次有关,而与系统阶次无关,从而简化了控制器的设计,降低了对系统可测性的要求。仿真结果表明,该时滞观测器控制系统可以很好地抑制系统的不确定性以及受到的外部干扰,是一种性能优良的鲁棒控制方法。     

Stochastic mean square exponential synchronisation of time-varying complex dynamical networks via pinning control

This paper investigates the problem of stochastic mean square exponential synchronisation of complex dynamical networks with time-varying delay via pinning control. By applying the Lyapunov method and stochastic analysis, criteria on mean square exponential synchronisation are established under linear feedback pinning control and adaptive feedback pinning control, which depend on the time-varying delay and stochastic perturbation. These results complement and improve the previously known results. Two numerical examples are given to illustrate the effectiveness and correctness of the derived theoretical results.