A double integral quadratic cost and tolerance of feedback nonlinearities

A double integral quadratic cost with an associated integral constraint on state trajectories is shown to result in a stable feedback control law for linear time-varying differential systems. The gain matrix for this control is obtained by integrating a Riccati-type matrix differential equation over a finite time interval and is shown to allow for a large class of nonlinearities in the feedback loop without destroying its asymptotically stable property. The class of nonlinearities is larger than that which is generally permitted for the standard steady-state linear optimal regulator, and a phase margin of 90 ° can be approached by the closed-loop system in the case of time-invarlant systems.     

State feedback stabilization for high-order stochastic nonlinear systems with zero dynamics

In this paper, for a class of high-order stochastic nonlinear systems with zero dynamics which are neither necessarily feedback linearizable nor affine in the control input, the problem of state feedback stabilization is investigated for the first time. Under some weaker assumptions, a smooth state feedback controller is designed, which ensures that the closed-loop system has an almost surely unique solution on [0,∞）, the equilibrium at the origin of the closed-loop system is globally asymptotically stable in probability, and all the states can be regulated to the origin almost surely. A simulation example demonstrates the control scheme.     

Stabilizing a linear system with quantized state feedback

The problem of stabilizing an unstable, time-invariant, discrete-time, linear system by means of state feedback when the measurements of the state are quantized is addressed. It is found that there is no control strategy that stabilizes the system in the traditional sense of making all closed-loop trajectories asymptotic to zero. If the system is not excessively unstable, feedback strategies that bring closed-loop trajectories arbitrarily close to zero for a long time can be implemented. It is also found that when the ordinary linear feedback of quantized state measurements is applied, the resulting closed-loop system behaves chaotically. The asymptotic pseudorandom closed-loop system dynamics differ substantially from what would be predicted by a conventional signal-with-noise analysis of the quantization's effects. Probabilistic reformulations of the stability problem in terms of the invariant measure are considered     

严格反馈非线性系统的自适应神经网络输出反馈控制

基于非线性反馈函数,文章设计神经网络状态观测器,解决一类非线性系统的输出反馈控制问题.非线性反馈神经网络观测器在系统存在不确定性函数的情况下实时估计系统状态.利用所获得的状态信号,设计了自适应神经网络动态面控制器,同时保证了闭环系统的稳定性和所有信号的有界性.通过调节设计参数的取值能够达到期望的闭环跟踪性能.数值仿真表明,所设计的状态观测器不需要对原系统做状态变换,能够克服输出反馈滑模控制器带来的抖震问题.     

一类非线性不确定动态系统的鲁棒稳定控制器设计及Benchmark问题求解

本文研究一类非线性不稳定动态系统的基于状态反馈的鲁棒稳定控制设计问题，提出了一种基于状态反馈的非线性控制律，该控制器使得闭环系统鲁棒稳定，对于Ｂｅｎｃｈｍａｒｋ问题验证了所提控制律的正确性和有效性。     

一类非线性不确定动态系统的鲁棒稳定控制器设计及Benchmark问题求解

本文研究一类非线性不确定动态系统的基于状态反馈的鲁棒稳定控制器设计问题，提出了一种基于状态反馈的非线性控制律，该控制器使得闭环系统鲁棒稳定．对于Ｂｅｎｃｈｍａｒｋ问题验证了所提控制律的正确性和有效性．     

Robust adaptive control for interval time-delay systems

1 Introduction The problem of time-delay is commonly encountered in various engineering systems, such as electric, pneumatic and hydraulic networks, long transmission lines, etc., and it is also a great source of systems instability and poor perfor- mance. During the last decades, we have seen an increasing interest for the control of this class of systems and many results have reported in the literature [1～5]. On the other hand, it has been recognized that nonlinear uncertainties are unavoid…     

A simple criterion for global stabilizability of a class of nonlinear singularly perturbed systems

In this paper, a simple criterion is proposed for the global stabilizability of a class of nonlinear singularly perturbed systems. Our approach is based on the global nonlinear controller canonical transformation and the integral manifold method. A globally stabilizing feedback control is also proposed such that the pre-specified design manifold becomes an exact slow integral manifold and the trajectories of the closed-loop system, starting from any initial states, are steered along the integral manifold to the origin.     

Global approximate output tracking for nonlinear systems

Addresses the global output tracking problem for nonlinear systems with singular points. For nonlinear systems which satisfy a suitable observability condition, the authors identify a class of smooth output trajectories which the system can track using continuous open-loop controls. This class includes all output trajectories generated by smooth state feedback. They then study the problem of approximate output tracking using discontinuous time-varying feedback controllers. Given a smooth output trajectory for which exact tracking is possible, the authors construct a discontinuous feedback controller which achieves robust tracking of the desired output trajectory in the face of perturbations. Finally, it is shown that their results can be applied to the control of a chain system, and some numerical results are presented to illustrate the performance of their controller     

Global practical stabilization of planar linear systems in the presence of actuator saturation and input additive disturbance

In this note, we revisit the problem of global practical stabilization for planar linear systems subject to actuator saturation and input additive disturbances. A parameterized linear state feedback law is designed such that, by tuning the value of the parameter, all trajectories of the closed-loop system converge to an arbitrarily small neighborhood of the origin in a finite time and remain in there.     

时滞系统的输出反馈滑模控制的一种奇异系统方法

利用一种奇异系统方法讨论了时滞系统的输出反馈滑模控制问题. 时滞系统的非线性项满足范数有界约束.首先,将滑动模态与线性切换面作为一个奇异时滞系统,基于奇异时滞系统的稳定性理论, 给出滑动模态稳定及切换面存在的线性矩阵不等式(Linear matrix inequality, LMI)充分条件.然后,给出使得系统闭环渐近稳定的静态输出反馈滑模控制器的设计方法,此控制器保证闭环 系统有限时间到达切换面.最后,用数值算例验证本文方法的有效性和正确性.     

一类不确定组合大系统的鲁棒分散控制

研究一类互联项与孤立了系统均含范数有界不确定性的非线性组合大系统的状态反馈鲁棒分散镇定问题,设计出线性状态反馈鲁棒分散控制器,使闭环系统在其平衡点处按指数渐近稳定,且鲁棒控制器具有全息结构,最后给出了一个数值例子,验证了所给结果的有效性。     

Designing Type-1 and Type-2 Fuzzy Logic Controllers via Fuzzy Lyapunov Synthesis for nonsmooth mechanical systems

In this paper, Fuzzy Lyapunov Synthesis is extended to the design of Type-1 and Type-2 Fuzzy Logic Controllers for nonsmooth mechanical systems. The output regulation problem for a servomechanism with nonlinear backlash is proposed as a case of study. The problem at hand is to design a feedback controller so as to obtain the closed-loop system in which all trajectories are bounded and the load of the driver is regulated to a desired position while also attenuating the influence of external disturbances. The servomotor position is the only measurement available for feedback; the proposed extension is far from trivial because of the nonminimum phase properties of the system. Performance issues of the Type-1 and Type-2 Fuzzy Logic Regulators that were designed are illustrated in experimental studies.     

Discontinuous <Emphasis Type="Italic">H</Emphasis><Subscript>∞</Subscript> control of underactuated mechanical systems with friction and backlash

Nonlinear H _∞-control is extended to discontinuous mechanical systems with degree of underactuation one, where nonlinear phenomena such as Coulomb friction and backlash are considered. The problem in question is to design a feedback controller via output measurements so as to obtain the closed-loop system in which all trajectories are locally ultimate bounded, and the underactuated link is regulated to a desired position while also attenuating the influence of external perturbations and nonlinear phenomena. It is considered that positions are the only measurements available for feedback in the system. Performance issues of the discontinuous H _∞-regulation controller are illustrated in an experimental study made for a rectilinear plant with friction modified to have a gap in the point of contact between bodies.     

Decentralized stabilization of large-scale feedforward systems using saturated delayed controls

This paper investigates the problem of decentralized stabilization via saturated delayed feedback. First, a new class of saturated delayed feedback controllers is proposed for a class of single-input feedforward nonlinear systems. Then, this design scheme is generalized for the setting of decentralized feedforward systems using saturated time-delayed feedback. The stability analysis for the closed-loop decentralized systems is rather simple based on the proposed feedback structure.     

Output recurrent wavelet neural network-based adaptive backstepping controller for a class of MIMO nonlinear non-affine uncertain systems

In this paper, an adaptive backstepping control problem is proposed for a class of multiple-input-multiple-output nonlinear non-affine uncertain systems. An output recurrent wavelet neural network (ORWNN) is used to approximate the unknown nonlinear functions to develop the proposed adaptive backstepping controller. The proposed ORWNN combines the advantages of wavelet-based neural network, fuzzy neural network, and output feedback layer to achieve higher approximation accuracy and faster convergence. According to the estimation of ORWNN, the control scheme is designed by backstepping approach such that the system outputs follow the desired trajectories. Based on the Lyapunov approach, our approach guarantees that the system outputs converge to a small neighborhood of the references signals, that is, all signals of the closed-loop system are semi-globally uniformly ultimately bounded. Finally, simulation results including double pendulums system and two inverted pendulums on carts system are shown to demonstrate the performance and effectiveness of our approach.     

具有未知视觉参数的非完整移动机器人的自适应动态反馈跟踪控制

基于视觉反馈和标准链式形式,研究了一类不确定非完整移动机器人的轨迹跟踪控制问题.首先,利用针孔摄像机模型,提出了一种新的基于视觉伺服的移动机器人运动学跟踪误差模型.基于这个模型,在具有不确定视觉参数的情形下,利用back-stepping技术,设计出了一种新的自适应动态反馈跟踪控制器,实现了全局渐近的轨迹跟踪,并通过李亚普诺夫方法严格证明了闭环系统的稳定性和估计参数的有界性.仿真结果证明了所提出的控制器的有效性.     

Robust control of nonlinear feedback passive systems

In this paper we consider a class of nonlinear systems with uncertain parameters which enter the system nonlinearly. We assume that the uncertain nonlinear system is minimum phase and the uncertain parameters are from a bounded compact set. The problem under consideration is the design of a nonlinear static state feedback controller such that the closed-loop system is passive for all admissible uncertainties.     

中立型时滞系统基于状态观测器的控制设计-LMI方法

研究一类中立型时滞系统基于状态观测器的反馈控制问题。目的是利用线性矩阵不等式(LMI)方法设计状态观测器和动态输出反馈控制器,使得相应的闭环系统渐近稳定。最后给出一个数值例子验证了本文所给结果的有效性。