Global finite-time stabilisation by output feedback for a class of uncertain nonlinear systems

This article considers the problem of global finite-time stabilisation by output feedback for a class of nonlinear systems comprised of a chain of power integrators perturbed by an uncertain vector field. To solve the problem, we first construct a homogeneous observer and controller in a recursive way for the nominal system without the perturbing nonlinearities. Then, using the homogeneous domination approach, we scale the homogeneous observer and controller with an appropriate choice of gain to render the uncertain nonlinear system globally finite-time stable. Due to the use of a reduced-order observer, the proposed output feedback controller is applicable to those systems with unknown gains associated with the power integrators.     

具有未知输出函数的非线性系统全局输出反馈控制

研究了一类具有未知输出函数的非线性系统全局输出反馈控制问题．由于输出函数未知,传统的观测器将无法实现．为解决这个问题,首先设计了一个与输出函数无关的状态补偿器,使得标称线性系统全局渐近稳定．然后,应用齐次控制方法通过适当选择增益参数,使得不确定非线性系统在有限时间内全局渐近稳定．数值算例表明该算法的有效性．     

Global finite-time stabilization by output feedback for planar systems without observable linearization

This note considers the problem of global finite-time stabilization by output feedback for a class of planar systems without controllable/observable linearization. A sufficient condition for the solvability of the problem is established. By developing a nonsmooth observer and modifying the adding a power integrator technique, we show that an output feedback controller can be explicitly constructed to globally stabilize the systems in finite time. As a direct application of the main result, global output feedback finite-time stabilization is achieved for the double linear integrator systems perturbed by some nonlinear functions which are not necessarily homogeneous.     

Global output feedback stabilisation of nonlinear time-delay systems with unknown output function

This paper studies the problem of global output feedback stabilisation for a class of nonlinear time-delay systems with the unknown output function. By constructing the appropriate Lyapunov–Krasovskii functional and observer, skillfully combining generalised adding a power integrator technique, sign function and homogeneous domination approach, an output feedback controller is designed to guarantee globally uniformly asymptotical stability of nonlinear time-delay systems with the unknown output function.     

Global finite-time stabilization by dynamic output feedback for a class of continuous nonlinear systems

This note studies the problem of global finite-time stabilization by dynamic output feedback for a class of continuous but nonsmooth nonlinear systems. By extending the adding-a-power-integrator technique and a special continuous observer design, a dynamic output feedback controller is explicitly constructed to render the systems globally finite-time stable. The novelty of the note is the development of a recursive design procedure, which takes full advantage of the continuous structure of the systems in constructing the state feedback stabilizer and the continuous observer with rigorously selected gains.     

Global output feedback stabilisation of high-order nonlinear systems with low-order and high-order nonlinearities

In this paper, we study the global output feedback stabilisation of a class of high-order nonlinear systems with more general low-order and high-order nonlinearities. By constructing the novel Lyapunov function and observer, based on the homogeneous domination theory together with adding a power integrator method, an output feedback controller is developed to guarantee the equilibrium of the closed-loop system globally uniformly asymptotically stable.     

Finite-time stabilization for a class of more general p-normal nonlinear systems with input and output nonlinearities

This study investigates the global finite-time state feedback stabilization for a class of more general p-normal nonlinear systems subjects to input time-delay and uncertain output function under rational powers. A novel control input compensation signal comprising a finite integral of previous control values is presented, and an equivalent system with control input dependent-free time delay is obtained by introducing a variable transformation technique that includes the compensation signal. A suitable controller is designed in line with the homogeneous domination method to ensure the globally finite-time stability of the closed-loop system. Finally, the effectiveness of the proposed control scheme is verified through a numerical simulation and an induction heater circuit system.     

Global finite-time stabilization for a class of switched nonlinear systems via output feedback

This paper addresses the problem of global finite-time stabilization for a class of uncertain switched nonlinear systems via output feedback under arbitrary switchings. Based on the adding a power integrator approach, we design a homogeneous observer and controller for the nominal switched system without the perturbing nonlinearities. Then, a scaling gain is introduced into the proposed output feedback stabilizer to implement global finite-time stability of the closed-loop system. In addition, the proposed approach can be also extended to a class of switched nonlinear systems with upper-triangular growth condition. Two examples are given to illustrate the effectiveness of the proposed method.     

Finite-time output feedback stabilisation for a class of feedforward nonlinear systems with input saturation

This paper considers the problem of global finite-time stabilisation by output feedback for a class of feedforward (upper triangular) nonlinear systems with input saturation. Based on the finite-time stability theorem, and by skillfully using the homogeneous domination approach and the nested saturation technique, a saturated output feedback controller is successfully constructed, which renders the origin of the closed-loop system globally finite-time stable. In simulation studies, a numerical example is illustrated to show the effectiveness of the control scheme. Moreover, the design strategy is successfully applied to solve the saturated finite-time control problem for vertical wheel on rotating table.     

Recursive design of finite-time convergent observers for a class of time-varying nonlinear systems

This paper considers the problem of designing globally finite-time convergent observers for a class of nonlinear systems with time-varying and output-dependent coefficients, which make the existing design approaches inapplicable. To solve this problem, a bottom-up design approach is first employed to recursively construct a finite-time convergent observer with time-varying coefficients for the nominal system. Then, using the homogeneous domination approach, we scale the finite-time convergent observer with an appropriate choice of gain for the original nonlinear system satisfying a Hölder condition. In addition, we show that the Hölder condition imposed on the nonlinearities can be removed for nonlinear systems with bounded trajectories.     

基于输出反馈和滑模控制的一类二阶非线性系统有限时间镇定方法

本文研究了一类具有不确定非线性动力学和未知外部扰动的二阶非线性系统的全局有限时间输出镇定问 题. 首先, 提出了一种全局状态反馈有限时间控制器, 实现了二阶非线性系统的有限时间镇定. 为了解决只有系统输 出可用这种更有挑战性的情况, 采用了一种新颖的设计思想, 即非分离原理. 构造了一个有限时间收敛的状态观测 器来估计未知状态. 在此观测器的基础上, 提出了一种基于输出的有限时间复合控制器. 基于李雅普诺夫方法, 证明 了整个闭环系统的全局有限时间稳定性. 仿真结果表明了理论的有效性.     

Finite-time output feedback stabilization of high-order uncertain nonlinear systems

This paper studies the problem of finite-time output feedback stabilization for a class of high-order nonlinear systems with the unknown output function and control coefficients. Under the weaker assumption that output function is only continuous, by using homogeneous domination method together with adding a power integrator method, introducing a new analysis method, the maximal open sector Ω of output function is given. As long as output function belongs to any closed sector included in Ω, an output feedback controller can be developed to guarantee global finite-time stability of the closed-loop system.     

Global output feedback stabilization of upper-triangular nonlinear time-delay systems

In this paper,the problem of global output feedback stabilization for a class of upper-triangular nonlinear systems with time-varying time-delay in the state is considered.The uncertain nonlinearities are assumed to be higher-order in the unmeasurable states.Based on the extended homogeneous domination approach,using a low gain observer in combination with controller,the delay-independent output feedback controller makes closed-loop system globally asymptotically stable under a homogeneous growth condition.     

Finite-time output feedback control for a class of stochastic low-order nonlinear systems

This paper discusses the problem of finite-time stabilisation for a class of stochastic low-order nonlinear systems via output feedback. By generalising the adding a power integrator technique, constructing an implementable reduced-order observer and using the stochastic finite-time stability criterion, a finite-time output feedback controller is presented to guarantee that the closed-loop system is finite-time stable in probability. A simulation example is provided to verify the effectiveness of the proposed design method.     

Controller design for nonlinear affine systems by control Lyapunov functions

This paper addresses the stabilization problems for nonlinear affine systems. First of all, the explicit feedback controller is developed for a nonlinear multiple-input affine system by assuming that there exists a control Lyapunov function. Next, based upon the homogeneous property, sufficient conditions for the continuity of the derived controller are developed. And then the developed control design methodology is applied to stabilize a class of nonlinear affine cascaded systems. It is shown that under some homogeneous assumptions on control Lyapunov functions and the interconnection term, the cascaded system can be globally stabilized. Finally, some interesting results of finite-time stabilization for nonlinear affine systems are also obtained.     

A globally convergent angular velocity observer for rigid bodymotion

The problem of obtaining the angular velocity of a rigid body from orientation and torque measurements only, without noisy numerical differentiation, is considered. A novel angular velocity/angular momentum observer for rigid body motion is presented. Using Euler quaternions and a mechanical energy function approach, it is shown that the observer estimates converge globally and that the convergence is eventually exponential. It is hoped that a mechanical energy function approach to rigid body control can be combined with the observer presented to lead to a globally stable, nonlinear, observer-based, rigid-body controller in which the observer and controller errors can be separated, in much the same way as one can separate controller and observer poles in the output feedback controllers of linear system theory     

Output feedback control for a class of stochastic high‐order nonlinear systems with time‐varying delays

This paper discusses the problem of output feedback stabilization for a more general class of stochastic high‐order nonlinear systems with time‐varying delays. On the basis of a subtle homogeneous observer and controller construction, and the homogeneous domination approach, the closed‐loop system is globally asymptotically stable in probability, by choosing an appropriate Lyapunov–Krasovskii functional. An example is given to illustrate the effectiveness of the proposed design procedure. Copyright © 2013 John Wiley & Sons, Ltd.     

输入饱和下的非线性积分系统的全局有限时间镇定

针对一类非线性积分系统, 利用有限时间控制技术, 提出了一种输入饱和情况下的全局有限时间控制方案. 首先, 基于有限时间 Lyapunov 稳定性理论, 设计镇定系统的全局有限时间递归控制器. 然后,将该递归控制器与饱和函数结合得到饱和控制器. 数学上严格证明了在该饱和控制器的作用下, 闭环系统满足全局有限时间稳定性. 仿真结果验证了该方法的有效性.     

输出约束的有限时间自适应区间二型模糊输出反馈PMSM伺服控制

针对永磁同步电机驱动的伺服系统在不确定性摩擦和未知负载的影响下难以达到高精度的控制效果,提出一种基于区间二型模糊系统的带有输出约束的有限时间自适应输出反馈控制方案.首先,构建一个基于非线性扰动观测器的区间二型模糊状态观测器,分别完成对于未知扰动和速度的估计,区间二型模糊系统完成对于非线性摩擦的逼近;然后,在此基础上,结合滤波误差补偿机制和有限时间技术,引入障碍Lyapunov函数和反步控制技术设计输出约束的自适应区间二型模糊输出反馈控制器;最后,根据Lyapunov稳定性理论提出严格的稳定性分析,保证闭环系统的所有信号均是有限时间内有界的,并通过数值仿真和实验验证了所提出方法的有效性.     

Robust nonlinear control of a three-tank system using finite-time disturbance observers

A finite-time disturbance observer-based robust control method is proposed for output tracking of the Inteco threetank system in the presence of mismatched uncertainties. The controller is designed in a backstepping manner. At each step of the virtual controller design, a robust feedback controller with some effective nonlinear damping terms is designed so that the system states remain in the feasible domain. The nonlinear uncertainty is compensated by a finite-time disturbance observer. And to avoid the shortcoming of “explosion of terms”, the dynamic surface control technique which employs a low-pass filter is adopted at each step of the virtual controller design. Attention is paid to reducing the measurement noise effects and to initialization technique of the system states and reference output trajectory. Theoretical analysis is performed to clarify the control performance. And the theoretical results are verified based on the experimental studies on the real Inteco three-tank system.