Robust output-feedback stabilization of a class of nonlinear systems with the nonlinearities of varied form

1 .INTRODUCTIONThe problem of global stabilization of nonlinearsystems by output feedback has received much at-tention. Unlike in the case of linear systems ,theseparation principle generally does not hold fornonlinear systems . This is one of the reasons whythe problemis more difficult . As investigated byRef .[1] ,some extra growth conditions onthe un-measurable states of the systemare usually neces-sary for the global stabilization of nonlinear sys-tems via output feedback. For exampl…     

基于T-S模型的非线性系统离散时间滑模控制

基于T-S模糊模型,讨论了一类非线性离散时间系统的控制问题。采用T-S模糊模型来描述非线性系统的动态模型,再将非线性系统的全局T-S模糊模型转化为线性不确定系统的模型。这样复杂的非线性系统的稳定问题就转化为线性不确定系统的鲁棒镇定问题。采用离散时间滑模控制方法实现线性不确定系统的鲁棒镇定。利用用线性矩阵不等式技术设计稳定的滑动模面,以降低非匹配不确定对系统的影响。给出了线性矩阵不等式形式的稳定滑动模面存在的充分条件。此外还给出了滑模控制律的设计方法。所给设计方法可保证系统鲁棒镇定,并且在滑动模面附近的抖振可明显减弱。最后,给出了truck-trailer的仿真算例,证明了所给方法的可行性和有效性。     

State feedback stabilization for a class of nonlinear time-delay systems via dynamic linear controllers

The dynamic linear state feedback control problem is addressed for a class of nonlinear systems subject to time-delay. First, using the dynamic change of coordinates, the problem of global state feedback stabilization is solved for a class of time-delay systems under a type of nonhomogeneous growth conditions. With the aid of an appropriate Lyapunov-Krasovskii functional and the adaptive strategy used in coordinates, the closed-loop system can be globally asymptotically stabilized by the dynamic linear state feedback controller. The growth condition in perturbations are more general than that in the existing results. The correctness of the theoretical results are illustrated with an academic simulation example.     

高阶随机非线性系统状态反馈镇定

针对一类高阶下三角随机非线性系统,提出一种新的镇定方案,采用增加一个幂积分的工具构建了一个全局稳定的光滑状态反馈控制律。通过反馈占有设计方法和Young不等式处理随机系统的非线性项,取消了对随机非线性系统反馈线性化和控制输入呈线性的要求,基于Lyapunov方法,证明了闭环系统依概率全局渐近稳定。最后,仿真实例说明了算法的可行性。     

一种新型的非线性随机大系统自适应镇定方法

研究了一类具有严反馈形式并含有Wiener噪声扰动的非线性随机大系统,其互联项满足线性增长约束。利用微分几何的理论,应用Backstepping算法,基于Lyapunov稳定性理论,选择了适合这类组合非线性系统的状态观测器,设计了自适应输出反馈分散控制律和自适应律,使得闭环,互联的非线性随机大系统实现了概率意义下的全局稳定,仿真结果表明了控制算法的有效性。     

Stabilization of nonlinear time-varying systems: a control lyapunov function approach

This paper presents a control Lyapunov function approach to the global stabilization problem for general nonlinear and time-varying systems. Explicit stabilizing feedback control laws are proposed based on the method of control Lyapunov functions and Sontag's universal formula.     

Stabilization of discrete nonlinear systems based on control Lyapunov functions

The stabilization of discrete nonlinear systems is studied. Based on control Lyapunov functions, a sufficient and necessary condition for a quadratic function to be a control Lyapunov function is given. From this condition, a continuous state feedback law is constructed explicitly. It can globally asymptotically stabilize the equilibrium of the closed-loop system. A simulation example shows the effectiveness of the proposed method.     

Adaptive Output Feedback Regulation for a Class of Uncertain Feedforward Time-Delay Nonlinear Systems

This paper addresses the global output feedback regulation problem for a class of uncertain feedforward time-delay nonlinear systems. Unlike to the previous works, the nonlinear functions in the class of systems under consideration are dominated by an input-output function multiplied by an unknown parameter and linear unmeasured states. By using only one dynamic gain and an appropriate Lyapunov-Krasovskii functionals, it is shown that the closed-loop system is globally asymptotically stable. Finally, a numerical example is provided to illustrate the effectiveness of the proposed design scheme.     

考虑输入饱和的直升机机动飞行LPV控制

针对直升机机动飞行过程中存在的输入饱和问题,提出了一种基于参数依赖Lyapunov的状态反馈控制方法。首先根据直升机非线性模型建立纵向线性变参数(linear parameter varying, LPV)模型,并采用逆仿真数值分析方法对悬停机动科目进行轨迹建模。基于吸引域与不变集理论,利用参数化线性矩阵不等式(parameterized linear matrix inequalities, PLMI),分析闭环系统的稳定条件。利用松弛变量技术将控制器PLMI条件转化为易于求解的线性矩阵不等式(linear matrix inequalities, LMI)条件,求解悬停机动轨迹跟踪控制律。仿真结果表明了所提模型和控制方法的可行性和有效性。     

An overview of the development of low gain feedback and low-and-high gain feedback

Low gain feedback refers to certain families of stabilizing state feedback gains that are parameterized in a scalar and go to zero as the scalar decreases to zero. Low gain feedback was initially proposed to achieve semi-global stabilization of linear systems subject to input saturation. It was then combined with high gain feedback in different ways for solving various control problems. The resulting feedback laws are referred to as low-and-high gain feedback. Since the introduction of low gain feedback in the context of semi-global stabilization of linear systems subject to input saturation, there has been effort to develop alternative methods for low gain design, to characterize key features of low gain feedback, and to explore new applications of the low gain and low-and-high gain feedback. This paper reviews the developments in low gain and low-and-high gain feedback designs.     

Robust Feedback Controller for Exponential Stability of Nonlinear Systems with Mismatched Uncertainties

The robust stabilization of nonlinear systems with mismatched uncertainties is investigated. Based on the stability of the nominal system, a new approach to synthesizing a class of continuous state feedback controllers for uncertain nonlinear dynamical systems is proposed. By such feedback controllers, the exponential stability of uncertain nonlinear dynamical systems can be guaranteed. The approach can give a clear insight to system analysis. An illustrative example is given to demonstrate the utilization of the approach developed. Simulation results show that the method presented is practical and effective.     

AN ALTERNATIVE APPROACH TO GLOBAL ROBUST OUTPUT REGULATION OF OUTPUT FEEDBACK SYSTEMS

The global robust output regulation problem of the output feedback systems has been extensively studied under various assumptions of the complexity and uncertainty. All these approaches boil down to a stabilization problem of a so-called augmented extended system. This paper will describe an alternative approach which converts the original problem into a stabilization problem of a so-called extended augmented system. As the extended augmented system is somewhat simpler than the augmented extended system, this alternative approach is also simpler than the first approach.     

Backstepping tracking control for nonlinear time-delay systems

1. INTRODUCTION The presence of time delay has a significant effect on system performance and destroys the stability of closed-loop system[1]. Therefore, the study on time-delay systems has important practical significance. Recen- tly,considerable progress has been made in this field[1~10]. According to the dependency of the designed contr-oller depends on the time delay, the control approa-ches for time-delay systems can be classified into two categories: delay-dependent[2~3,10] and dela…     

Robust stabilization for multi-input polytopic nonlinear systems

This paper deals with the problem of the stabilization for multi-input polytopic nonlinear systems. Based on the robust control Lyapunov function, a sufficient condition for the existence of time-invariant, continuous, asymptotically stabilizing state feedback controller is derived. It is shown that the obtained sufficient condition is also necessary if there exists a state feedback controller such that the closed-loop system has a robust Lyapunov function for all possible uncertainties. Moreover, a universal formula for constructing stabilizing controller is proposed and the existence of the corresponding Lyapunov function is proven. Particularly, a Lyapunov function is constructed for the polytopic nonlinear system in canonical form. Finally, the feasibility of the proposed control law is verified by a numerical example.     

New Results on H∞ Control for Nonlinear Conformable Fractional Order Systems

This paper deals with H_∞ control problem for nonlinear conformable fractional order systems. The authors first derive new sufficient condition for exponential stability of nonlinear conformable fractional order systems based on Lyapunov-like function method for conformable fractional order systems and linear matrix inequalities(LMIs) approach. Then, by introducing a new concepts of H_∞ control problem for nonlinear conformable fractional order systems, the authors study H_∞ performance analysis and H_∞ state feedback controller design problems for the considered systems. In terms of LMIs, a sufficient condition is proposed to ensure the nonlinear conformable fractional order systems are not only exponentially stable, but also satisfy H_∞ performance γ. An explicit expression for state feedback controllers is also designed to make the closed-loop system is exponentially stable with H_∞performance γ. Finally, numerical examples are given to illustrate the validity and effectiveness of the proposed results.     

混沌系统基于T-S模糊模型的控制方法

将模糊控制技术应用于混沌控制中，可以克服反馈线性化等传统方法对参数完全精确已知的限制；用T-S模糊系统来逼近非线性系统，它的IF-THEN规则后件由线性状态空间子系统构成，进而可以应用模糊系统的控制理论求得模糊控制器，用此非线性控制器来控制非线性系统，以求良好的控制效果；模糊规则后件部分以局部线性方程形式给出的T-S模糊模型可以通过调整相关参数很好地逼近混沌系统，基于该模型采用平行分散补偿技术设计出具有相同规则数目的模糊控制器，控制器所有参数可以通过求解一组线性矩阵不等式一次性得到。仿真结果验证了该方法的有效性。     

Global Stabilization of Nonlinear Systems with Byrnes—Isidori Normal Form

1　IntroductionThe problem of the asymptotic stabilization of minimum phase nonlinear systems viasmooth state feedback has been well studied in[1— 6 ].One major methodology is by useof the nonlinear analog of the nonlinear zero dynamics notion so that,un…     

不确定线性时滞系统时滞相关状态反馈鲁棒镇定

利用Lyapunov-Krasovskii泛函方法,基于积分不等式,讨论了不确定线性时变时滞系统时滞相关状态反馈鲁棒镇定问题。采用线性化处理技术将非线性矩阵不等式（nonlinear matrix inequality, NLMI）转化为线性矩阵不等式（linear matrix inequality, LMI）,获得的鲁棒镇定准则只有一个易于选择的待定参数,避免了参数选择不当带来的保守性,数值例子说明本文方法的有效性。     

Fuzzy Static Output Feedback <Emphasis Type="Italic">H</Emphasis><Subscript>∞</Subscript> Control for Nonlinear Systems Subject to Parameter Uncertainties

This study is concerned with the stabilization issue of nonlinear systems subject to parameter uncertainties. An interval type-2 T-S fuzzy model is used to represent the nonlinear systems subject to parameter uncertainties. An interval type-2 fuzzy static output feedback controller is designed to synthesize the interval type-2 T-S fuzzy systems. The membership-function-dependent stability conditions are derived by utilizing the information of upper and lower membership functions. The proposed stability conditions are presented in the form of linear matrix inequalities (LMIs). LMI-based stability conditions for interval type-2 fuzzy static output feedback H_∞ control synthesis are also developed. Several simulation examples are given to show the superiority of the proposed approach.