Robust stabilization of stochastic differential inclusion systems with time delay

This paper is concerned with robust stabilization of stochastic differential inclusion systems with time delay.A nonlinear feedback law is established by using convex hull quadratic Lyapunov function s...     

一类不确定切换系统的鲁棒状态反馈镇定

研究了一类扰动项不满足匹配条件的不确定切换系统的鲁棒镇定问题.在每个子系统均不能镇定的情况下,利用完备性条件和多李雅普诺夫函数方法,分别得到了不确定切换系统可镇定的充分条件.状态矩阵和控制输入矩阵同时带有时变、未知且有界的不确定性,基于凸组合技术和LMI方法,设计出鲁棒状态反馈控制器及相应的切换策略,使得闭环系统在其平衡点处是渐近稳定的.最后仿真结果表明所设计的控制器及切换策略的正确有效性.     

Global stabilization of MIMO minimum-phase nonlinear systems without strict triangular conditions

An extension of backstepping to a class of multivariable minimum-phase nonlinear systems is proposed. The systems are assumed to be in a special interlaced form which includes a lower triangular form as a special case. The extension involves the recursive application of backstepping and augmentation.     

Robust stabilization of infinite dimensional systems by finite dimensional controllers

The problem of robustly stabilizing an infinite dimensional system with transfer function G, subject to an additive perturbation Δ is considered. It is assumed that: G ε ₀(σ) of systems introduced by Callier and Desoer [3]; the perturbation satisfies |W₁ΔW₂| < ε, where W₁ and W₂ are stable and minimum phase; and G and G + Δ have the same number of poles in ⁺. Now write W₁GW₂=G₁ + G₁, where G₁ is rational and totally unstable and G₂ is stable. Generalizing the finite dimensional results of Glover [12] this family of perturbed systems is shown to be stabilizable if and only if ε σ_min (G^*₁)( = the smallest Hankel singular value of G^*₁). A finite dimensional stabilizing controller is then given by where 2 is a rational approximation of G₂ such that

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) and K₁ robustly stabilizes G₁ to margin ε. The feedback system (G, K) will then be stable if |W₁ΔW₂| _∞< ε − Δ.     

Robust stabilization of linear differential inclusion system with time delay

This paper is concerned with robust stabilization of linear differential inclusion systems with time delay. A nonlinear feedback law is established by using convex hull quadratic Lyapunov functions to make the state exponentially stable. An example is given to illustrate the effectiveness of the proposed method.     

Constructive stabilization for quadratic input nonlinear systems

In this paper stabilization of nonlinear systems with quadratic multi-input is considered. With the help of control Lyapunov function (CLF), a constructive parameterization of controls that globally asymptotically stabilize the system is proposed. Two different cases are considered. Firstly, under certain regularity assumptions, the feasible control set is parameterized, and continuous feedback stabilizing controls are designed. Then for the general case, piecewise continuous stabilizing controls are proposed. The design procedure can also be used to verify whether a candidate CLF is indeed a CLF. Several illustrative examples are presented as well.     

Stability and stabilization of nonlinear discrete‐time stochastic systems

This paper mainly studies the locally/globally asymptotic stability and stabilization in probability for nonlinear discrete‐time stochastic systems. Firstly, for more general stochastic difference systems, two very useful results on locally and globally asymptotic stability in probability are obtained, which can be viewed as the discrete versions of continuous‐time Itô systems. Then, for a class of quasi‐linear discrete‐time stochastic control systems, both state‐ and output‐feedback asymptotic stabilization are studied, for which, sufficient conditions are presented in terms of linear matrix inequalities. Two simulation examples are given to illustrate the effectiveness of our main results.     

Robust stabilization of singularly perturbed systems

We discuss the problem of designing stabilizing controllers for singularly perturbed systems on the basis of simplified models. In [1], it was shown that a constant gain output feedback controller designed on the basis of the simplified model need not stabilize the ‘true’ system containing both fast and slow modes. This phenomenon was then expanded to include the case where the simplified system is strictly proper in [2]. The objectives of this note are threefold: (i) to show that, given any proper system and any stabilizing controller for it that is proper but not strictly proper, there exists a singular perturbation of the system that is destabilized by that controller, (ii) to show that any strictly proper controller for a singularly perturbed system designed on the basis of a reduced order model will stabilize the true system for sufficiently small values of the fast dynamics parameter, and (iii) to provide a characterization, in the same spirit as [3,4], of the set of all strictly proper controllers that stabilize a given proper plant. By combining these results, it is possible to generate the class of all robustly stabilizing controllers for a given singularly perturbed system.     

奇异摄动系统鲁棒镇定问题

讨论了确定与不确定奇异摄动系统的稳定性问题。首先给出了确定系统稳定及不确定系统鲁棒稳定的条件,同时给出摄动参数的稳定上界,其次,对不稳定系统,给出了状态反馈可镇定的条件及控制器的求解。这些条件均可由MATLAB中的求解器求解。最后,数值实例验证了该方法的可行性和有效性。     

不确定曲面上非完整移动机器人的鲁棒镇定

针对在不确定曲面上运动的非完整轮式移动机器人设计了鲁棒实际镇定控制律,使得机器人系统具有对曲面而引入的重力干扰的鲁棒性。设计过程中使用参数有界但未知的二次曲面来近似不确定曲面。整个设计过程构建于李群,综合了横截函数方法、积分器backstepping和Lyapunov重设计技术.在讨论了轮式移动机器人的运动学子系统对李群SE(2)的标准群运算的左不变性之后,构造了一个有界横截函数,由它确定了相应的嵌入目标子流形.然后,对移动机器人的运动学误差系统设计了光滑的“虚拟”镇定律,使得误差变量指数镇定,从而也将机器人运动学子系统的状态镇定到先前定义的目标子流形.最后,使用积分器backstepping将该光滑“虚拟”控制律拓展到标称动力学系统,并通过重设计,得到鲁棒实际镇定控制律.仿真结果验证了算法的有效性.     

Robust stabilization of nonlinear cascaded systems

This paper considers the problem of robust stabilization for an uncertain nonlinear system which is a cascaded interconnection of two subsystems. Both of the subsystems are allowed to be nonlinear, multi-variable, and containing uncertain parameters. We present a new approach to designing stabilizing controllers which assure both robust global asymptotic stability and local quadratic stability. Compared with existing results, the assumptions required for such robust stabilizing controllers to exist are significantly simplified.     

Continuous simultaneous stabilization of single‐input nonlinear stochastic systems

This paper investigates the simultaneous stabilization of a collection of continuous single‐input non‐linear stochastic systems, with coefficients that are not necessarily locally Lipschitz. A sufficient condition for the existence of a continuous simultaneously stabilizing feedback control is proposed — it is based on the generalized stochastic Lyapunov theorem and on the technique of stochastic control Lyapunov functions. This condition is also necessary, provided that the system's coefficients satisfy some regularity conditions. Moreover, the proposed feedback can be chosen to be bounded under the assumption that appropriate control Lyapunov functions are known. All the proposed simultaneously stabilizing state feedback controllers are explicitly constructed. Finally, two simulation examples are provided to demonstrate the effectiveness of the proposed approach.     

Simultaneous stabilization for a collection of nonlinear control systems in canonical form

A controller design method is provided to simultaneously stabilize a collection of nonlinear control systems in canonical form. It is shown that, under a mild assumption, any collection of nonlinear systems in canonical form can be simultaneously stabilized by one continuous state feedback controller. A constructive universal formula is presented explicitly. An illustrative example is given to demonstrate the validity of the method. Copyright © 2009 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society     

On the simultaneous stabilization of stochastic nonlinear systems

In this paper, the problem of simultaneous stabilization in probability by state feedback is investigated for a class of stochastic nonlinear systems whose drift and diffusion terms are dependent on the control and for which classical methods are not applicable. Under the assumption that a collection of stochastic control Lyapunov functions (SCLFs) is known and based on the generalized stochastic Lyapunov theorem, we derive sufficient conditions for the simultaneous stabilization in probability by a continuous state feedback controller that we explicitly compute. We also derive a necessary condition when the system coefficients satisfy some regularity conditions. This work generalizes previous results on the simultaneous stabilization of stochastic nonlinear systems. The obtained results are illustrated by a numerical example.     

Quadratic stabilization of switched nonlinear systems

In this paper, the problem of quadratic stabilization of multi-input multi-output switched nonlinear systems under an arbitrary switching law is investigated. When switched nonlinear systems have uniform normal form and the zero dynamics of uniform normal form is asymptotically stable under an arbitrary switching law, state feedbacks are designed and a common quadratic Lyapunov function of all the closed-loop subsystems is constructed to realize quadratic stabilizability of the class of switched nonlinear systems under an arbitrary switching law. The results of this paper are also applied to switched linear systems. Supported partially by the National Natural Science Foundation of China (Grant No. 50525721)     

一类不确定非线性系统的全局鲁棒有限时间镇定

对一类不确定非线性系统提出了一种连续的全局鲁棒有限时间控制律．首先,针对标称系统设计出了一种状态反馈控制律,应用Lyapunov直接稳定性理论和Lasalle不变性原理证明了闭环标称系统的全局渐近稳定性,同时具有负的齐次度;其次,引入辅助变量和采用有限时间收敛的二阶滑模Super—twisting算法,设计出了对不确定性和干扰进行抑制的补偿控制项,并根据有限时间Lyapunov函数给出了补偿控制项参数的取值范围;最后,综合得到一种连续的使实际闭环系统有限时间收敛到平衡点的鲁棒镇定控制律．仿真结果表明了所提控制律的有效性．     

临界状态下三维仿射控制系统的局部光滑镇定

讨论三维仿射非线性控制系统,在具有零和一对共轭纯虚数特征值的临界状态下的局部光滑镇定性.首先,应用非奇异线性状态变换和时间尺度变换,将系统转化成标准形式.之后,运用形式级数法的思想和扩展正则判别函数法,构造多组线性方程组,给出确定光滑控制律和闭环系统李雅普诺夫函数的一种方法,从而得到该标准化系统局部光滑镇定的充分条件.示例说明该方法是有效的.     

Robust global stabilization of linear systems with input saturation via gain scheduling

The problem of robust global stabilization of linear systems subject to input saturation and input‐additive uncertainties is revisited in this paper. By taking advantages of the recently developed parametric Lyapunov equation‐based low gain feedback design method and an existing dynamic gain scheduling technique, a new gain scheduling controller is proposed to solve the problem. In comparison with the existing ?₂‐type gain scheduling controller, which requires the online solution of a state‐dependent nonlinear optimization problem and a state‐dependent ?₂ algebraic Riccati equation (ARE), all the parameters in the proposed controller are determined a priori. In the absence of the input‐additive uncertainties, the proposed controller also partially recovers Teel's ?_∞‐type scheduling approach by solving the problem of global stabilization of linear systems with actuator saturation. The ?_∞‐type scheduling approach achieves robustness not only with non‐input‐additive uncertainties but also requires the closed‐form solution to an ?_∞ ARE. Thus, the proposed scheduling method also addresses the implementation issues of the ?_∞‐type scheduling approach in the absence of non‐input‐additive uncertainties. Copyright © 2009 John Wiley & Sons, Ltd.     

一类多输入级联非线性切换系统的全局镇定

研究一类带有部分线性系统的多输入级联非线性切换系统的全局镇定问题. 首先, 给出保证线性部分有一致规范型的充分条件. 其次, 利用一致规范型及其零动态的共同二次Lyapunov函数设计状态反馈使得线性部分在任意切换律下镇定. 最后, 通过构造共同Lyapunov函数能实现闭环系统在任意切换律下的全局渐近稳定性.