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.     

一类扩展结构大系统的分散有限时间鲁棒关联镇定

研究一类扩展结构大系统分散有限时间鲁棒关联镇定问题. 扩展结构大系统是在原结构系统上增加新子系统而构成的, 在原系统分散控制律确定不变的情况下, 设计新加入子系统的鲁棒分散控制律, 使扩展后的系统仍能保持有限时间关联稳定. 利用LMI 方法推导此类系统基于状态反馈和输出反馈的分散有限时间关联镇定的充分条件, 并给出扩展子系统的相应控制器的设计方法. 最后通过仿真实验表明了所提出方法的可行性和有效性.

     

Decentralized stabilization of time-varying large-scale interconnected systems

In this paper, two classes are defined of time-varying large-scale interconnected systems that can always be stabilized by time-varying decentralized local feedback. The results extend previous ones. In addition, some useful properties are obtained.     

不确定奇异大系统分散鲁棒预测控制

针对一类不确定奇异关联大系统,讨论了当系统状态不可测时,基于输出反馈的分散鲁棒预测控制问题.通过构造Lyapunov函数以及应用线性矩阵不等式方法,将"min-max"优化问题转化为凸优化问题求解,从而得到了输出反馈分散控制器存在的充分条件和显示表达式.证明了优化问题在初始时刻的可行解能保证奇异闭环大系统渐近稳定且正则无脉冲.仿真结果验证了算法的有效性.     

Decentralized adaptive output-feedback stabilization for large-scale stochastic nonlinear systems

In this paper, the problem of decentralized adaptive output-feedback stabilization is investigated for large-scale stochastic nonlinear systems with three types of uncertainties, including parametric uncertainties, nonlinear uncertain interactions and stochastic inverse dynamics. Under the assumption that the inverse dynamics of the subsystems are stochastic input-to-state stable, an adaptive output-feedback controller is constructively designed by the backstepping method. It is shown that under some general conditions, the closed-loop system trajectories are bounded in probability and the outputs can be regulated into a small neighborhood of the origin in probability. In addition, the equilibrium of interest is globally stable in probability and the outputs can be regulated to the origin almost surely when the drift and diffusion vector fields vanish at the origin. The contributions of the work are characterized by the following novel features: (1) even for centralized single-input single-output systems, this paper presents a first result in stochastic, nonlinear, adaptive, output-feedback asymptotic stabilization; (2) the methodology previously developed for deterministic large-scale systems is generalized to stochastic ones. At the same time, novel small-gain conditions for small signals are identified in the setting of stochastic systems design; (3) both drift and diffusion vector fields are allowed to be dependent not only on the measurable outputs but some unmeasurable states; (4) parameter update laws are used to counteract the parametric uncertainty existing in both drift and diffusion vector fields, which may appear nonlinearly; (5) the concept of stochastic input-to-state stability and the method of changing supply functions are adapted, for the first time, to deal with stochastic and nonlinear inverse dynamics in the context of decentralized control.     

Global robust stabilization of feedforward systems with uncertainties

This paper studies the global robust stabilization problem for a class of feedforward systems that is subject to both dynamic and time-varying static uncertainties. A small gain theorem-based bottom-up recursive design is developed for constructing a nested saturation control law. At each recursion, two versions of small gain theorem with restrictions are employed to establish the global attractiveness and local stability of the closed-loop system at the equilibrium point, respectively.     

Pseudo-decentralized adaptive stabilization of large-scale feedforward nonlinear systems

In this paper, we propose a pseudo-decentralized adaptive control scheme for a class of large-scale feedforward nonlinear systems with unknown nonlinear effects within subsystems and unknown nonlinear interactions among subsystems. The local controller of each subsystem takes a nested saturation feedback, using the state of its own subsystem, and the saturation levels are tuned online in a switching manner via a set of switching logics, which requires some binary flag communication among subsystems. Global asymptotic regulation of the closed-loop states is achieved.     

Decentralized state-feedback stabilization and robust control of uncertain large-scale systems with integrally constrained interconnections

This paper is concerned with a problem of stabilization and robust control design for interconnected uncertain systems. A new class of uncertain large-scale systems is considered in which interconnections between subsystems as well as uncertainties in each subsystem are described by integral quadratic constraints. The problem is to design a set of local (decentralized) controllers which stabilize the overall system and guarantee robust disturbance attenuation in the presence of the uncertainty in interconnections between subsystems as well as in each subsystem. The paper presents necessary and sufficient conditions for the existence of such a controller. The proposed design is based on recent absolute stabilization and minimax optimal control results and employs solutions of a set of game-type Riccati algebraic equations arising in H_∞ control.     

Decentralized stabilization of large-scale systems with structured uncertainties

The decentralized stabilization problem of large-scale systems with structured time-varying uncertainties is considered. A new sufficient condition is established for asymptotically stabilizing the large-scale perturbed systems using decentralized state feedback controllers. We also consider the use of optimal Perron weightings to reduce conservatism and the extension of the results to discrete-time large-scale systems with structured uncertainties. An illustrative example is given to demonstrate that the new sufficient condition is less conservative than the one reported recently. Another example is also given to illustrate the use of the sufficient condition for stability robustness of discrete-time large-scale systems.     

数值界不确定性关联大系统分散鲁棒H∞控制

针对一类状态阵,控制输入阵及关联阵中存在数值界不确定性的关联大系统,研究其分散鲁棒H∞状态反馈和输出反馈控制器设计问题.基于有界实引理,推导出了其存在分散鲁棒H∞控制器的充分条件,即一组矩阵不等式有解.利用Schur补引理,通过固定不同变量,提出了一种构建分散控制器的同伦迭代线性矩阵不等式方法.所获得的控制器使闭环大系统鲁棒稳定,并且达到给定的H∞性能指标.最后用数值例子说明了所提的设计方法的有效性.     

不确定关联大系统分散鲁棒H∞输出反馈控制

针对一类状态矩阵和控制矩阵存在参数不确定性关联大系统,研究其分散鲁棒H∞输出反馈控制问题.基于有界实引理将其鲁棒分散H∞动态输出反馈控制器的解归结为一个非线性矩阵不等式(NLMI),先通过选取适当的同伦函数来表示该非线性矩阵不等式,再通过Schur补引理将其化为两个双线性矩阵不等式,最后通过迭代算法求解该控制器,使闭环大系统鲁棒渐进稳定,并且满足给定的H∞性能指标.     

不确定广义大系统分散鲁棒H∞保性能控制

针对一类状态矩阵和控制矩阵存在参数不确定的广义大系统,研究其分散鲁棒H∞保性能控制问题,系统中不确定项具有数值界,可不满足匹配条件.基于广义系统的有界实引理,应用线性矩阵不等式(LMI)方法,给出了不确定广义大系统存在分散鲁棒H∞保件能控制器的一个LMI条件,并用这个线性矩阵不等式系统的可行解提供了一组分散鲁棒H∞保性能控制律的参数化表示,最后用例子说明该方法的应用.     

Decentralized robust controller design for uncertain large-scale systems with control delays

This paper presents a decentralized robust controller design for a class of interconnected dynamic systems with control delays and parametric uncertainty. The parameter uncertainties are considered unknown but norm bounded. By applying the Lyapunov stability theorem, two new delay-dependent sufficient conditions are established in terms of linear matrix inequalities, and linear memoryless state feedback controllers are designed to maintain the robust stability for the class of systems under study. It is shown that either no tuning procedure is required or only one parameter from each inequality needs to be tuned. An example is presented to demonstrate the application of the results presented here.     

Decentralized robust disturbance attenuation for a class of large-scale nonlinear systems

We solve the problem of decentralized H_∞ almost disturbance decoupling for a class of large-scale nonlinear uncertain systems in the absence of matching conditions. The method combines ideas from decentralized adaptive control and centralized nonlinear H_∞ control. We relax earlier assumptions on the uncertain time-varying interconnections which are demanded to be only bounded by general nonlinear functions in this work.     

时滞关联大系统的分散鲁棒容错控制

针对不确定时滞关联大系统,提出了一种分散鲁棒容错控制方法。目的是当发生传感器或执行器故障以及具有参数不确定时,使系统仍保持渐进稳定。基于Lyapunov稳定性理论,给出了该系统在传感器失效时具有容错性能的充分条件及控制器的设计步骤,并将结果推广到执行器失效的情况。最后通过实例仿真验证了方法的正确性,并对仿真结果进行了分析。     

参数不确定广义大系统的分散鲁棒镇定控制

应用线性矩阵不等式(LMI)方法研究了参数不确定广义大系统的分散鲁棒镇定控制问题，系统中不确定项具有数值界，可不满足匹配条件．基干不确定项的表达形式，给出了存在分散鲁棒控制器的LMI条件．仿真例子表明，LMI方法求解简单、便干应用。     

一类结构不确定性的离散时滞大系统的分散镇定

研究了一类离散时滞大系统的时滞相关鲁棒分散镇定问题, 系统的不确定与标称系统具有结构相似性. 通过构造性的差分格式, 将时滞相关鲁棒分散镇定控制器的存在条件转化为一列线性矩阵不等式的可行解问题. 提出了控制时滞及控制器的时滞鲁棒性概念, 在获得分散镇定控制器的同时给出了鲁棒时滞上界的求解, 因此比现有文献的结果更具有实际应用价值.     

Decentralized robust control for a class of large-scale interconnected systems with uncertainties

The design problem of decentralized robust controllers is considered for a class of large-scale systems. The system considered in this paper is composed of interconnected subsystems with time-varying uncertainties. For such large-scale uncertain systems, we give a simple und new method whereby we can derive the sufficient conditions for asymptotically stabilizing the overall system using decentralized feedback robust controllers. An illustrative example is given to demonstrate the design procedure of the decentralized feedback robust controllers, in the light of the method developed in this paper.     

Decentralized robust output and estimated state feedback controls for large-scale uncertain systems

This paper considers the design of decentralized robust output controls. The system under consideration is composed of interconnected subsystems with time-varying uncertainties. The decentralized control is based on the information of the local output. No communication is allowed among subsystems. The proposed control strategy is a combination of direct and indirect decentralized controls. The salient feature of the controls is that they require only information about the possible bounds of uncertainties.