Block sparse design of distributed controllers for dynamical network systems

This study proposes a controller design method based on block sparse optimization for dynamical network systems. The objective of the controller is to stabilize dynamical network systems with a given convergence rate. The block sparse optimization minimizes the number of controlled nodes. This study is unique in that the structure of the controller is constrained by the network topology of the system. Additionally, the proposed design problem is separable in terms of the distributed optimization over networks. The proposed method is applicable to controller design for the pinning control of consensus systems and the optimal vaccine allocation for epidemic spreading processes.     

一类时滞线性系统的鲁棒非脆弱控制器设计

基于线性矩阵不等式（LMI）方法,研究一类时滞线性系统的鲁棒非脆弱控制器的设计问题.在假定控制器增益扰动范数有界的前提下,对不确定时滞线性系统设计了鲁棒非脆弱状态反馈控制器,同时以一个LMI的形式给出了状态反馈控制器存在的充分条件,而且该LMI是与时滞相关的,因而具有较小的保守性.数值例子证明了该设计方法的有效性和可行性.     

Switching fuzzy controller design based on switching Lyapunov function for a class of nonlinear systems

This paper presents a switching fuzzy controller design for a class of nonlinear systems. A switching fuzzy model is employed to represent the dynamics of a nonlinear system. In our previous papers, we proposed the switching fuzzy model and a switching Lyapunov function and derived stability conditions for open-loop systems. In this paper, we design a switching fuzzy controller. We firstly show that switching fuzzy controller design conditions based on the switching Lyapunov function are given in terms of bilinear matrix inequalities, which is difficult to design the controller numerically. Then, we propose a new controller design approach utilizing an augmented system. By introducing the augmented system which consists of the switching fuzzy model and a stable linear system, the controller design conditions based on the switching Lyapunov function are given in terms of linear matrix inequalities (LMIs). Therefore, we can effectively design the switching fuzzy controller via LMI-based approach. A design example illustrates the utility of this approach. Moreover, we show that the approach proposed in this paper is available in the research area of piecewise linear control.     

A linear differential operator approach to flatness based tracking for linear and non-linear systems

This contribution presents a flatness based solution to the tracking for linear systems in differential operator representation. Since the differential operator representation is a flat system representation, tracking controllers can easily be designed using dynamic output feedback. Then, the differential operator approach for flatness based tracking of linear systems is extended to non-linear systems. The design of the resulting linear time varying dynamic output feedback controller is based on a linearization about the trajectory, which directly yields the differential operator representation. Different from the non-linear flatness based controller design the new approach uses linear methods, both in stabilizing the tracking and in computing the output feedback controller. The proposed design procedure assures exact tracking in the steady state when no disturbances are present. A simple example demonstrates the design of a dynamic output feedback controller for the tracking of a non-linear system.     

Decoupler and PID controller design of TITO systems

This paper treats controller design and tuning for systems with two input signals and two output signals in the process industry. Two design methods that can be combined to form a core in an algorithm for automatic design and tuning for the considered systems are presented. The proposed controller consists of a decoupler and a diagonal PID controller. The decoupler has the property that as little dynamics as possible is introduced in the decoupler. The PID design method is based on exhaustive search. The methods are combined and tested in an industrial environment in a paper mill.     

带有外干扰的滞后离散广义系统鲁棒H∞控制器设计:LMI方法

研究了带有外部干扰与状态滞后的离散广义系统鲁棒控制器的设计问题. 在对系统进行稳定分析的基础上, 给出了系统可以鲁棒镇定的条件, 并且将这一条件表示为线性矩阵不等式 (LMI)的形式, 从而使得控制器的设计问题可利用现有的LMI方法解决.     

基于观测器的具有反馈增益变化的广义系统H∞控制

介绍了一类广义系统H∞控制器的设计过程.通过设计基于观测器的具有反馈增益变 化的广义控制器,借助于带有广义约束的广义代数Riccati不等式(GARI),给出闭环广义系统 容许且传递函数的H∞范数有界的充要条件.通过解带有广义约束的GARI得到该控制器的设 计方法,并且控制器的参数矩阵只需使观测器容许.     

An Intelligent Design for a PID Controller for Nonlinear Systems

The proportional integral derivative (PID) controller is the most frequently used controller design for industrial applications because of its favorable response and simplicity of adjustment. However, PID manual tuning is traditionally based on engineering experience, and adjusting nonlinear or unknown systems is extremely difficult. In promoting an intelligent controller design theory that can be applied to the control of various systems, this paper proposes a nonlinear control design method that involves determining the optimal solution and obtaining the transfer function of an unknown system by using sequential quadratic programming. In addition, this paper presents a case study of an induction motor V/F speed control to demonstrate the effectiveness of the proposed method based on MATLAB simulation. The results prove that the design of the proposed intelligent PID controller is more robust than traditional controller designs.     

非线性大系统的分散自适应模糊控制*

本文针对非线性大系统，利用模糊系统的逼近能力，提出了一种分散自适应模糊控制器设计的系统方法。控制结构中采用分散模糊系统去自适应补偿过程不确定性，同时用模糊控制器的输出代替常规变结构控制律中的符号函数。利用李亚普诺夫理论，证明了控制算法是全局稳定的，跟踪误差可收敛到零的一个领域内。     

Optimal control of nonlinear systems: a predictive control approach

A new nonlinear predictive control law for a class of multivariable nonlinear systems is presented in this paper. It is shown that the closed-loop dynamics under this nonlinear predictive controller explicitly depend on design parameters (prediction time and control order). The main features of this result are that an explicitly analytical form of the optimal predictive controller is given, on-line optimisation is not required, stability of the closed-loop system is guaranteed, the whole design procedure is transparent to designers and the resultant controller is easy to implement. By establishing the relationship between the design parameters and time-domain transient, it is shown that the design of an optimal generalised predictive controller to achieve desired time-domain specifications for nonlinear systems can be performed by looking up tables. The design procedure is illustrated by designing an autopilot for a missile.     

Robust PI controller design for nonlinear systems via fuzzymodeling approach

The design problem of proportional and proportional-plus-integral (PI) controllers for nonlinear systems is studied. First, the Takagi-Sugeno (T-S) fuzzy model with parameter uncertainties is used to approximate the nonlinear systems. Then a numerically tractable algorithm based on the technique of iterative linear matrix inequalities is developed to design a proportional (static output feedback) controller for the robust stabilization of the system in T-S fuzzy model. Next, we transform the problem of PI controller design to that of proportional controller design for an augmented system and thus bring the solution of the former problem into the configuration of the developed algorithm. Finally, the proposed method is applied to the design of robust stabilizing controllers for the excitation control of power systems. Simulation results show that the transient stability can be improved by using a fuzzy PI controller when large faults appear in the system, compared to the conventional PI controller designed by using linearization method around the steady state     

Asymptotic stabilization of high‐order feedforward systems with delays in the input

This paper deals with the state feedback controller design for a class of high‐order feedforward (upper‐triangular) nonlinear systems with delayed inputs. The uncertainties in the systems are assumed to be dominated by higher‐order nonlinearities multiplying by a constant growth rate. The designed controller, which is a continuous but not smooth feedback, could achieve global asymptotical stability. Based on the appropriate state transformation of time‐delay systems, the problem of controller design can be converted into the problem of finding a parameter, which can be obtained by appraising the nonlinear terms of the systems. The nonlinear systems considered here are more general than conventional feedforward systems and they could be viewed as generalized feedforward systems. Two examples are given to show the effectiveness of the proposed design procedure. Copyright © 2009 John Wiley & Sons, Ltd.     

T-S模糊系统的局部稳定

讨论了T-S模糊系统的局部稳定性及控制器设计问题．给出连续T-S模糊系统局部稳定的定义,利用非二次Lyapunov函数和线性矩阵不等式（LMI）方法得到连续T-S模糊系统局部稳定的充分条件,并给出了基于LMI的局部镇定控制器设计方法．该方法不同于已有的全局稳定控制器设计方法,为判别模糊系统的稳定提供了新的选择．最后通过数值算例演示了控制器的设计方法。并证明了该方法的可行性。     

Design and analysis of optimal controller for fuzzy systems with input constraint

In this paper, we present a design method of the optimal and robust controller subject to the constraint on control inputs for continuous-time Takagi-Sugeno (TS) fuzzy systems. In order to establish this design method, we consider an optimal and robust control problem for nonlinear dynamic systems. For this problem, we present an analytic way which can provide the optimal controller for nonlinear dynamic systems by the dynamic programming approach and the inverse optimal approach. Moreover, we analyze the robustness property of the proposed optimal controller with respect to a class of input uncertainties by the passivity approach. Then, based on the theoretical results presented in this paper, we formulate the design problem of the optimal and robust controller with input constraint for continuous-time TS fuzzy systems as the semidefinite programming problem, and find the controller by solving it. The usefulness of the proposed approach is illustrated by considering the three-axis attitude stabilization problem of rigid spacecraft.     

一类控制系数未知但等同高阶非线性系统的稳定控制设计

本文研究了一类控制系数未知但等同高阶非线性系统的状态反馈稳定控制设计问题. 尽管该类系统具有不确定性, 即控制系数未知,但本文没有采用自适应技术, 而是通过选取适当的设计参数, 从而得到了设计该类非线性系统稳定控制器的新方法, 并基于反推技术, 给出了稳定控制器的设计步骤. 所设计的状态反馈控制器使得闭环系统全局渐近稳定, 并保持在原点的平衡性.     

奇异摄动系统的H∞控制: 基于奇异系统的方法

实际系统的奇异系统模型往往通过忽略系统的奇异摄动系统模型微分项系数矩阵中的小时间参数得到.然而, 传统的奇异系统控制器设计很少考虑微分项系数矩阵的摄动. 本文拓展了现有奇异系统输出动态反馈H_∞控制器的设计, 使得当实际闭环系统中存在小时间参数时, 仍然能保持稳定并且满足一定的H_∞性能指标. 仿真算例说明了本文提出方法的有效性.     

Adaptive output control of nonlinear systems with uncertain dead-zone nonlinearity

In this note, we present a new scheme to design adaptive controllers for uncertain systems preceded by unknown dead-zone nonlinearity. The control design is achieved by introducing a smooth inverse function of the dead-zone and using it in the controller design with backstepping technique. For the design and implementation of the controller, no knowledge is assumed on the unknown system parameters. It is shown that the proposed controller not only can guarantee stability, but also transient performance.     

一类符号反对称结构系统的稳定性及其应用

结合矩阵论中的可反对称条件, 提出一种稳定的具有符号反对称结构的系统, 并将其作为非线性系统的镇定控制目标. 面向符号反对称结构系统的控制方法存在递推构造法和直接设计方法两种: 递推构造法面向具有上三角结构的系统, 包括已有逆推控制和逆推自适应控制, 并可具有更多的可调参数; 直接设计法适用于低维系统, 对于一些系统可以设计出更简单的控制器. 对于Lorenz混沌同步系统的仿真说明了面向反对称结构系统直接设计法有效性.     

基于观测器的广义线性系统降阶H∞控制器设计

本文研究基于Luenberger观洲器的广义系统降阶H∞控制器的设计问题,并且该观测器是关于干扰解耦的。首先是提出了广义系统H∞状态反馈控制问题的一个充要条件,并利用线性矩阵不等式方法求解出广义系统的H∞状态反馈增益。然后对该H∞状态反馈增益进行渐进降阶观测,基于广义Sylvester矩阵方程的显式通解的参数化设计方法,实现了广义系统的降阶H∞控制。本文最主要的工作是给出了相应的广义线性系统降阶H∞控制器的设计算法。在文章的最后给出了一个例子,用来说明降阶算法的有效性。     

Backstepping for nonsmooth systems

The paper presents a constructive control design for integrator backstepping in nonsmooth systems. The approach is based on non smooth analysis and Lyapunov stability for nonsmooth systems and is similar in spirit with the robust control designs that have appeared in literature, but is applicable to a larger class of systems. The backstepping controller is first applied to the case of a unicycle driven by a new discontinuous kinematic controller yielding global asymptotic convergence with bounded inputs. Then it is used to implement a sliding mode controller in a hybrid system. Simulations results not only verify the convergence properties but also reveal the ability of the new backstepping controller to suppress chattering.