A gradient flow approach to on-line robust pole assignment for synthesizing output feedback control systems

Pole assignment is a basic design method for synthesis of feedback control systems. In this paper, a gradient flow approach is presented for robust pole assignment in synthesizing output feedback control systems. The proposed approach is shown to be capable of synthesizing linear output feedback control systems via on-line robust pole assignment. Convergence of the gradient flow can be guaranteed. Moreover, with appropriate design parameters the gradient flow converges exponentially to an optimal solution to the robust pole assignment problem and the closed-loop control system based on the gradient flow is globally exponentially stable. These desired properties make it possible to apply the proposed approach to slowly time-varying linear control systems. Simulation results are shown to demonstrate the effectiveness and advantages of the proposed approach.     

Parametric state feedback design of linear distributed-parameter systems

The parametric approach for the design of state feedback controllers has been formulated so far only for linear lumped-parameter systems. It yields an explicit parametric expression for the state feedback gain given the closed-loop eigenvalues and the set of corresponding parameter vectors. This contribution presents a parameterisation of state feedback controllers for linear distributed-parameter systems with scalar state and distributed control. By introducing the closed-loop eigenvalues and the parameter vectors as design parameters, an explicit expression for the state feedback is obtained. In contrast to the pure eigenvalue assignment, the parameterisation allows the assignment not only of the closed-loop eigenvalues but also of the closed-loop eigenfunctions. The usefulness of the proposed parametric approach is demonstrated by decoupling the transfer behaviour of a MIMO diffusion system with respect to its dominant modes.     

A parametric approach to finite-dimensional control of linear distributed-parameter systems

This article considers the design of finite-dimensional compensators for distributed-parameter systems using eigenvalue assignment. The proposed compensator consists of an observer estimating additional outputs and a static feedback of the measurable and the estimated outputs. Since the additional outputs can be asymptotically reconstructed, the compensator can be designed using the separation principle, i.e. the closed-loop eigenvalues are given by the observer eigenvalues and the eigenvalues resulting from the static output feedback control. In order to solve the corresponding eigenvalue assignment problem, the parametric approach for the design of static output feedback controllers in finite-dimensions is extended to distributed-parameter systems. By using a parameter optimisation it is possible to assign all closed-loop eigenvalues within specified regions of the complex plane in order to stabilise the system and to assure a desired control performance. A heat conductor is used to demonstrate the proposed design procedure.     

基于输出反馈特征结构配置的重构控制系统设计

推出了一种利用特征结构配置设计重构控制系统的新方法. 当故障后的系统满足m+r-1≥n的条件时, 通过重新设计一输出反馈增益阵, 使重构后的闭环故障系统的特征值全部恢复到故障前的位置, 特征向量也在可配置子空间中尽量接近故障前相应的闭环系统特征向量, 从而使重构后的系统性能最大程度地恢复到故障前的系统性能. 这种方法的优点是重构系统的稳定性可得到保证, 且计算输出反馈增益阵的算法相对简单. 应用实例和仿真结果说明本文方法的有效性.     

The decoupling of generalized state-space systems via statefeedback

The input-output decoupling problem of generalized state-space systems (GSS) via proportional state feedback is studied. The following three major issues are resolved: the necessary and sufficient conditions for the problem to have a solution, the general analytical expressions of the controller matrices, and the general analytical expressions of the diagonal elements of the closed-loop system. It is concluded that the approach presented seems to be a quite powerful tool for solving several feedback design problems for GSS systems. Using this method, problems such as decoupling and simultaneous pole assignment and decoupling via output feedback are successfully studied     

Global stabilization of a class of time-delay nonlinear systems

This paper is concerned with the problem of global stabilization by state feedback and output feedback for a class of time-delay nonlinear systems that are dominated by a triangular system satisfying linear growth conditions. By solving the Lyapunov equation and constructing the appropriate Lyapunov-Krasovskii functionals (LKF), the linear and memoryless state feedback controller and output feedback controller making the closed-loop system globally asymptotically stable (GAS) are explicitly constructed respectively. Comparing our design scheme with the backstepping method which has been widely used to deal with strictly feedback nonlinear systems, our design scheme is much simpler and more efficient. An example is given to show that the proposed design procedures are very simple and efficient.     

基于特征结构配置的二阶线性系统鲁棒容错控制设计

研究基于特征结构配置的二阶线性系统鲁棒容错控制设计问题,目的是重新设计状态反馈控制律,使得故障闭环系统和正常闭环系统具有相同的特征值.两闭环系统的特征向量依最小二乘法接近,而且能通过极小化灵敏度指标提高系统的鲁棒性.基于状态反馈特征结构配置的参数化结果,将系统灵敏度指标优化问题转化为含有约束条件的优化问题,并提出了鲁棒容错控制设计方法.数值算例及其仿真结果验证了所提出设计方法的有效性.     

线性离散周期系统输出反馈参数化极点配置

采用周期输出反馈的途径, 考虑了线性离散时间周期系统的极点配置问题. 通过将闭环单值性矩阵进行一系列转化, 周期输出反馈律的求解问题可以转化为一类Sylvester矩阵方程的求解问题. 利用Sylvester矩阵方程的最新结果, 可以将输出反馈增益表示为参数化形式, 从而得到了能够实现极点配置的所有输出反馈控制器. 数值算例验证了方法的有效性.     

State and output feedback boundary control for a coupled PDE-ODE system

This note is devoted to stabilizing a coupled PDE-ODE system with interaction at the interface. First, a state feedback boundary controller is designed, and the system is transformed into an exponentially stable PDE-ODE cascade with an invertible integral transformation, where PDE backstepping is employed. Moreover, the solution to the resulting closed-loop system is derived explicitly. Second, an observer is proposed, which is proved to exhibit good performance in estimating the original coupled system, and then an output feedback boundary controller is obtained. For both the state and output feedback boundary controllers, exponential stability analyses in the sense of the corresponding norms for the resulting closed-loop systems are provided. The boundary controller and observer for a scalar coupled PDE-ODE system as well as the solutions to the closed-loop systems are given explicitly.     

具有方差和极点约束的不确定系统鲁棒H∞输出反馈控制

针对一类具有范数有界不确定性的连续系统和二次矩阵不等式区域,考虑系统具有方差和区域极点约束的输出反馈控制器设计问题．为此首先导出闭环系统区域稳定的充分必要条件．然后用线性矩阵不等式方法给出输出反馈控制器存在的一个充分条件．在此充分条件下闭环系统是鲁棒区域稳定的且具有H∞性能以及当干扰为白噪声信号时其稳态状态方差有限．接下来用矩阵分解方法给出输出反馈控制器增益矩阵的求解过程．最后通过一个仿真实例说明本文所提出的控制器设计方法的有效性．     

Pole assignment in a specified disk

The problem of assigning all poles of a closed-loop system in a specified disk by state feedback is considered for both continuous and discrete systems. A state feedback control law is determined by using a discrete Riccati equation. This kind of pole assignment problem is namedD-pole assignment, and its relation to the optimal control problem and its robustness properties are discussed. The gain and phase margins for all closed-loop poles to stay inside the specified diskDare determined for the proposed control.     

具有方差和极点约束的不确定系统鲁棒H∞输出反馈控制

针对一类具有范数有界不确定性的连续系统和二次矩阵不等式区域, 考虑系统具有方差和区域极点约束 的输出反馈控制器设计问题. 为此首先导出闭环系统区域稳定的充分必要条件. 然后用线性矩阵不等式方法给出输出反馈控制器存在的一个充分条件. 在此充分条件下闭环系统是鲁棒区域稳定的且具有H-infinity性能以及当干扰为白噪声信号时其稳态状态方差有限. 接下来用矩阵分解方法给出输出反馈控制器增益矩阵的求解过程. 最后通过一个仿真实例说明本文所提出的控制器设计方法的有效性.     

用输出反馈配置鲁棒极点*

本文讨论了线性定常多变量系统在时域上用输出反馈配置鲁棒极点的问题。用输出反馈配置极点时,有一些自由度,可以利用这些自由度指定特征向量。本文给出一种数值方法,它用于选择一组尽可能正交的特征向量,使闭环系统矩阵A+BKC尽可能接近正规,从而使闭环极点对于矩阵的系数变化是鲁棒的。     

Parametric control to a type of quasi-linear second-order systems via output feedback

This paper considers the design of output feedback control for a type of quasi-linear second-order systems with the time-varying coefficient matrices containing the state variables and a time-varying parameter vector. Based on the solution to a type of second-order generalised Sylvester matrix equations, general complete parameterisation of a quasi-linear output feedback controller is established with respect to the state variables, the time-varying parameter vector, the constant closed-loop system and another two groups of arbitrary parameters, and also for the left and right closed-loop eigenvectors matrices. With the proposed parametric output feedback control, the closed-loop system can be transformed into a constant linear system with desired eigenstructure. Finally, simulation results are provided to illustrate the convenience and effectiveness of application in the general spacecraft rendezvous problem.     

一类连续区间系统的鲁棒圆盘极点配置

针对一类连续线性区间系统,基于线性矩阵不等式,介绍一类能够将给出的连续区间系统的闭环系统的极点配置到指定圆盘中的状态反馈和输出反馈增益矩阵的设计方法.这类设计方法也包括分别基于执行器故障和传感器故障的可靠控制器的设计方法,基于矩阵的谱半径不大于自身的最大奇异值的理论以及矩阵的Schur补引理,将矩阵的最大奇异值限定后就...     

离散时间部分状态反馈模型参考自适应控制

本文针对线性不确定性系统, 给出了部分状态反馈直接模型参考自适应控制设计方案以及详细的系统稳 定性、输出跟踪性能分析. 控制器设计基于降维观测器和参数化方法. 此方案采用反馈控制, 反馈信号不仅仅依赖 全状态信息或者输出信号, 而是任意不超过系统维数的可测信号. 因此, 部分状态反馈控制是包含状态反馈、输出 反馈控制的新的控制方案, 缓解了状态反馈对状态信息的限制, 降低了输出反馈控制结构的复杂性. 通过引入辅助 信号, 本文证明了输出匹配条件的存在性、所有闭环系统信号的有界性以及渐近输出跟踪性能. 仿真结果验证了该 方案的有效性.     

Adaptive neural output feedback control for stochastic nonlinear time-delay systems with unknown control directions

This paper first focuses on the problem of adaptive output feedback stabilization for a more general class of stochastic nonlinear time-delay systems with unknown control directions. By using a linear state transformation, the original system is transformed to a new system for which control design becomes feasible. Then a novel adaptive neural network (NN) output feedback control strategy, which only contains one adaptive parameter, is developed for such systems by combining the input-driven filter design, the backstepping technique, the NN’s parameterization, the Nussbaum gain function method and the Lyapunov–Krasovskii approach. The proposed control design guarantees that all signals in the closed-loop systems are 4-moment (or 2-moment) semi-globally uniformly bounded. Finally, two simulation examples are given to demonstrate the effectiveness and the applicability of the proposed control design.     

Globally asymptotic stabilization for nonlinear time-delay systems with ISS inverse dynamics

The output feedback stabilization is considered for a class of nonlinear time-delay systems with inverse dynamics in this paper.An appropriate state observer is constructed for the unmeasurable system states in order to realize the control objective.By adopting the backstepping and Lyapunov-Krasovskii functional methods,a systematic design procedure for a memoryless output feedback control law is presented.It is shown that the designed controller can make the closed-loop system globally asymptotically stable while keeping all signals bounded.An illustrative example is discussed to show the effectiveness of the proposed control strategy.