线性离散时滞系统的输出反馈镇定

针对一类带有区间时变时滞的线性离散系统,研究静态输出反馈镇定问题和动态输出反馈镇定问题。通过构造合适的Lyapunov函数,并使用Jensen不等式技术和时滞区间因子技术处理其差分,分别给出了系统可由静态输出反馈和动态输出反馈镇定的时滞依赖的充分条件。后使用矩阵分块技术从理论上证明了所给出的镇定判据比文献中已有的具有更小的保守性。对获得的理论结果进行了数值仿真,仿真结果既表明了所提出方法的正确性和可应用性,也说明了增加时滞区间因子数可以减少镇定判据的保守性。     

离散线性时滞系统的鲁棒稳定性判据

研究了离散线性时滞系统的鲁棒稳定性问题。首先，利用差分方程的特点，将该系统进行了转化，且转化后系统的鲁棒稳定性蕴含着原系统的鲁棒稳定性；然后，利用离散Lyapunov函数方法，通过构造一个适当的离散Lyapunov函数，并借助于向量不等式和矩阵范数的性质，给出所讨论系统鲁棒稳定的充分条件，且该条件是以矩阵范数的形式给出的且是时滞相关的。最后，给出一个算例，说明所得判据的有效性。     

Fast moving horizon state estimation for discrete-time systems with linear constraints

Fast moving horizon state estimation for nonlinear discrete-time systems affected by disturbances is addressed by means of imperfect optimization at each time instant based on few iterations of the gradient, conjugate gradient, and Newton algorithms. Linear constraints on the state vector are taken into account through a projection on the subspace associated with such constraints. The stability of the estimation error for the resulting scheme is proved under suitable conditions. The effectiveness of the proposed approach is showcased via simulation results in comparison with moving horizon estimation based on complete optimization and extended Kalman filtering.     

Alternative optimal filter for linear state delay systems

In this paper, the optimal filtering problem for linear systems with state delay over linear observations is treated using the optimal estimate of the state transition matrix. As a result, the alternative optimal filter is derived in the form similar to the traditional Kalman–Bucy one, i.e. consists of only two equations, for the optimal estimate and the estimation error variance. This presents a significant advantage in comparison to the previously obtained optimal filter (IEEE Trans. Autom. Control 2005; 50 :684–690), which includes a variable number of covariance equations, unboundedly growing as the filtering horizon tends to infinity. Performances of the two optimal filters are compared in example; the obtained results are discussed. Copyright © 2006 John Wiley & Sons, Ltd.     

运用静态反馈分析设计离散饱和线性系统

给出了控制饱和单输入状态反馈系统是全局渐近稳定还是区域渐近稳定的充分性条件,且对区域渐近稳定的情况计算其不变吸引椭球,运用Ricatti方程迭代法设计控制器以使所得椭球尽量大;对多输入控制饱和系统输出反馈系统,给出其吸引域的描述;最后用算例说明方法的有效性。     

基于线性二次型的受电弓最优输出跟踪器设计

随着电力机车运行速度的不断提高,受电弓与接触网之间的压力波动越来越严重。为了减小弓网之间的压力波动,提高电力机车运行的稳定性。针对二元受电弓与接触网简化动力学模型,从受电弓主动控制角度出发,利用最优控制理论中线性二次型控制进行分析研究。根据线性二次型性能指标中误差与控制能量最小化原理,进行最优输出跟踪器设计。通过MATLAB仿真软件对系统输出接触力进行动态仿真,并得到跟踪误差曲线。分析结果表明,最优输出跟踪器跟踪能力很强,能有效提高弓网接触压力的稳定性,改善弓网受流质量。针对弓网系统模型,线性二次型是一种有效的控制策略。     

Online optimal and adaptive integral tracking control for varying discrete-time systems using reinforcement learning

Conventional closed-form solution to the optimal control problem using optimal control theory is only available under the assumption that there are known system dynamics/models described as differential equations. Without such models, reinforcement learning (RL) as a candidate technique has been successfully applied to iteratively solve the optimal control problem for unknown or varying systems. For the optimal tracking control problem, existing RL techniques in the literature assume either the use of a predetermined feedforward input for the tracking control, restrictive assumptions on the reference model dynamics, or discounted tracking costs. Furthermore, by using discounted tracking costs, zero steady-state error cannot be guaranteed by the existing RL methods. This article therefore presents an optimal online RL tracking control framework for discrete-time (DT) systems, which does not impose any restrictive assumptions of the existing methods and equally guarantees zero steady-state tracking error. This is achieved by augmenting the original system dynamics with the integral of the error between the reference inputs and the tracked outputs for use in the online RL framework. It is further shown that the resulting value function for the DT linear quadratic tracker using the augmented formulation with integral control is also quadratic. This enables the development of Bellman equations, which use only the system measurements to solve the corresponding DT algebraic Riccati equation and obtain the optimal tracking control inputs online. Two RL strategies are thereafter proposed based on both the value function approximation and the Q-learning along with bounds on excitation for the convergence of the parameter estimates. Simulation case studies show the effectiveness of the proposed approach.     

Local fill reduction techniques for sparse symmetric linear systems

Local algorithms for obtaining pivot orderings for sparse symmetric coefficient matrices are reviewed together with their mathematical background, appropriate data structures and details of efficient implementation. Heuristics that go beyond the classical Minimum Degree and Minimum Local Fill scoring functions are discussed, illustrated, improved and extensively tested on a test suite of matrices from various applications. Our tests indicate that the presented techniques have the potential of accelerating circuit simulation significantly.     

基于观测器的控制时滞线性系统的最优跟踪控制

研究了控制时滞线性系统的二次型最优跟踪控制问题.首先将控制时滞系统转化为无时滞系统,再将最优跟踪问题转化成等价系统的最优调节问题.然后,通过求解Riccati方程,设计含动态观测器的前馈-反馈最优跟踪控制律,利用构造参考输入观测器解决了前馈补偿器的状态物理不可实现问题.仿真实例验证了所设计的最优跟踪控制律的有效性.     

多机系统利用模态最优线性组合法的降阶分析

在多机电力系统小扰动稳定分析与控制中,利用原始系统状态空间方程的坐标变换,根据具有附加条件的最优分析方法,建立二次型性能指标,以主导模态坐标近似来描述非主导模态坐标,从而建立模态最优线性组合降阶法的等值模型,由等值模型可以分析所有状态变量的动态变化过程.以双轴同步发电机模型为基础,综合考虑自动励磁调节系统,详细推导多机系统原始的状态空间方程.以一3机9节点实例建立原始状态空间方程,采用模态最优线性组合法获得降阶后的等值模型,由降阶前后动态特性曲线的近似重合论证了模态最优线性组合降阶法的有效性.     

基于最优线性组合理论的动态稳定模型等效研究

一个高阶的电力系统模型必然给电力系统稳定性分析与计算带来困难。提出合理选择主导特征值和重要状态变量,利用最优线性组合理论分析电力系统动态稳定模型的降阶。采用简单电力系统模型,完整地考虑发电机组的励磁、调速、电力系统稳定器以及阻尼绕组,建立高阶模型。由降阶前后状态变量的动态特性曲线论证了最优线性组合法可以获得精度较高的降阶模型。     

基于线性最优控制和积分控制的励磁控制器设计

为了进一步改善传统线性最优励磁控制中的动态性能和调节精度,基于同步发电机的派克模型推导出了供设计线性最优励磁控制规律用的单机无穷大系统的线性化状态空间方程。以该方程为基础,设计了一种同时以机端电压、有功功率、无功功率、角速度、功角作为反馈量的线性最优励磁控制器,将发电机功角、无功功率这两个与稳定性和品质密切相关的重要参量引入控制规律。同时,为了提高机端电压的调节精度,基于稳态调整与动态调节区分开来的思想,将积分调节引入励磁控制规律。通过Matlab进行算例仿真,结果表明所设计的励磁控制规律与传统规律相比,能够有效地提高电力系统在大、小扰动下的稳定性,同时在电压调节精度方面亦有所改善。     

Hydrothermal optimal power flow based on a combined linear andnonlinear programming methodology

The author's consider a new formulation of optimal power flow (OPF) that makes it eminently suitable for accurate incremental modeling. G. Zoutendijk's method of feasible directions (1960) for solving the nonlinear programming problems is adapted for the solution of the OPF. Hydraulic modeling of systems with a considerable share of hydraulic generation is considered. The method is very efficient as it is designed to exploit the special structure of the problem     

Novel direct optimal and indirect method for discretization of linear fractional systems

This paper addresses the problem of discretization of fractional differintegrators and fractional systems in general. Two new discretization schemes are proposed—optimal direct method, and computationally inexpensive indirect method. The proposed methods are highly flexible and suitable for obtaining both general purpose and specialized, application-specific approximations. Both proposed methods outperform recently proposed approximations, as it is shown in several illustrative examples.     

Construction of a robust adaptive regulator for time-varying discrete time systems

A robust adaptive regulator is constructed for single-input/single-output discrete time systems modelled by a linear time-varying difference equation that includes an error term to incorporate model errors and/or disturbances. It is assumed that the parameters of the nominal model belong to a known bounded convex set and that the ‘frozen time’ nominal model is stabilizable for all possible parameter values. The estimation of the parameters of the nominal model is carried out using a standard gradient-type algorithm with a projection operation. An adaptive regulator is then constructed from the solution to a finite time Riccati equation. It is shown that the resulting closed-loop system is globally stable if the mean of the parameter time variations is sufficiently small and if the model error is sufficiently small, but where the disturbances applied to the plant may be arbitrarily large.     

基于线性二次最优LQR的直线倒立摆控制系统研究分析

以自动控制领域典型的实验、教研设备-倒立摆系统作为研究对象,通过对控制原理分析、数学建模分析、状态反馈设计、MATLAB仿真,然后在搭建的实验平台上用LQR方法编程实现对其最优控制。系统成功起摆与保持倒立控制的实现,验证了建模的正确性与控制方式的有效性。     

An adaptive model predictive control strategy for a class of discrete-time linear systems with parametric uncertainty

In this study, an adaptive model predictive control (MPC) strategy is proposed for a class of discrete-time linear systems with parametric uncertainty. In the presented adaptive MPC, an updating law is firstly designed to update the estimated parameters online. By utilizing the estimated parameters, a standard MPC optimization problem for unconstrained systems is established. Then, to deal with constrained systems, the min–max MPC technique is developed under the set-based approach for the estimated parameters. Furthermore, it is shown theoretically that the recursive feasibility and closed-loop stability can be rigorously proved, respectively. Finally, numerical simulations and comparative analysis are presented to illustrate the superiority of the proposed algorithms in control performance.