H_∞ Control with Multiple Delays in Measurements

Based on an innovation analysis method in the Krein space,a sufficient and necessary condition is given for the existence of the solution of H_∞control problem for a linear continuous- time system with multiple delays.By introducing a re-organized innovation sequence,the H_∞control problem with delayed measurements is converted into a linear quadratic(LQ)problem and a delay- free H_2 estimation problem in the Krein space.The controller is given in terms of two forward Riccati equations and a backward Riccati equation.     

H-infinity measurement-feedback control for discrete-time systems with a single measurement delay

H-infinity control problem for linear discrete-time systems with instantaneous and delayed measurements is studied. A necessary and sufficient condition for the existence of the H-infinity controller is derived by applying reorganized innovation analysis approach in Krein space. The measurement-feedback controller is designed by performing two Riccati equations. The presented approach does not require the state augmentation.     

esign of power controller in CDMA system with power and SIR error minimization

In this paper, an uplink power control problem is considered for code division multiple access （CDMA） systems. A distributed algorithm is proposed based on linear quadratic optimal control theory. The proposed scheme minimizes the sum of the power and the error of signal-to-interference ratio （SIR）. A power controller is designed by constructing an optimization problem of a stochastic linear quadratic type in Krein space and solving a Kalman filter problem.     

Design of power controller in CDMA system with power and SIR error minimization

In this paper, an uplink power control problem is considered for code division multiple access (CDMA) systems. A distributed algorithm is proposed based on linear quadratic optimal control theory. The proposed scheme minimizes the sum of the power and the error of signal-to-interference ratio (SIR). A power controller is designed by constructing an optimization problem of a stochastic linear quadratic type in Krein space and solving a Kalman filter problem.     

H_∞ Control for 2-D Discrete State Delayed Systems in the Second FM Model

This paper is concerned with the problem of H_∞control for two-dimensional (2-D) discrete state delay systems described by the second Fornasini and Marchesini (FM) state- space model.A sufficient condition to have an H_∞noise atten- uation for this 2-D system is given in terms of a certain linear matrix inequality (LMI).The optimal H_∞controller is obtained by solving a convex optimization problem.Finally,a simulation example is given to illustrate the effectiveness of the proposed result.     

具有时变时滞的离散系统的H_∞控制(英文)

This paper is concerned with the finite horizon H∞ control for discrete-time systems with time-varying delay in con- trol and exogenous input channels.By defining a binary variable,the problem is first transformed into the one with multiple input channels,each of which has a constant delay.Then,the problem is solved by using the duality principle between the H∞ control problem and smoothing estimation problem for an associated system without delays.The solution is given in terms of one standard Riccati diff...     

线性多变量系统的鲁棒耗散控制

Robust quadratic dissipative control for a class of linear multi-variable systems with parameter uncertainties is considered, where the uncertainties are expressed in a linear fractional form. For the nominal system without uncertainties, the equivalence between quadratic dissipativeness and positive realness is established, and conditions are derived for linear systems to be quadratic dissipative. As for uncertain systems, it is shown that the robust quadratic dissipative control problem for the uncertain system can be reduced to the corresponding problem for a related system without uncertainties. The control problem concerned can be solved using LMI approach. The results of the paper unify existing results on H1 control and positive real control and provide a more flexible and less conservative control design method.     

Robust H_∞ control for discrete-time polytopic uncertain systems with linear fractional vertices

The robust H∞ control problem for discrete-time uncertain systems is investigated in this paper. The uncertain systems are modelled as a polytopic type with linear fractional uncertainty in the vertices. A new linear matrix inequality (LMI) characterization of the H∞ performance for discrete systems is given by introducing a matrix slack variable which decouples the matrix of a Lyapunov function candidate and the parametric matrices of the system. This feature enables one to derive sufficient conditions for discrete uncertain systems by using parameter-dependent Lyapunov functions with less conservativeness. Based on the result, H∞ performance analysis and controller design are carried out. A numerical example is included to demonstrate the effectiveness of the proposed results.     

H-infinity deconvolution filtering： a Krein space approach in state-space setting

This note is concerned with the H-infinity deconvolution filtering problem for linear time-varying discretetime systems described by state space models, The H-infinity deconvolution filter is derived by proposing a new approach in Krein space. With the new approach, it is clearly shown that the central deconvolution filter in an H-infinity setting is the same as the one in an H2 setting associated with one constructed stochastic state-space model. This insight allows us to calculate the complicated H-infinity deconvolution filter in an intuitive and simple way. The deconvolution filter is calculated by performing Riccati equation with the same order as that of the original system.     

具有干扰输入的不确定奇异系统的有限时间控制器设计

The concept of finite-time stability for linear singular system isinduced in this paper. Finite-time control problem is considered for linear singular systems with time-varying parametricuncertainties and exogenous disturbances. The disturbance satisfies a dynamical system with parametric uncertainties. Asufficient condition is presented for robust finite-ime stabilization via state feedback. The condition is translated to a feasibility problem involving restricted linear matrix inequalities (LMIs). A detailed solving method is proposed for the restricted linear matrix inequalities. Finally, an example is given to show the validity of the results.     

广义系统H∞多步预报器设计

基于格林空间中的新息分析方法和卡尔曼滤波理论, 首次给出了广义系统H_∞多步预报器存在的充要条件和一种简单的计算方法. 本文将广义系统的H_∞多步预报问题转化为带有当前观测和时滞观测的格林空间中广义系统最小方差估计问题, 然后引入新息重组序列解决该最小方差估计问题. 通过求解维数与变换后的系统相同的两个黎卡提方程得到了H_∞预报器, 避免了处理带观测时滞系统时常采用的系统增广方法. 数值例子表明利用本文的新息重组方法计算广义系统H_∞多步预报器比用系统增广方法计算量小.     

H∞ Control of Discrete-Time Systems With Multiple Input Delays

This paper is concerned with the finite horizon H_infin full-information control for discrete-time systems with multiple control and exogenous input delays. We first establish a duality between the H_infin full-information control and the H₂ smoothing of a stochastic backward system in Krein space. Like the duality between the linear quadratic regulation (LQR) of linear systems without delays and the Kalman filtering, the established duality allows us to address complicated multiple input delay problems in a simple way. Indeed, by applying innovation analysis and standard projection in Krein space, in this paper we derive conditions under which the H_infin full-information control is solvable. An explicit controller is constructed in terms of two standard Riccati difference equations of the same order as the original plant (ignoring the delays). As special cases, solutions to the H_infin state feedback control problem for systems with delays only in control inputs and the H_infin control with preview are obtained. An example is given to demonstrate the effectiveness of the proposed H_infin control design     

基于Krein空间的线性离散时变系统H∞故障估计

研究一类受L2范数有界未知输入影响的线性离散时变系统H∞故障估计问题. 首先将系统H∞故障估计归结为二次型最小化问题, 然后引入相应的Krein空间系统, 应用Krein空间Kalman滤波理论, 推导并证明H∞故障估计问题可解的充要条件, 给出基于矩阵Riccati方程的H∞故障估计器设计, 为故障估计问题提供新的理论方法, 并通过算例验证本文提出方法的有效性.     

An innovation approach to H/sub /spl infin// fixed-lag smoothing for continuous time-varying systems

This note studies the finite horizon H/sub /spl infin// fixed-lag smoothing problem for linear continuous time-varying systems. A technique named as reorganized innovation analysis in Krein space is developed to give a necessary and sufficient condition for the existence of an H/sub /spl infin// fixed-lag smoother. The condition is given in terms of the boundedness of two matrix functions which are derived from the solutions of two Riccati differential equations (RDEs), one standard H/sub /spl infin// filtering RDE and one H/sub 2/ type of RDE. Examples demonstrate the proposed H/sub /spl infin// fixed-lag smoother design and the fact that the existence of an H/sub /spl infin// smoother does not depend on the solvability of H/sub /spl infin// filtering.     

离散系统多步观测时滞的H∞输出反馈控制

针对一类多观测时滞离散系统,本文提出了基于Krein空间理论解决H∞输出反馈问题的新方法．利用H∞输出反馈控制问题与不定二次型之间的关系,时滞系统的H∞控制问题分解为LQ问题和时滞的H∞估计问题．通过重组观测,时滞的H∞估计问题可转化为无时滞的H∞估计问题,从而给出由两个Riccati方程决定的H∞控制器存在的充要条件．本文的方法不需要增广系统．     

Linear estimation in Krein spaces. I. Theory

The authors develop a self-contained theory for linear estimation in Krein spaces. The derivation is based on simple concepts such as projections and matrix factorizations and leads to an interesting connection between Krein space projection and the recursive computation of the stationary points of certain second-order (or quadratic) forms. The authors use the innovations process to obtain a general recursive linear estimation algorithm. When specialized to a state-space structure, the algorithm yields a Krein space generalization of the celebrated Kalman filter with applications in several areas such as H ^∞-filtering and control, game problems, risk sensitive control, and adaptive filtering     

Risk-sensitive filtering for discrete-time systems with time-varying delay

In this paper, the risk-sensitive filtering problem with time-varying delay is investigated. The problem is transformed into Krein space as an equivalent optimisation problem. The observations with time-varying delays are restructured as ones with multiple constant delays by defining a binary variable model with respect to the arrival process of observations, containing the same state information as the original. Finally, the reorganised innovation analysis approach in Krein space allows the solution to the proposed risk-sensitive filtering in terms of the solutions to Riccati and matrix difference equations.     

Design of power controller in CDMA system with power and SIR error minimization

In this paper, an uplink power control problem is considered for code division multiple access (CDMA) systems. A distributed algorithm is proposed based on linear quadratic optimal control theory. The proposed scheme minimizes the sum of the power and the error of signal-to-interference ratio (SIR). A power controller is designed by constructing an optimization problem of a stochastic linear quadratic type in Krein space and solving a Kalman filter problem.