Robust H ∞ Filtering for Uncertain Time-Delay Systems: Matrix Inequality Approach

In this paper, a new robust H _∞ filtering problem for uncertain time-delay systems is considered. Based on the Lyapunov method, a design criterion of the robust H _∞ filter, in which the filtering process remains asymptotically stable for all admissible uncertainties and the transfer function from the disturbance inputs to error state outputs satisfies the prespecified H _∞ norm upper bound constraint, is derived in terms of matrix inequalities. The inequalities can be solved easily by efficient convex optimization algorithms. A numerical example is included to illustrate the validity of the proposed design approach.     

A Class of Filtering Superoptimal Preconditioners for Highly Ill-Conditioned Linear Systems

Popular preconditioners for conjugate gradient methods often reveal poor regularization properties that make them useless for very ill-conditioned linear systems arising in inverse problems. Recent results have awakened the interest towards the Tyrtyshnikov superoptimal preconditioners since it has been demonstrated that they exhibit good filtering capabilities. Here, in order to improve the regularizing behaviour, we generalize the definition of superoptimal preconditioner. Later on, by means of this more general definition, we develop a particular family of preconditioners for Toeplitz highly ill-conditioned linear systems.     

Inversion of Hyperoutput Time-Delay Systems

Doklady Mathematics - The inversion of a linear time-invariant time-delay system is considered. For such systems, a canonical form with isolated zero dynamics is obtained, system invariant zeros...     

随机时滞教学系统的最优习得策略

认识非线性随机时滞现象的内在机理、运演性态和掌握其内在规律己成为当今非线性随机动力学理论分析与数值分析的重要主题.基于教学论、自组织理论和非线性随机时滞动力学等理论及其有关研究成果,构建教学系统的非线性随机时滞Logistic模型,寻求教学系统的演化规律,并在此基础上研究教学系统的最优习得策略和提出相应教学建议,期望能促进教学系统有序发展;同时,也期望能促使教学论与非线性随机动力学等理论联姻,拓展与丰富教学论的研究领域,为教学论研究提供一个新的学科视角的支持与论证.     

Robust Reliable Control for Uncertain Time-Delay Systems with IQC Performance

A robust reliable control with integral quadratic constraint (IQC) performance for a class of uncertain systems with state and input delays is considered in this paper. Two classes of failure situations for sensor or actuator are studied. In the first class, a delay-dependent criterion for time-delay systems without perturbations is proposed to design the reliable control with IQC performance. Next, a criterion for uncertain time-delay systems with parameter uncertainties is obtained via simple derivations. The linear matrix inequality (LMI) approach is used to design a robust reliable state feedback control with IQC performance. In the second class, a reliable control with IQC performance is also provided from he previous method. A numerical example is given to illustrate the effectiveness of the procedure. The research reported here was supported by the National Science Council of Taiwan, ROC under Grant NSC 95-2221-E-022-019.     

一类非线性时滞混沌系统的自适应脉冲同步

针对一类非线性时滞混沌系统,提出了一种新的自适应脉冲同步方案.首先基于Lyapunov稳定性理论、自适应控制理论及脉冲控制理论设计了自适应控制器、脉冲控制器及参数自适应律,然后利用推广的Barbalat引理,理论证明响应系统与驱动系统全局渐近同步,并给出了相应的充分条件.方案利用参数逼近Lipschitz常数,从而取消了Lipschitz常数已知的假设.两个数值仿真例子表明本方法的有效性.     

非线性时滞系统的直接自适应模糊控制

针对一类具有摄动的严格反馈非线性时滞系统,基于后推设计方法,利用第一类模糊系统的逼近能力,提出了一种新的直接自适应控制方案。该方案避免了虚拟控制增益符号已知的假设。设计中引入连续鲁棒项对系统的摄动部分进行抑制。通过理论分析,证明了闭环系统是半全局一致终结有界的,跟踪误差收敛到一个小的残差集内。     

Inequalities for Subgradients of a Value Functional in Differential Games for Time-Delay Systems

Doklady Mathematics - A two-person zero-sum positional differential game is considered in which the motion of a dynamical system is described by a nonlinear delay equation and the initial motion...     

Finite-Dimensional Filtering and Control for Continuous-Time Nonlinear Systems

Abstract

A partially observed stochastic control problem is considered in continuous time where both the state and observation processes are given by non-linear dynamics. Measure change techniques applied to the cost process allow both state and observation processes to be thought of as linear. If the cost is given a special form, this transformation changes the original non-linear problem into a linear one.     

基于参数依赖Lyapunov泛函不确定时滞系统的H_∞性能分析

研究了具有凸多面体不确定性时滞系统的H∞性能分析问题.基于参数依赖的Lyapunov泛函,导出了系统具有给定H∞性能指标的充分条件.进而,将系统最优H∞性能指标的求取问题转化为一个具有线性矩阵不等式约束的凸优化问题,后者可以应用现有的凸优化方法方进行有效的求解.所提出的方法具有更小的保守性.最后,给出的数值例子说明了提出结果的有效性.     

On Observer Design for a Class of Nonlinear Systems Including Unknown Time-Delay

The observer design for nonlinear systems with unknown, bounded, time-varying delays, on both input and state, is still an open problem for researchers. In this paper, a new observer design for a class of nonlinear system with unknown, bounded, time-varying delay was presented. For the proof of the observer stability, a Lyapunov–Krasovskii function was chosen. Sufficient assumptions are provided to prove the practical stability of the proposed observer. Furthermore, the exponential convergence of the observer was proved in the case of a constant time delay. Simulation results were shown to illustrate the feasibility of the proposed strategy.

     

Optimal Control of Nonlinear Time-Delay Systems with Persistent Disturbances

This paper is concerned with the optimal control of a class of nonlinear time-delay systems affected by external persistent disturbances. A feedforward and feedback optimal control (FFOC) law, consisting of analytical linear feedforward and feedback terms and the limit of a compensation sequence, is obtained by a successive approximation approach (SAA). In order to obtain a physically realizable feedforward control, a disturbance observer is introduced in the exosystem. Simulation results demonstrate the validity of the SAA and the robustness of the FFOC. Communicated by Q. C. Zhao This work was supported by the National Natural Science Foundation of China, Grant 60574023 and the Natural Science Foundation of Qingdao City of China, Grant 05-1-JC-94.     

Optimal Disturbances of Bistable Time-Delay Systems Modeling Virus Infections

For bistable time-delay dynamical systems modeling the dynamics of viral infections and the virusinduced immune response, an efficient approach is proposed for constructing optimal disturbances of steady states with a high viral load that transfer the system to a state with a low viral load. Functions approximating the behavior of drugs within the framework of well-known pharmacokinetic models are used as basis functions. Optimal disturbances are sought in the W ₂ ¹ norm. It is shown that optimal disturbances found in this norm are superior to those found in the L₂ norm as applied to the development of adequate therapeutic strategies.     

Block Projection Methods for Linear Systems

The aim of this paper is to provide a theory of block projection methods for the solution of a system of linear equations with multiple right-hand sides. Our approach allows to obtain recursive algorithms for the implementation of these methods.     

Relaxation Methods for Non-Hermitian Linear Systems

For the matrix equation Ax = b, we consider here two splittings A = M₁ ? N₁ = M₂ ? N₂ of the matrix A, where M ₁ ? (A + A*)/2 is the Hermitian part of A, and M ₂ ? I + (A ? A*)/2 is the identity plus the skew-Hermitian part of A. To these two splittings of A, we apply an extrapolation, with extrapolation factor ω, and we find associated regions for ω, in the complex plane, for which these extrapolated splittings yield convergent iterative methods. From this, further applications to semiiterative methods are indicated.