Quasi-ISS/ISDS observers for interconnected systems and applications

This paper considers interconnected nonlinear dynamical systems and studies observers for such systems. For single systems the notion of quasi-input-to-state dynamical stability (quasi-ISDS) for reduced-order observers is introduced and observers are investigated using error Lyapunov functions. It combines the main advantage of ISDS over input-to-state stability (ISS), namely the memory fading effect, with reduced-order observers to obtain quantitative information about the state estimate error. Considering interconnections quasi-ISS/ISDS reduced-order observers for each subsystem are derived, where suitable error Lyapunov functions for the subsystems are used. Furthermore, a quasi-ISS/ISDS reduced-order observer for the whole system is designed under a small-gain condition, where the observers for the subsystems are used. As an application, we prove that quantized output feedback stabilization for each subsystem and the overall system is achievable, when the systems possess a quasi-ISS/ISDS reduced-order observer and a state feedback law that yields ISS/ISDS for each subsystem and therefor the overall system with respect to measurement errors. Using dynamic quantizers it is shown that under the mentioned conditions asymptotic stability can be achieved for each subsystem and for the whole system.     

Enhancement on stability criteria for linear systems with interval time-varying delays

In this paper, the problem of stability for linear systems with interval time-varying delays is investigated. By constructing a suitable augmented Lyapunov-Krasovskii functional and utilizing Wirtinger-based integral inequality, two sufficient conditions for guaranteeing the asymptotic stability of the concerned systems are derived within the framework of linear matrix inequalities (LMIs). The superiority and validity of the proposed criteria are verified by comparing maximum delay bounds under various conditions via two numerical examples.     

Robust distributed maximum likelihood estimation with dependent quantized data

In this paper, we consider the distributed maximum likelihood estimation (MLE) with dependent quantized data under the assumption that the structure of the joint probability density function (pdf) is known, but it contains unknown deterministic parameters. The parameters may include different vector parameters corresponding to marginal pdfs and parameters that describe the dependence of observations across sensors. Since MLE with a single quantizer is sensitive to the choice of thresholds due to the uncertainty of pdf, we concentrate on MLE with multiple groups of quantizers (which can be determined by the use of prior information or some heuristic approaches) to fend off against the risk of a poor/outlier quantizer. The asymptotic efficiency of the MLE scheme with multiple quantizers is proved under some regularity conditions and the asymptotic variance is derived to be the inverse of a weighted linear combination of Fisher information matrices based on multiple different quantizers which can be used to show the robustness of our approach. As an illustrative example, we consider an estimation problem with a bivariate non-Gaussian pdf that has applications in distributed constant false alarm rate (CFAR) detection systems. Simulations show the robustness of the proposed MLE scheme especially when the number of quantized measurements is small.     

Optimal state estimation for stochastic systems: an informationtheoretic approach

In this paper, we examine the problem of optimal state estimation or filtering in stochastic systems using an approach based on information theoretic measures. In this setting, the traditional minimum mean-square measure is compared with information theoretic measures, Kalman filtering theory is reexamined, and some new interpretations are offered. We show that for a linear Gaussian system, the Kalman filter is the optimal filter not only for the mean-square error measure, but for several information theoretic measures which are introduced in this work. For nonlinear systems, these same measures generally are in conflict with each other, and the feedback control policy has a dual role with regard to regulation and estimation. For linear stochastic systems with general noise processes, a lower bound on the achievable mutual information between the estimation error and the observation are derived. The properties of an optimal (probing) control law and the associated optimal filter, which achieve this lower bound, and their relationships are investigated. It is shown that for a linear stochastic system with an affine linear filter for the homogeneous system, under some reachability and observability conditions, zero mutual information between estimation error and observations can be achieved only when the system is Gaussian     

广义离散随机线性系统自校正最优预报器

运用现代时间序列分析[1]的方法研究广义离散随机线性系统最优及自适应状态估计. 将状态估计转化为输出预报和白噪声估计,从而提出了系统的最优预报器,并且证明最优预 报器对于初始值的选取渐近稳定.在噪声统计未知时提出了自校正预报器.仿真例子说明了 其有效性.     

Optimal asymptotic identification under bounded disturbances

The intrinsic limitation of worst-case identification of linear time-invariant systems using data corrupted by bounded disturbances, when the unknown plant is known to belong to a given model set, is studied. This is done by analyzing the optimal worst-case asymptotic error achievable by performing experiments using any bounded input and estimating the plant using any identification algorithm. It is shown that under some topological conditions on the model set, there is an identification algorithm which is asymptotically optimal for any input, and the optimal asymptotic error is characterized as a function of the inputs. These results, which hold for any error metric and disturbance norm, are applied to three specific identification problems: identification of stable systems in the l₁ norm, identification of stable rational systems in the H_∞ norm and identification of unstable rational systems in the gap metric. For each of these problems, the general characterization of optimal asymptotic error is used to find near-optimal inputs to minimize the error     

一类具有Markov跳跃参数的不确定混合线性时滞系统鲁棒稳定性研究

讨论了一类具有Markov跳跃参数的不确定混合线性时滞系统的鲁棒稳定性问题．分别给出了非匹配条件下不确定部分范数上界已知时使混合线性系统以概率1渐近稳定的充分条件,和匹配条件下不确定部分范数上界未知时同样可以实现混合系统以概率1渐近稳定的鲁棒自适应控制设计方案．文章研究结果表明,此控制方案对混合线性时滞系统的不确定部分是有效的．     

Stability-constrained model predictive control

This paper presents a new approach to guaranteeing stability of model predictive control (MPC). A stability constraint is computed and propagated forward at each stage as a constraint on the magnitude of the predicted state vector for a state-space controllable-form realization. It is shown that asymptotic stability is guaranteed for the case of constrained multi-input linear time-invariant systems under full-state measurement or with state estimation for any prediction horizon and any optimization objective function     

On stability of linear time-delay systems with multiple delays

In this article, delay-dependent stability criteria for linear retarded and neutral systems with multiple delays are proposed by employing the Lyapunov-Krasovskii functional approach and integral inequality. By the N-segmentation of delay length, we obtain more relaxed results on the delay bounds which guarantee the asymptotic stability of the linear retarded and neutral systems with multiple delays. Simulation results show that the stability boundary calculated by the proposed stability criteria are very near to the real stability boundary of the example systems. Moreover, it is shown that the proposed stability criteria are less conservative than several other existing criteria.     

State feedback stabilization of discrete linear switching systems subject to nonsymmetrical state and control bounds

Stabilization problem of discrete-time linear switching systems with bounds on the state and control input is solved in this paper.First,the synthesis of state feedback controllers that ensure the stab...     

Improved results on stability and stabilization criteria for uncertain linear systems with time-varying delays

In this paper, the problems of stability and stabilization for linear systems with time-varying delays and norm-bounded parameter uncertainties are considered. By constructing augmented Lyapunov functionals and utilizing auxiliary function-based integral inequalities, improved delay-dependent stability and stabilization criteria for guaranteeing the asymptotic stability of the system are proposed with the framework of linear matrix inequalities. Four numerical examples are included to show that the proposed results can reduce the conservatism of stability and stabilization criteria by comparing maximum delay bounds.     

Stochastic linear control over a communication channel

We examine linear stochastic control systems when there is a communication channel connecting the sensor to the controller. The problem consists of designing the channel encoder and decoder as well as the controller to satisfy some given control objectives. In particular, we examine the role communication has on the classical linear quadratic Gaussian problem. We give conditions under which the classical separation property between estimation and control holds and the certainty equivalent control law is optimal. We then present the sequential rate distortion framework. We present bounds on the achievable performance and show the inherent tradeoffs between control and communication costs. In particular, we show that optimal quadratic cost decomposes into two terms: A full knowledge cost and a sequential rate distortion cost.     

A new optimal multirate control of linear periodic andtime-invariant systems

The optimal multirate design of linear, continuous-time, periodic and time-invariant systems is considered. It is based on solving the continuous linear quadratic regulation (LQR) problem with the control being constrained to a certain piecewise constant feedback. Necessary and sufficient conditions for the asymptotic stability of the resulting closed-loop system are given. An explicit multirate feedback law that requires the solution of an algebraic discrete Riccati equation is presented. Such control is simple and can be easily implemented by digital computers. When applied to linear time-invariant systems, multirate optimal feedback optimal control provides a satisfactory response even if the state is sampled relatively slowly. Compared to the classical single-rate sampled-data feedback in which the state is always sampled at the same rate, the multirate system can provide a better response with a considerable reduction in the optimal cost. In general, the multirate scheme offers more flexibility in choosing the sampling rates     

On the Achievable Delay Margin Using LTI Control for Unstable Plants

Handling delays in control systems is difficult and is of long-standing interest. It is well known that, given a finite-dimensional linear time-invariant (FDLTI) plant and controller forming a strictly proper stable feedback connection, closed-loop stability will be maintained under a small delay in the feedback loop, although most closed loop systems become unstable for large delays. One previously unsolved fundamental problem in this context is whether, for a given FDLTI plant, an arbitrarily large delay margin can be achieved using LTI control. Here, we adopt a frequency domain approach and demonstrate that, for a strictly proper real rational plant, there is a uniform upper bound on the delay that can be tolerated when using an LTI controller, if and only if the plant has at least one closed right half plane pole not at the origin. We also give several explicit upper bounds on the achievable delay margin, and, in some special cases, demonstrate that these bounds are tight.     

广义离散随机线性系统最优递推预报方法及其渐近稳定性

讨论广义离散随机线性系统最优状态估计问题,运用新息理论和射影的方法提出了 广义离散随机线性系统最优递推预报器和滤波器,证明了递推预报器对于初始值的选取渐近 稳定.     

Stability and robust stability of positive linear Volterra difference equations

We first introduce a class of positive linear Volterra difference equations. Then, we offer explicit criteria for uniform asymptotic stability of positive equations. Furthermore, we get a new Perron–Frobenius theorem for positive linear Volterra difference equations. Finally, we study robust stability of positive equations under structured perturbations and affine perturbations. Two explicit stability bounds with respect to these perturbations are given. Copyright © 2008 John Wiley & Sons, Ltd.     

An LMI based criterion for the global asymptotic stability of 2-D discrete state-delayed systems with saturation nonlinearities

This paper deals with the problem of global asymptotic stability of a class of two-dimensional (2-D) discrete systems described by the Fornasini–Marchesini second local state-space (FMSLSS) model in presence of saturation nonlinearities and state delays in each of the two independent directions of information propagation. A linear matrix inequality (LMI) based criterion for the global asymptotic stability of such systems is presented. It is shown that several previously reported stability criteria for 2-D discrete FMSLSS model with saturation nonlinearities are recovered from the presented approach as special cases.     

具有数据包丢失的离散随机不确定系统的线性最优满阶估值器

研究了具有数据包丢失和随机不确定性离散随机线性系统的状态估计问题.其中数据包丢失是随机的,且满足Bernoulli分布,系统矩阵中的随机不确定性由一个白色乘性噪声来描述.首先,通过配方方法,提出了最小均方意义下的无偏最优线性递推满阶滤波器.所提出的滤波器用到了当前时刻和最近时刻接收到的观测来保证线性最优性.与多项式滤波和增广滤波器相比,本文的滤波器具有较小的计算负担.然后,基于所获得的线性滤波器推导了线性最优预报器和平滑器.进一步研究了线性最优估值器的渐近稳定性,给出了稳态特性存在的一个充分条件.最后,通过两个仿真例子验证了所提估计算法的优越性.     

关于线性时变离散系统的稳定性

本文研究线性时变离散系统的稳定性，采用一种解的估计技巧，简化了［１］用Ｇａｕｓｓ－Ｓｅｉｄｅｌ迭代法建立的稳定性判据的证明，并获得一些新的代数判据。