Intelligent Control of Discrete Linear Systems Based on a Supervised Adaptive Multiestimation Scheme

A pole-placement based adaptive controller synthesised from a multiestimation scheme is designed for linear plants. A higher level switching structure between the various estimation schemes is used to supervise the reparameterisation of the adaptive controller in real time. The basic usefulness of the proposed scheme is to improve the transient response so that the closed-loop stability is guaranteed. The switching process is subject to a minimum dwelling or residence time within which the supervisor is not allowed to switch between the multiple estimation schemes. The high level supervision is based on the multiestimation identification scheme. The residence time condition guarantees the closed-loop stability. The above higher level switching structure is on-line supervised by a closed-loop tracking error based algorithm. This second supervision on-line tunes the free design parameters which appear as time varying weights in the loss function of the above switching structure. Thus, the closed-loop behaviour, compared to the constant parameter case one, is improved when the design parameter is not tightly initialised. Both supervisors are hierarchically organised in the sense that they act on the system at different rates. Furthermore, a projection algorithm has been considered in the estimation scheme in order to include a possible a priori knowledge of the estimates parameter vector value in the estimation algorithm.     

Robust recursive identification of multidimensional linear regression models

Stochastic adaptive estimation and control algorithms involving recursive prediction estimates have guaranteed convergence rates when the noise is not ‘too’ coloured, as when a positive-real condition on the noise mode is satisfied. Moreover, the whiter the noise environment the more robust are the algorithms. This paper shows that for linear regression signal models, the suitable introduction of while noise into the estimation algorithm can make it more robust without compromising on convergence rates. Indeed, there are guaranteed attractive convergence rates independent of the process noise colour. No positive-real condition is imposed on the noise model.     

Forward/backward prediction solution for adaptive noisy FIR filtering

An important and hard problem in signal processing is the estimation of parameters in the presence of observation noise. In this paper, adaptive finite impulse response (FIR) filtering with noisy input-output data is considered and two developed bias compensation least squares (BCLS) methods are proposed. By introducing two auxiliary estimators, the forward output predictor and the backward output predictor are constructed respectively. By exploiting the statistical properties of the cross-correlation function between the least squares (LS) error and the forward/backward prediction error, the estimate of the input noise variance is obtained; the effect of the bias can thereafter be removed. Simulation results are presented to illustrate the good performances of the proposed algorithms. Supported by the National Natural Science Foundation of China for Distinguished Young Scholars (Grant No. 60625104), the Ministerial Foundation of China (Grant No. A2220060039) and the Fundamental Research Foundation of BIT (Grant No. 1010050320810)     

Convergence of continuous-time partitioned adaptive state estimators

The asymptotic behaviour of Bayes optimal adaptive state estimation schemes (also called the partitioned adaptive estimation algorithms) for continuous-time linear dynamic Gauss-Markov systems with unknown parameters is investigated. The unknown system parameters are asssumed to belong to a finite set. The results are developed through, weak consistency of the maximum likelihood and the maximum a posteriori probability estimates of the unknown parameters.     

A constrained edit distance between unordered labeled trees

This paper considers the problem of computing a constrained edit distance between unordered labeled trees. The problem of approximate unordered tree matching is also considered. We present dynamic programming algorithms solving these problems in sequential timeO(|T ₁|×|T ₂|×(deg(T ₁)+deg(T ₂))× log₂(deg(T ₁)+deg(T ₂))). Our previous result shows that computing the edit distance between unordered labeled trees is NP-complete.This research was supported by the Natural Sciences and Engineering Research Council of Canada under Grant No. OGP0046373.     

一种基于二阶梯度估计的自适应算法

在自适应信号处理中得到广泛应用的LMS算法,对信号模型及特性有着极其严格的限 制,这些限制在很多实际情况中并不能保证得到满足.相对LMS算法,基于中心差的梯度估 计自适应算法,其适应面则要广泛得多.但是,该算法存在着收敛速度慢,所需采样点数多的 缺点.为此本文提出一种适应于平稳情况的新的估计算法,除首次估计需做采样外,在收敛过 程中无需再做采样.与传统的中心差算法相比,本文算法具有较快的收敛速度和较好的失调 性能.     

Univied Parallel Lattice Structures for Block Time—Recursive Real—Valued Duiscrete Gabor Transforms

In this paper,the 1-D real-valued discrete Gabor transform(RDGT)proposed in the previous work and its relationship with the complex-valued discrete Gabor transform(CDGT)are briefly reviewed.Block time-recursive RDGT algorithms for the efficient and fast computation of the 1-D RDGT coefficients and for the fast reconstruction of the original signal from the coefficients are developed in both critical sampling and oversampling cases.Unified parallel lattice structuires for the implementation of the algorithms are studied.And the computational complexity analysis and comparison show that the proposed algorithms provide a more efficient and faster approach to the computation of the discrete Gabor transforms.     

A fast and adaptive method for complex-valued SAR image denoising based on <Emphasis Type="Italic">l</Emphasis><Subscript><Emphasis Type="Italic">k</Emphasis></Subscript> norm regularization

This paper developed a fast and adaptive method for SAR complex image denoising based on l _k norm regularization, as viewed from parameters estimation. We firstly establish the relationship between denoising model and ill-posed inverse problem via convex half-quadratic regularization, and compare the difference between the estimator variance obtained from the iterative formula and biased Cramer-Rao bound, which proves the theoretic flaw of the existent methods of parameter selection. Then, the analytic expression of the model solution as the function with respect to the regularization parameter is obtained. On this basis, we study the method for selecting the regularization parameter through minimizing mean-square error of estimators and obtain the final analytic expression, which resulted in the direct calculation, high processing speed, and adaptability. Finally, the effect of regularization parameter selection on the resolution of point targets is analyzed. The experiment results of simulation and real complex-valued SAR images illustrate the validity of the proposed method. Supported by the National Natural Science Foundation of China (Grant No. 60572136), the Fundamental Research Fund of NUDT (Grant No. JC0702005)     

Fault-Tolerant Recursive Least-Squares Computations on a Mesh-Connected Parallel Processor

Recursive least squares (RLS) is a popular iterative method used for the modeling of systems while in operation. RLS provides an estimate for unknown parameters of a system based on some known parameters and inputs and outputs of that system. This technique is used frequently in digital signal processing and control applications, where it is not possible to completely determine the current state of the system. The RLS procedure incurs intensive computations in every iteration of the algorithm. To implement RLS in situ at a reasonable sampling rate, the complexity of the system's model must be reduced, or the available computing power must be increased. This paper examines methods for increasing the computing power by implementing RLS algorithms on a parallel processing platform. While there has been a large body of research on using parallel processors for the computation of adaptive algorithms, little of this research has examined fault tolerant aspects. As fault tolerance is a critical aspect of any real-time system, this work will examine some factors that should be considered when implementing a real-time adaptive algorithm on a parallel processor system.     

Adaptive control of Hammerstein–Wiener nonlinear systems

The Hammerstein–Wiener model is a block-oriented model, having a linear dynamic block sandwiched by two static nonlinear blocks. This note develops an adaptive controller for a special form of Hammerstein–Wiener nonlinear systems which are parameterized by the key-term separation principle. The adaptive control law and recursive parameter estimation are updated by the use of internal variable estimations. By modeling the errors due to the estimation of internal variables, we establish convergence and stability properties. Theoretical results show that parameter estimation convergence and closed-loop system stability can be guaranteed under sufficient condition. From a qualitative analysis of the sufficient condition, we introduce an adaptive weighted factor to improve the performance of the adaptive controller. Numerical examples are given to confirm the results in this paper.     

Identification of block-oriented nonlinear systems using orthonormal bases

In this paper, new noniterative algorithms for the identification of (multivariable) block-oriented nonlinear models consisting of the interconnection of linear time invariant systems and static nonlinearities are presented. The proposed algorithms are numerically robust, since they are based only on least squares estimation and singular value decomposition. Two different block-oriented nonlinear models are considered in this paper, viz., the Hammerstein model, and the Wiener model. For the Hammerstein model, the proposed algorithm provides consistent estimates even in the presence of colored output noise, under weak assumptions on the persistency of excitation of the inputs. For the Wiener model, consistency of the estimates can only be guaranteed in the noise free case. Key in the derivation of the results is the use of basis functions for the representation of the linear and nonlinear parts of the models. The performance of the proposed identification algorithms is illustrated through simulation examples of two benchmark problems drawn from the process control literature, viz., a binary distillation column and a pH neutralization process.     

Randomized competitive algorithms for the list update problem

We prove upper and lower bounds on the competitiveness of randomized algorithms for the list update problem of Sleator and Tarjan. We give a simple and elegant randomized algorithm that is more competitive than the best previous randomized algorithm due to Irani. Our algorithm uses randomness only during an initialization phase, and from then on runs completely deterministically. It is the first randomized competitive algorithm with this property to beat the deterministic lower bound. We generalize our approach to a model in which access costs are fixed but update costs are scaled by an arbitrary constantd. We prove lower bounds for deterministic list update algorithms and for randomized algorithms against oblivious and adaptive on-line adversaries. In particular, we show that for this problem adaptive on-line and adaptive off-line adversaries are equally powerful.A preliminary version of these results appeared in a joint paper with S. Irani in theProceedings of the 2nd Symposium on Discrete Algorithms, 1991 [17].This research was partially supported by NSF Grants CCR-8808949 and CCR-8958528.This research was partially supported by NSF Grant CCR-9009753.This research was supported in part by the National Science Foundation under Grant CCR-8658139, by DIMACS, a National Science Foundation Science and Technology center, Grant No. NSF-STC88-09648.     

盲信号分离的自适应算法研究

盲信号分离在信号处理界一直有着重要的地位,其目的就是要根据观测到的混合数据向量恢复出混合前的原始信号。论述LMS和RLS两种进行盲信号分离的自适应算法,并使用它们对合成数据进行实验,考察算法的特性和效果,并进行比较分析。结果表明：LMS算法与RLS算法相比,RLS算法的收敛性能更好一些,而RLS的稳定性则存在振荡问题,在实际应用中需要选择合适的方法和参数。     

A several complex variables approach to feedback stabilization of linear neutral delay-differential systems

In this paper we consider the problem of uniform asymptotic stabilization of neutral delay differential systems by a suitable choice of linear feedback law, where the controller is static and at timet ₀ has full knowledge ofx(t ₀) ⁿ as well asx(t ₀ – d) for finitely many delays present in the system. Using complex analysis in several variables in a Banach algebra context we present a solution to this problem in the form of a sufficient condition for the existence of such a stabilizing feedback gain. This condition is a weak form of (algebraic) reachability together with a condition, which we call resolvability, on the solution of an associated algebraic Riccati equation. In the case of commensurable delays our results apply to neutral systems having aD-operator which is stable in the sense of Cruz and Hale. In the non-commensurate case, our results hold for systems with aD-operator satisfying a stronger condition on the spectrum of the evolution equation, which we call formal stability. A graphical criterion, in the spirit of the multi-dimensional Nyquist theory, is presented for formal stability ofD. We find these results especially interesting in light of recent work [39] which shows that, for a special class of systems, formal stability is necessary for stabilization by a feedback gain of the type considered here. This, in fact, gives a counterexample [39] to the well known condition of Pandolfi [40].Included among our results is an extension to the neutral case of the result in [11] which states that if the pointwise Kronecker indices are constant then the system is feedback equivalent to a delay-free system. As corollaries to this result we obtain some existing results [33] on canonical forms for time-delay systems, and, in addition, exhibit a large class of systems which are resolvable.Research partially supported by NASA under Grant NSG-2265 and NSF under Grant ENG-79-09459.Research partially supported by the NSF under Grants ECS-8017184 an INT-7902976 at Washington University and ECS-8214262 at Cornell University.     

High Speed Adaptive Signal Progressing Using the Delta Operator

Fan, H., and De, P., High Speed Adaptive Signal Progressing Using the Delta Operator, Digital Signal Processing11 (2001), 3–34.In this paper the use of the delta operator, i.e., a scaled difference operator, in adaptive signal processing with fast sampling is presented. It is recognized that most discrete-time signals and systems are the result of sampling continuous-time signals and systems. When sampling is fast, all resulting signals and systems tend to become ill conditioned and thus difficult to deal with using the conventional algorithms. The delta operator based algorithms, as will be developed in this paper, are numerically better behaved under finite precision implementations for fast sampling. Therefore, they provide many improvements in terms of numerical accuracy and/or convergence speed. Furthermore, the delta operator based algorithms can in most cases be shown to have meaningful continuous-time limits as the sampling becomes faster and faster. Thus they function as a bridge in unifying discrete-time algorithms with continuous-time algorithms. This enhances our insight into and overall understanding of these various algorithms. In this paper, several well-known algorithms in statistical and adaptive signal processing will be cast into their delta operator counterparts. Some new delta operator based algorithms will also be developed. Whenever applicable, corresponding continuous-time limits of these delta operator based algorithms will be pointed out. Computer simulation results using finite precision implementation will also be presented for some of the new algorithms, which generally show much improvement compared with the results from using traditional algorithms.     

时变谐波参数检测

本文以自适应线性组合器为基础,采用递归最小二乘法进行时变谐波参数的跟踪检测。当信号的基波频率发生变化时,采用分段检测的思想,对每小段信号先采用插值快速傅立叶变换法检测该段基波频率,作为自适应线性组合器的输入,然后采用递归最小二乘法进行幅度和相位的跟踪检测。该方法利用递归最小二乘法跟踪速度快的特点,实现了时变谐波的快速跟踪检测。实验结果验证了所提方法的有效性和准确性。     

Recursive identification of time-varying systems: Self-tuning and matrix RLS algorithms

In this paper, a new parallel adaptive self-tuning recursive least squares (RLS) algorithm for time-varying system identification is first developed. Regularization of the estimation covariance matrix is included to mitigate the effect of non-persisting excitation. The desirable forgetting factor can be self-tuning estimated in both non-regularization and regularization cases. We then propose a new matrix forgetting factor RLS algorithm as an extension of the conventional RLS algorithm and derive the optimal matrix forgetting factor under some reasonable assumptions. Simulations are given which demonstrate that the performance of the proposed self-tuning and matrix RLS algorithms compare favorably with two improved RLS algorithms recently proposed in the literature.     

System reduction via truncated Hankel matrices

The problem of approximating Hankel operators of finite or infinite rank by lower-rank Hankel operators is considered. For efficiency, truncated Hankel matrices are used as the intermediate step before other existing algorithms such as theCF algorithms are applied to yield the desirable approximants. If the Hankel operator to be approximated is of finite rank, the order of approximation by truncated Hankel operators is obtained. It is also shown that when themths-number is simple, then rational symbols of the best rank-m Hankel approximants of thenth truncated Hankel matrices converge uniformly to the corresponding rational symbol of the best rank-m Hankel approximant of the original Hankel operator asn tends to infinity. Supported by SDIO/IST managed by the U.S. Army under Contract No. DAAL03-87-K-0025 and also supported by the National Science Foundation under Grant No. DMS 8602337. Supported by SDIO/IST managed by the U.S. Army under Contract No. DAAL03-87-K-0025. Supported by the National Science Foundation under Grant No. DMS 8602337.     

On the parallel-decomposability of geometric problems

There is a large and growing body of literature concerning the solutions of geometric problems on mesh-connected arrays of processors. Most of these algorithms are optimal (i.e., run in timeO(n ^1/d ) on ad-dimensionaln-processor array), and they all assume that the parallel machine is trying to solve a problem of sizen on ann-processor array. Here we investigate the situation where we have a mesh of sizep and we are interested in using it to solve a problem of sizen >p. The goal we seek is to achieve, when solving a problem of sizen >p, the same speed up as when solving a problem of sizep. We show that for many geometric problems, the same speedup can be achieved when solving a problem of sizen >p as when solving a problem of sizep.The research of M. J. Atallah was supported by the Office of Naval Research under Contracts N00014-84-K-0502 and N00014-86-K-0689, the Air Force Office of Scientific Research under Grant AFOSR-90-0107, the National Science Foundation under Grant DCR-8451393, and the National Library of Medicine under Grant R01-LM05118. Jyh-Jong Tsay's research was partially supported by the Office of Naval Research under Contract N00014-84-K-0502, the Air Force Office of Scientific Research under Grant AFOSR-90-0107, and the National Science Foundation under Grant DCR-8451393.     

When is a controllerH ∞-optimal?

This paper examines conditions under which a given single input, single output, linear time invariant control system isH ^∞-optimal with respect to weighted combinations of its sensitivity function and its complementary sensitivity function. The specific weighting functions considered are defined in terms of the given plant and nominal controller. This paper shows that a large class of practical controllers areH ^∞-optimal, including typical stable controllers. This research was supported in part by the National Science Foundation under Grant No. ECS-8451519, grants from Honeywell, 3M, Sperry, and E. F. Johnson Company, ONR Research Grant N00014-82-C-0157, and AFOSR Research Grant F49620-86-C-0001.