Parameter estimation in uncertain models of nonlinear dynamic systems

An extension of the classical least-squares identification technique is described and applied in a digital simulation study of a simple chemical reactor.     

Channel-parameter estimation for turbo trellis coded modulation in OFDM systems

In this paper, a blind maximum-likelihood channel-parameter estimation algorithm is developed for turbo trellis coded modulation (TTCM) in orthogonal frequency division multiplexing (OFDM) systems. We modify the Baum-Welch (BW) parameter estimation algorithm to provide a computationally efficient solution for error performance. The bit-error performance of the TTCM-OFDM scheme has been investigated in AWGN, Rayleigh, Rician channels with and without channel-state information (CSI) for different Doppler shifts, signal-to-noise ratios (SNR), iteration numbers, number of subcarriers, and frame sizes. Published in Russian in Radiotekhnika i Elektronika, 2007, Vol. 52, No. 3, pp. 458–468. The text was submitted by the authors in English.     

Recursive state estimation for linear dynamic systems under algebraic constraints

A minimum variance recursive linear estimator is discussed for linear dynamic systems where the state vector is also subject to linear algebraic equality constraints.<>     

Delay-dependent robust H_\infty control for 2-D discrete nonlinear systems with state delays

This paper investigates the problem of robust \(H_\infty \) control for a class of 2-D (two-dimensional) discrete state delayed systems with sector nonlinearity described by a model of Roesser type. Firstly, a delay-dependent sufficient condition of robust exponential stability for such 2-D discrete systems is derived in linear matrix inequalities (LMIs) form. Secondly, a delay-dependent exponential stability criterion with \(H_\infty \) performance for the considered systems is also proposed. Then a state feedback \(H_\infty \) controller is constructed based on the above results. Finally, numerical examples are given to illustrate the effectiveness of the proposed method.     

Joint state and parameter estimation for a target-directed nonlinear dynamic system model

We present a new approach to joint state and parameter estimation for a target-directed, nonlinear dynamic system model with switching states. The model, recently proposed for representing speech dynamics, is called the hidden dynamic model (HDM). The model parameters, subject to statistical estimation, consist of the target vector and the system matrix (also called "time-constants"), as well as parameters characterizing the nonlinear mapping from the hidden state to the observation. We implement these parameters as the weights of a three-layer feedforward multilayer perceptron (MLP) network. The new estimation approach is based on the extended Kalman filter (EKF), and its performance is compared with the traditional expectation-maximization (EM) based approach. Extensive simulation results are presented using both approaches and under typical HDM speech modeling conditions. The EKF-based algorithm demonstrates superior convergence performance compared with the EM algorithm, but the former suffers from excessive computational loads when adopted for training the MLP weights. In all cases, the simulated model output converges to the given observation sequence. However, only in the case where the MLP weights or the target vector are assumed known do the time-constant parameters converge to their true values. We also show that the MLP weights never converge to their true values, thus demonstrating the many-to-one mapping property of the feedforward MLP. We conclude that, for the system to be identifiable, restrictions on the parameter space are needed.     

Use of meixner functions in estimation of Volterra kernels of nonlinear systems with delay

Volterra series representation of nonlinear systems is a mathematical analysis tool that has been successfully applied in many areas of biological sciences, especially in the area of modeling of hemodynamic response. In this study, we explored the possibility of using discrete time Meixner basis functions (MBFs) in estimating Volterra kernels of nonlinear systems. The problem of estimation of Volterra kernels can be formulated as a multiple regression problem and solved using least squares estimation. By expanding system kernels with some suitable basis functions, it is possible to reduce the number of parameters to be estimated and obtain better kernel estimates. Thus far, Laguerre basis functions have been widely used in this framework. However, research in signal processing indicates that when the kernels have a slow initial onset or delay, Meixner functions, which can be made to have a slow start, are more suitable in terms of providing a more accurate approximation to the kernels. We, therefore, compared the performance of Meixner functions, in kernel estimation, to that of Laguerre functions in some test cases that we constructed and in a real experimental case where we studied photoreceptor responses of photoreceptor cells of adult fruitflies (Drosophila melanogaster). Our results indicate that when there is a slow initial onset or delay, MBF expansion provides better kernel estimates.     

The dynamics of group codes: state spaces, trellis diagrams, andcanonical encoders

A group code C over a group G is a set of sequences of group elements that itself forms a group under a component-wise group operation. A group code has a well-defined state space Σ_k at each time k. Each code sequence passes through a well-defined state sequence. The set of all state sequences is also a group code, the state code of C. The state code defines an essentially unique minimal realization of C. The trellis diagram of C is defined by the state code of C and by labels associated with each state transition. The set of all label sequences forms a group code, the label code of C, which is isomorphic to the state code of C. If C is complete and strongly controllable, then a minimal encoder in controller canonical (feedbackfree) form may be constructed from certain sets of shortest possible code sequences, called granules. The size of the state space Σ_k is equal to the size of the state space of this canonical encoder, which is given by a decomposition of the input groups of C at each time k. If C is time-invariant and ν-controllable, then |Σ_k|=Π_1⩽j⩽v|F_j/F _j-1|^j, where F₀ ⊆···⊆ Fν is a normal series, the input chain of C. A group code C has a well-defined trellis section corresponding to any finite interval, regardless of whether it is complete. For a linear time-invariant convolutional code over a field G, these results reduce to known results; however, they depend only on elementary group properties, not on the multiplicative structure of G. Moreover, time-invariance is not required. These results hold for arbitrary groups, and apply to block codes, lattices, time-varying convolutional codes, trellis codes, geometrically uniform codes and discrete-time linear systems     

Robust filtering for discrete nonlinear fractional transformation systems

In this brief, we consider robust filtering problems for uncertain discrete-time systems. The uncertain plants under consideration possess nonlinear fractional transformation (NFT) representations which are a generalization of the classical linear fractional transformation (LFT) representations. The proposed NFT is more practical than the LFT, and moreover, it leads to substantial performance gains as well as computational savings. For this class of systems, we derive linear-matrix inequality characterizations for H/sub 2/, & H/sub /spl infin//, and mixed filtering problems. Our approach is finally validated through a number of examples.     

An adaptive sliding-mode controller for discrete nonlinear systems

This paper presents a sliding-mode controller for a class of nonlinear discrete-time systems. The proposed controller uses a modified switching function that produces a low-chattering control signal. In order to improve the controller performance, an adaptive term is added to the original sliding-mode algorithm. This new feature uses an artificial neural network for online identification of the modeling error. Simulations and experimental results illustrate the main characteristics and performance of this approach,     

Nonlinear state estimation for uncertain systems with an integralconstraint

This paper considers a problem of robust filtering for a class of uncertain nonlinear systems. The solution involves a set-valued state estimate that is obtained by solving a Hamilton-Jacobi-Bellman equation. In addition, a less computationally intensive approximate solution to the problem is obtained for filtering problems defined over a large time interval. The paper also presents an approximate solution to the robust filtering problem, which leads to a robust version of the extended Kalman filter     

Separation of estimation and control for discrete time systems

An attempt is made to coordinate the numerous results relating to separation of estimation and control in discrete time stochastic control theory. The results vary widely depending upon the assumptions about linearity, criteria, information pattern, constraints, and noise distributions. Some of the less well-known underlying concepts are discussed with the help of a fairly general model.     

Robust iterative learning control with rectifying action for nonlinear discrete time-delayed systems

This paper addresses the two-dimensional (2-D) linear inequalities based robust Iterative Learning Control (ILC) for nonlinear discrete systems with time delays. The proposed two-gain ILC rule has a rectifying action to iterative initial error and external disturbances. It guarantees a reduced bound of the ILC tracking error against the iteration-varying initial error and disturbances. For the iteration-invariant initial error and disturbances, the ILC tracking error can be driven to convergence, and a complete tracking to reference trajectory beyond the initial time point is even achieved as the control gain is specifically selected. An example is used to validate the proposed ILC method.     

Background memory area estimation for multidimensional signalprocessing systems

Memory cost is responsible for a large amount of the chip and/or board area of customized video and image processing system realizations. In this paper, we present a novel technique-founded on data-flow analysis which allows one to address the problem of background memory size evaluation for a given nonprocedural algorithm specification, operating on multidimensional signals with affine indexes. Most of the target applications are characterized by a huge number of signals, so a new polyhedral data-flow model operating on groups of scalar signals is proposed. These groups are obtained by a novel analytical partitioning technique, allowing to select a desired granularity, depending on the application complexity. The method incorporates a way to tradeoff memory size with computational and controller complexity     

Implementation of indirect neuro-control for nonlinear dynamic systems

This paper represents identification and control designs using neural networks for a class of nonlinear dynamic systems. The proposed neuro-controller is a combination of a linear controller and a neural network trained by an indirect neuro-control scheme. The proposed neuro-controller is implemented and tested on an IBM PC-based bar system, and is applicable to many dc-motor-driven precision servo mechanisms. The algorithm and experimental results are described. The experimental results are shown to be superior to those of conventional control.     

SVM multiregression for nonlinear channel estimation in multiple-input multiple-output systems

This paper addresses the problem of multiple-input multiple-output (MIMO) frequency nonselective channel estimation. We develop a new method for multiple variable regression estimation based on Support Vector Machines (SVMs): a state-of-the-art technique within the machine learning community for regression estimation. We show how this new method, which we call M-SVR, can be efficiently applied. The proposed regression method is evaluated in a MIMO system under a channel estimation scenario, showing its benefits in comparison to previous proposals when nonlinearities are present in either the transmitter or the receiver sides of the MIMO system.     

一种非线性动态网络的离散分析算法设计及实现

在非线性动态网络响应分析中,采用Volterra级数法可以导出与线性系统传递函数相似的非线性传递函数,能使非线性系统用线性化和系统化方法达到精确分析.本文利用方波函数的积分变换具有将时域内的微分、积分运算变换成方波域内的矩阵代数运算的性质,将一类非线性动态网络响应求解的Volterra级数解的连续时域递推算法转化为离散算式,解决了连续算式中广义卷积积分的迭加计算麻烦的问题.文中给出了该算法,仿真结果证明了它的有效性.     

Static state estimation in electric power systems

A static state estimator is a collection of digital computer programs which convert telemetered data into a reliable estimate of the transmission network structure and state by accounting for 1) small random metering-communication errors; 2) uncertainties in system parameter values; 3) bad data due to transients and meter-communication failures; and 4) errors in the network structure due to faulty switch-circuit breaker status information. The overall state estimation process consists of four steps: 1) hypothesize mathematical structure; 2) estimate state vector; 3) detect bad data and/or structure errors; and identify bad data and/or structure errors. The problem is characterized by high dimensionality and the need for real-time solutions using limited computer time and storage. Various methods of solution are discussed and compared.