Bias‐eliminating least‐squares identification of errors‐in‐variables models with mutually correlated noises

This paper proposes a bias‐eliminating least‐squares (BELS) approach for identifying linear dynamic errors‐in‐variables (EIV) models whose input and output are corrupted by additive white noise. The method is based on an iterative procedure involving, at each step, the estimation of both the system parameters and the noise variances. The proposed identification algorithm differs from previous BELS algorithms in two aspects. First, the input and output noises are allowed to be mutually correlated, and second, the estimation of the noise covariances is obtained by exploiting the statistical properties of the equation error of the EIV model. Copyright © 2012 John Wiley & Sons, Ltd.     

Development of numerical linear algebra algorithms in dynamic fixed‐point format: a case study of Lanczos tridiagonalization

Proper range and precision analysis play an important role in the development of fixed‐point algorithms for embedded system applications. Numerical linear algebra algorithms used to find singular value decomposition of symmetric matrices are suitable for signal and image‐processing applications. These algorithms have not been attempted much in fixed‐point arithmetic. The reason is wide dynamic range of data and vulnerability of the algorithms to round‐off errors. For any real‐time application, the range of the input matrix may change frequently. This poses difficulty for constant and variable fixed‐point formats to decide on integer wordlengths during float‐to‐fixed conversion process because these formats involve determination of integer wordlengths before the compilation of the program. Thus, these formats may not guarantee to avoid overflow for all ranges of input matrices. To circumvent this problem, a novel dynamic fixed‐point format has been proposed to compute integer wordlengths adaptively during runtime. Lanczos algorithm with partial orthogonalization, which is a tridiagonalization step in computation of singular value decomposition of symmetric matrices, has been taken up as a case study. The fixed‐point Lanczos algorithm is tested for matrices with different dimensions and condition numbers along with image covariance matrix. The accuracy of fixed‐point Lanczos algorithm in three different formats has been compared on the basis of signal‐to‐quantization‐noise‐ratio, number of accurate fractional bits, orthogonality and factorization errors. Results show that dynamic fixed‐point format either outperforms or performs on par with constant and variable formats. Determination of fractional wordlengths requires minimization of hardware cost subject to accuracy constraint. In this context, we propose an analytical framework for deriving mean‐square‐error or quantization noise power among Lanczos vectors, which can serve as an accuracy constraint for wordlength optimization. Error is found to propagate through different arithmetic operations and finally accumulate in the last Lanczos vector. It is observed that variable and dynamic fixed‐point formats produce vectors with lesser round‐off error than constant format. All the three fixed‐point formats of Lanczos algorithm have been synthesized on Virtex 7 field‐programmable gate array using Vivado high‐level synthesis design tool. A comparative study of resource usage and power consumption is carried out. Copyright © 2015 John Wiley & Sons, Ltd.     

Design of unknown‐input reduced‐order observers for a class of nonlinear fractional‐order time‐delay systems

This paper considers the design of reduced‐order state observers for fractional‐order time‐delay systems with Lipschitz nonlinearities and unknown inputs. By using the Razumikhin stability theorem and a recent result on the Caputo fractional derivative of a quadratic function, a sufficient condition for the asymptotic stability of the observer error dynamic system is presented. The stability condition is obtained in terms of linear matrix inequalities, which can be effectively solved by using existing convex algorithms. Numerical examples and simulation results are given to illustrate the effectiveness of the proposed design approach.     

Experience replay–based output feedback Q‐learning scheme for optimal output tracking control of discrete‐time linear systems

This paper focuses on solving the adaptive optimal tracking control problem for discrete‐time linear systems with unknown system dynamics using output feedback. A Q‐learning‐based optimal adaptive control scheme is presented to learn the feedback and feedforward control parameters of the optimal tracking control law. The optimal feedback parameters are learned using the proposed output feedback Q‐learning Bellman equation, whereas the estimation of the optimal feedforward control parameters is achieved using an adaptive algorithm that guarantees convergence to zero of the tracking error. The proposed method has the advantage that it is not affected by the exploration noise bias problem and does not require a discounting factor, relieving the two bottlenecks in the past works in achieving stability guarantee and optimal asymptotic tracking. Furthermore, the proposed scheme employs the experience replay technique for data‐driven learning, which is data efficient and relaxes the persistence of excitation requirement in learning the feedback control parameters. It is shown that the learned feedback control parameters converge to the optimal solution of the Riccati equation and the feedforward control parameters converge to the solution of the Sylvester equation. Simulation studies on two practical systems have been carried out to show the effectiveness of the proposed scheme.     

CMOS high‐precision loser‐take‐all circuit

This paper presents a new current‐mode CMOS loser‐take‐all circuit. The proposed circuit consists of a basic cell that allows implementation of a multi‐input configuration by repeating the cell for each additional input. A high‐speed feedback structure is employed to determine the minimum current among the applied inputs. The significant feature of the circuit is its high accuracy and high‐speed operation. Additionally, the input dynamic range of the circuit can be efficiently controlled via the biasing current. HSPICE simulation results are presented to verify the performance of the circuit, where under a supply voltage of 2.5 V, bias current of 100 µA, and frequency of 10 MHz, the input dynamic range increases within 0–100 µA and the corresponding error remains as low as 0.4%. © 2014 Institute of Electrical Engineers of Japan. Published by John Wiley & Sons, Inc.     

The innovation algorithms for multivariable state‐space models

This paper derives the input‐output representation of the dynamical system described by a linear multivariable state‐space model and the corresponding multivariate linear regressive model (ie, multivariate equation‐error model). A projection identification algorithm, a multivariate stochastic gradient identification algorithm, and a multi‐innovation stochastic gradient (MISG) identification algorithm are proposed for multivariate equation‐error systems by using the negative gradient search and the multi‐innovation identification theory. The convergence analysis of the MISG algorithm indicates that the parameter estimation errors converge to zero under the persistent excitation condition. Finally, a numerical example illustrates the effectiveness of the proposed algorithms.     

Multi‐objective optimization power control for code division multiple access systems

In code division multiple access (CDMA) communication systems, the communication channel is usually corrupted with time‐varying interferences, which include channel fading, multiple access interference, round‐trip delay, and noise. Power control is an important issue for CDMA systems to achieve higher communication link quality and better system capacity under time‐varying interferences. In the previous studies, most of power control algorithms only considered the user's target signal‐to‐interference‐and‐noise‐ratio (SINR) to maintain quality of service. In this study, a multi‐objective optimization method is proposed for power control design in CDMA systems. With a shadow system and an h _∞ filter to compensate for the round‐trip delay, the proposed power control scheme can simply adjust transmission power to achieve the best compromise between several objectives, such as minimization of SINR deviation, minimization of power consumption, and minimization of the system outage. Several simulation results are given to confirm the performance of the proposed power control scheme. Copyright © 2013 John Wiley & Sons, Ltd.     

Generalized forgetting functions for on‐line least‐squares identification of time‐varying systems

The problem of on‐line identification of a parametric model for continuous‐time, time‐varying systems is considered via the minimization of a least‐squares criterion with a forgetting function. The proposed forgetting function depends on two time‐varying parameters which play crucial roles in the stability analysis of the method. The analysis leads to the consideration of a Lyapunov function for the identification algorithm that incorporates both prediction error and parameter convergence measures. A theorem is proved showing finite time convergence of the Lyapunov function to a neighbourhood of zero, the size of which depends on the evolution of the time‐varying error terms in the parametric model representation. Copyright © 2001 John Wiley & Sons, Ltd.     

Large‐scale super‐Gaussian sources separation using Fast‐ICA with rational nonlinearities

Independent component analysis (ICA) is one of the most powerful methods for solving blind source separation problem. In various ICA methods, the Fast‐ICA is an excellent algorithm, and it finds the demixing matrix that optimizes the nonlinear contrast function. There are three original contrast functions in the Fast‐ICA to separate super‐Gaussian and sub‐Gaussian sources, and their respective derivatives are similar to nonlinearities used in neural networks. For the separation of large‐scale super‐Gaussian sources, however, the contrast functions and the nonlinearities are not optimal owing to high computational cost. To solve this potential problem, this paper proposes four rational polynomial functions to replace the original nonlinearities. Because the rational polynomials can be quickly evaluated, when they are used in the Fast‐ICA, the computational load of the algorithms can be effectively reduced. The proposed rational functions are derived by the Pade approximant from Taylor series expansion of the original nonlinearities. To reduce the error of approximation, we make the behaviors of rational functions approach that of the original ones within an effective range as well as possible. The simulation results show that the Fast‐ICA algorithms with rational nonlinearities not only can speed up the convergence but also improve the separation performance of super‐Gaussian blind source separation. Copyright © 2016 John Wiley & Sons, Ltd.     

A convex optimization algorithm for frequency‐domain identification in the v‐gap metric

This paper proposes a convex optimization algorithm to minimize the v‐gap metric for parameter estimation of a SISO system using frequency‐domain measurements. According to a geometrical interpretation for this metric, its evaluation for two SISO linear systems is the supreme of sine values of the apertures between their normalized right graph symbols. As a result, the minimization of the v‐gap metric becomes that of the maximum of sine values of those apertures at sampling frequencies and can be efficiently solved by a sequence of feasibility problems with a decreasing line search. Compared with the related algorithms, the proposed one has global convergence and much lower computational loads. Finally, a numerical simulation shows the effectiveness of the proposed algorithm. Copyright © 2014 John Wiley & Sons, Ltd.     

Simulation error minimization identification based on multi‐stage prediction

Classical prediction error minimization (PEM) methods are widely used for model identification, but they are also known to provide satisfactory results only in specific identification conditions, e.g. disturbance model matching. If these conditions are not met, the obtained model may have quite different dynamical behavior compared with the original system, resulting in poor long range prediction or simulation performance, which is a critical factor for model analysis, simulation, model‐based control design. In the mentioned non‐ideal conditions a robust and reliable alternative is based on the minimization of the simulation error. Unfortunately, direct optimization of a simulation error minimization (SEM) criterion is an intrinsically complex and computationally intensive task. In this paper a low‐complexity approximate SEM approach is discussed, based on the iteration of multi‐step PEM methods. The soundness of the proposed approach is demonstrated by showing that, for sufficiently high prediction horizons, the k‐steps ahead (single‐ or multi‐step) PEM criteria converge to the SEM one. Identifiability issues and convergence properties of the algorithm are also discussed. Some examples are provided to illustrate the mentioned properties of the algorithm. Copyright © 2010 John Wiley & Sons, Ltd.     

Delay‐dependent model reduction for continuous‐time switched state‐delayed systems

This paper studies the problem of exponential H_∞ model reduction for continuous‐time switched delay system under average dwell time (ADT) switching signals. Time delay under consideration is interval time varying. Our attention is focused on the construction of the desired reduced order models, which guarantee that the resulting error systems under ADT switching signals are exponentially stable with an H_∞ norm bound. By introducing a block matrix and making use of the ADT approach, delay‐dependent sufficient conditions for the existence of reduced order models are derived and formulated in terms of strict linear matrix inequalities (LMIs). Owing to the absence of non‐convex constraints, it is tractable to construct an admissible reduced order model. The effectiveness of the proposed methods is illustrated via two numerical examples. Copyright © 2011 John Wiley & Sons, Ltd.     

Adaptive fuzzy backstepping dynamic surface control for a class of MIMO nonlinear systems with input delays and state time‐varying delays

In this paper, an adaptive fuzzy backstepping dynamic surface control (DSC) approach is developed for a class of MIMO nonlinear systems with input delays and state time‐varying delays. The unknown continuous nonlinear functions are expressed as the linearly parameterized form by using the fuzzy logic systems, and then, by combining the backstepping technique, the appropriate Lyapunov–Krasovskii functionals, and the ‘minimal learning parameters’ algorithms with the DSC approach, the adaptive fuzzy tracking controller is designed. Our development is able to eliminate the problem of ‘explosion of complexity’ inherent in the existing backstepping‐based methods. It is proven that the proposed design method can guarantee that all the signals in the closed‐loop system are bounded and the tracking error is smaller than a prescribed error bound. Finally, simulation results are provided to show the effectiveness of the proposed approach. Copyright © 2014 John Wiley & Sons, Ltd.     

Optimal and self‐tuning weighted measurement fusion Kalman filters and their asymptotic global optimality

For the multisensor linear discrete time‐invariant stochastic systems with unknown noise variances, using the correlation method, the information fusion noise variance estimators with consistency are given by taking the average of the local noise variance estimators. Substituting them into two optimal weighted measurement fusion steady‐state Kalman filters, two new self‐tuning weighted measurement fusion Kalman filters with a self‐tuning Riccati equation are presented. By the dynamic variance error system analysis (DVESA) method, it is rigorously proved that the self‐tuning Riccati equation converges to the steady‐state optimal Riccati equation. Further, by the dynamic error system analysis (DESA) method, it is proved that the steady‐state optimal and self‐tuning Kalman fusers converge to the global optimal centralized Kalman fuser, so that they have the asymptotic global optimality. Compared with the centralized Kalman fuser, they can significantly reduce the computational burden. A simulation example for the target tracking systems shows their effectiveness. Copyright © 2010 John Wiley & Sons, Ltd.     

Threshold computation for fault detection in a class of discrete‐time nonlinear systems

In this paper, we address the problem of designing robust thresholds for fault detection in discrete‐time nonlinear uncertain systems in the presence of process disturbances. Both constant and dynamic thresholds are proposed. For the computation of constant thresholds, a generalized framework based on signal norms is developed. Different kinds of constant thresholds are studied in the framework proposed. Using linear matrix inequalities (LMI) techniques, algorithms are derived for the computation of these thresholds. Similarly, the dynamic threshold is designed by deriving an inequality on the upper bound of the modulus of the residual signal. This inequality is based on the solution of discrete‐time nonlinear uncertain systems. The simulation examples illustrate that false alarms are successfully eliminated using the proposed thresholds. Copyright © 2010 John Wiley & Sons, Ltd.     

Three‐stage multiphase‐switched‐capacitor boost DC‐AC inverter

A closed‐loop scheme of a three‐stage multiphase‐switched‐capacitor boost DC‐AC inverter (MPSCI) is proposed by combining the multiphase operation and sinusoidal‐pulse‐width‐modulation (SPWM) control for low‐power step‐up DC‐AC conversion and regulation. In this MPSCI, the power unit contains two parts: MPSC booster (front) and H‐bridge (rear). The MPSC booster is suggested for an inductor‐less step‐up DC‐DC conversion, where three voltage doublers in series are controlled with multiphase operation for boosting voltage gain up to 2³ = 8 at most. The H‐bridge is employed for DC‐AC inversion, where four solid‐state switches in H‐connection are controlled with SPWM to obtain a sinusoidal AC output. In addition, SPWM is adopted for enhancing output regulation not only to compensate the dynamic error, but also to reinforce robustness to source/loading variation. The relevant theoretical analysis and design include: MPSCI model, steady‐state/dynamic analysis, voltage conversion ratio, power efficiency, stability, capacitance selection, total harmonic distortion (THD), output filter, and closed‐loop control design. Finally, the closed‐loop MPSCI is simulated, and the hardware circuit is implemented and tested. All the results are illustrated to show the efficacy of the proposed scheme. Copyright © 2011 John Wiley & Sons, Ltd.     

Sparse leaky‐LMS algorithm for system identification and its convergence analysis

In this paper, a novel adaptive filter for sparse systems is proposed. The proposed algorithm incorporates a log‐sum penalty into the cost function of the standard leaky least mean square (LMS) algorithm, which results in a shrinkage in the update equation. This shrinkage, in turn, enhances the performance of the adaptive filter, especially, when the majority of unknown system coefficients are zero. Convergence analysis of the proposed algorithm is presented, and a stability criterion for the algorithm is derived. This algorithm is given a name of zero‐attracting leaky‐LMS (ZA‐LLMS) algorithm. The performance of the proposed ZA‐LLMS algorithm is compared to those of the standard leaky‐LMS and ZA‐LMS algorithms in sparse system identification settings, and it shows superior performance compared to the aforementioned algorithms. Copyright © 2013 John Wiley & Sons, Ltd.     

Distributed‐Intelligence Approaches for Weighted Just‐in‐Time Production

This paper considers the dynamic flexible‐flow shop scheduling problem in which the manufacturing environment consists of multiple stages with multiple machines at each stage. All jobs must go through all stages in sequence in order to become a product, and the processing time for each product on each machine is different. There exists a delivery time between machines of neighboring stages, and the release time of each job is unknown, which means that a new job may be released into the system at any time. The objective of this work is to minimize the total earliness and tardiness penalties of all jobs, or to achieve just‐in‐time production. Previous researches did much on the static scheduling of such problem with different objectives, whereas little effort has been made on dynamic scheduling for such problem, which is more difficult than the static problem but becomes more and more important under the increasingly competitive manufacturing industry. Therefore, to address such need, efforts are made on dynamic scheduling and several distributed‐intelligence approaches are proposed in this paper. Featured by concurrent computing, the distributed‐intelligence approaches have been tested on two different manufacturing environments, whose result tells that the proposed approaches deliver competitive performance for the targeted problem. © 2010 Institute of Electrical Engineers of Japan. Published by John Wiley & Sons, Inc.     

Filter‐based perturbation control of low‐frequency oscillation in voltage‐mode H‐bridge DC–AC inverter

This paper presents a new additional perturbation control method for suppressing low‐frequency oscillation in voltage‐mode H‐bridge DC–AC inverter. The stability boundary of the H‐bridge inverter is investigated from its small‐signal averaged model. High input voltage and light load would cause low‐frequency oscillation in this system. To this end, a filter‐based perturbation control (FBPC) is proposed for eliminating this oscillation, by using an analog filter to extract the unexpected signal and applying it to the control loop. Theoretical results show a larger stability range of the controlled system with the proposed FBPC. The simulation and experiment results show that the proposed controller can control the low‐frequency oscillation in H‐bridge DC–AC inverter well. Copyright © 2014 John Wiley & Sons, Ltd.     

State estimation of discrete‐time systems with arbitrarily correlated noises

In this paper, the state estimation problem for discrete‐time systems is considered where the noises affecting such systems do not require any constraint condition for the correlation and distribution, that is, the noises can be arbitrarily correlated and arbitrarily distributed random vector. For this, two filtering algorithms based on the criterion of linear minimum mean‐square error are proposed. The first algorithm is an optimal algorithm that can exactly compute the linear minimum mean‐square error estimate of system states. The second algorithm is a suboptimal algorithm that is proposed to reduce the computation and storage load of the proposed optimal algorithm. Computer simulations are carried out to evaluate the performance of the proposed algorithms. Copyright © 2013 John Wiley & Sons, Ltd.