On Velocity‐Based Local Model Networks For Nonlinear Identification

This paper exposes the strengths and weaknesses of the recently proposed velocity‐based local model (LM) network. The global dynamics of the velocity‐based blended representation are directly related to the dynamics of the underlying local models, an important property in the design of local controller networks. Furthermore, the sub‐models are continuous‐time and linear providing continuity with established linear theory and methods. This is not true for the conventional LM framework, where the global dynamics are only weakly related to the affine sub‐models. In this paper, a velocity‐based multiple model network is identified for a highly nonlinear dynamical system. The results show excellent dynamical modelling performances, highlighting the value of the velocity‐based approach for the design and analysis of LM based control. Three important practical issues are also addressed. These relate to the blending of the velocity‐based local models, the use of normalised Gaussian basis functions and the requirement of an input derivative.     

Study of multi-branch structure of Universal Learning Networks

In this paper, multi-branch structure of Universal Learning Networks (ULNs) is studied to verify its effectiveness for obtaining compact models, which have neurons connected with other neurons using more than two branches having nonlinear functions. Multi-branch structure has been proved to have higher representation/generalization ability and lower computational cost than conventional neural networks because of the nonlinear function of the multi-branches and the reduction of the number of neurons to be used. In addition, learning of delay elements of multi-branch ULNs has improved their potential to build up a compact dynamical model with higher performances and lower computational cost when applied for identifying dynamical systems.     

Two highly efficient second-order algorithms for training feedforward networks

We present two highly efficient second-order algorithms for the training of multilayer feedforward neural networks. The algorithms are based on iterations of the form employed in the Levenberg-Marquardt (LM) method for nonlinear least squares problems with the inclusion of an additional adaptive momentum term arising from the formulation of the training task as a constrained optimization problem. Their implementation requires minimal additional computations compared to a standard LM iteration. Simulations of large scale classical neural-network benchmarks are presented which reveal the power of the two methods to obtain solutions in difficult problems, whereas other standard second-order techniques (including LM) fail to converge.     

Recursive identification of nonlinear plants operating in closed loop using kernel representations

In this paper, we extend the family of algorithms presented in Algorithms for identification of continuous time nonlinear systems. A passivity approach. In A. Isidori, F. Ramnabhi-Lagarrigue, & W. Respondek (Eds.), Nonlinear control in the year 2000, vol. 2 (pp. 13-44) Berlin: Springer; (Automatica 37 (2000) 469) for the identification of continuous time nonlinear plants operating in closed loop. The new algorithms presuppose that one can construct a stable kernel representation for the “to be identified model” structure. The new theory results in a less restrictive passivity condition. The main novelty is that the identification of unstable plants can be tackled by an appropriate choice of the kernel representation, i.e. there is an additional degree of freedom when constructing the kernel representation. The implicit stability of the controller is still required by the new passivity condition.     

图卷积网络增强的非负矩阵分解社区发现方法

非负矩阵分解（nonnegative matrix factorization,NMF）因其有效性和易解释性强被广泛应用于社区发现领域。然而,现有大多数基于NMF的社区发现方法都是线性的,无法有效处理复杂网络的非线性特征,从而导致社区发现性能还有待进一步提高。针对该问题,提出了一种图卷积网络（graph convolutional network,GCN）增强的非线性NMF社区发现方法NMFGCN。NMFGCN包含两个主要模块：GCN和NMF,其中GCN用于学习网络节点表示,NMF将节点表示作为输入获得网络的社区表示。此外,提出一个联合优化方法以训练NMFGCN,不仅使得NMFGCN具有非线性特征表示能力,而且可以使得GCN和NMF相互促进并获得更好的社区划分结果。在人工合成网络和真实网络上进行大量实验,结果表明NMFGCN优于目前基于NMF的社区发现方法,从而证明NMFGCN确实可以提高NMF社区发现方法的性能。此外,NMFGCN还优于DeepWalk和LINE常用图表示学习方法。     

Neural Networks Based Control of Mobile Robots: Development and Experimental Validation

The paper proposes a neural networks approach to the solution of the tracking problem for mobile robots. Neural networks based controllers are investigated in order to exploit the nonlinear approximation capabilities of the nets for modeling the kinematic behavior of the vehicle and for reducing unmodeled tracking errors contributions. The training of the nets and the control performances analysis have been done in a real experimental setup. The proposed solutions are implemented on a PC‐based control architecture for the real‐time control of the LabMate mobile base and are compared with classical kinematic control schemes. Experimental results are satisfactory in terms of tracking errors and computational efforts. © 2003 Wiley Periodicals, Inc.     

A SAX-GA approach to evolve investment strategies on financial markets based on pattern discovery techniques

This paper presents a new computational finance approach, combining a Symbolic Aggregate approXimation (SAX) technique together with an optimization kernel based on genetic algorithms (GA). The SAX representation is used to describe the financial time series, so that, relevant patterns can be efficiently identified. The evolutionary optimization kernel is here used to identify the most relevant patterns and generate investment rules. The proposed approach was tested using real data from S&P500. The achieved results show that the proposed approach outperforms both B&H and other state-of-the-art solutions.     

Multifeedback-Layer Neural Network

The architecture and training procedure of a novel recurrent neural network (RNN), referred to as the multifeedback-layer neural network (MFLNN), is described in this paper. The main difference of the proposed network compared to the available RNNs is that the temporal relations are provided by means of neurons arranged in three feedback layers, not by simple feedback elements, in order to enrich the representation capabilities of the recurrent networks. The feedback layers provide local and global recurrences via nonlinear processing elements. In these feedback layers, weighted sums of the delayed outputs of the hidden and of the output layers are passed through certain activation functions and applied to the feedforward neurons via adjustable weights. Both online and offline training procedures based on the backpropagation through time (BPTT) algorithm are developed. The adjoint model of the MFLNN is built to compute the derivatives with respect to the MFLNN weights which are then used in the training procedures. The Levenberg-Marquardt (LM) method with a trust region approach is used to update the MFLNN weights. The performance of the MFLNN is demonstrated by applying to several illustrative temporal problems including chaotic time series prediction and nonlinear dynamic system identification, and it performed better than several networks available in the literature     

基于Levenberg-Marquardt算法和最小二乘方法的小波网络混合学习算法

本文针对小波网络现有学习算法的不足,把Levenberg-Marquardt算法(简称LM算法)和最小二乘算法有机地结合在一起,提出了一种新的小波网络混合学习算法.在该混合算法中LM算法用来训练小波网络的非线性参数,而最小二乘算法用来训练线性参数.最后以辩识一个混沌系统为例进行了数值仿真,并与改进的BP算法和单纯LM算法进行了比较,结果说明了所提算法具有很好的收敛性能和收敛速度.     

A multiple model approach for predictive control of nonlinear hybrid systems

This paper presents modeling and control of nonlinear hybrid systems using multiple linearized models. Each linearized model is a local representation of all locations of the hybrid system. These models are then combined using Bayes theorem to describe the nonlinear hybrid system. The multiple models, which consist of continuous as well as discrete variables, are used for synthesis of a model predictive control (MPC) law. The discrete-time equivalent of the model predicts the hybrid system behavior over the prediction horizon. The MPC formulation takes on a similar form as that used for control of a continuous variable system. Although implementation of the control law requires solution of an online mixed integer nonlinear program, the optimization problem has a fixed structure with certain computational advantages. We demonstrate performance and computational efficiency of the modeling and control scheme using simulations on a benchmark three-spherical tank system and a hydraulic process plant.     

A general and easy computational method for functions of fuzzy numbers

Dong and Wong (1987) showed that the discretization method of Schmucker(1984) can give quite irregular and incorrect membership functions. The method of Dubois and Prade (1980) requires that the function be increasing over the solution space; and the nonlinear programming method of Baas and Kwakernaak (1977), although exact, requires very restrictive conditions, and its implementation is cumbersome except for the simplest algebraic functions. Therefore, the aim of the paper is to propose a general and easy computational method for functions of fuzzy numbers. We use the maximum (minimum) nonlinear programming method to derive the upper (lower) bound of the α-cut representation of fuzzy sets. Our nonlinear programming problem is to maximize (minimize) the combination of functions of fuzzy numbers, subject to the interval of the α-cut representation for functions of fuzzy numbers. The method has been implemented in a GINO package, and its results are general and efficient     

Subband neural networks prediction for on-line audio signal recovery

In this paper, a subbands multirate architecture is presented for audio signal recovery. Audio signal recovery is a common problem in digital music signal restoration field, because of corrupted samples that must be replaced. The subband approach allows for the reconstruction of a long audio data sequence from forward-backward predicted samples. In order to improve prediction performances, neural networks with spline flexible activation function are used as narrow subband nonlinear forward-backward predictors. Previous neural-networks approaches involved a long training process. Due to the small networks needed for each subband and to the spline adaptive activation functions that speed-up the convergence time and improve the generalization performances, the proposed signal recovery scheme works in online (or in continuous learning) mode as a simple nonlinear adaptive filter. Experimental results show the mean square reconstruction error and maximum error obtained with increasing gap length, from 200 to 5000 samples for different musical genres. A subjective performances analysis is also reported. The method gives good results for the reconstruction of over 100 ms of audio signal with low audible effects in overall quality and outperforms the previous approaches.     

On-line implementation of a nonlinear distributed observer for a multizone furnace — comparative study with a nonlinear filter

The dynamic behavior of an experimental multizone electrical furnace is described by nonlinear partial differential equations. On this basis, a nonlinear distributed observer of the load temperature profiles is designed. The resulting observer equations are discretized by orthogonal collocation on finite elements and implemented on-line on a PC. The observer shows very good properties: easy tuning, robustness and small computer resources. Some experimental results and computer simulations are presented and discussed. Moreover, a comparison is performed between the observer and a distributed extended Kalman filter, including on-line performances and computational implementation aspects. It is shown that the observer requires less computational effort for similar performances.     

Fast neural networks for diesel engine control design

Advanced engine control systems require accurate dynamic models of the combustion process, which are substantially nonlinear. This contribution presents the application of fast neural net models for engine control design purposes. After briefly introducing a special local linear radial basis function network (LOLIMOT) the process of building adequate dynamic engine models is discussed in detail. These neuro-models are then integrated into an upper-level emission optimization tool which calculates a cost function for exhaust versus consumption/torque and determines optimal engine settings. A DSP-based process computer system allows a fast application of the optimization tool at the engine test stand.     

Robust scalable stabilisability conditions for large-scale heterogeneous multi-agent systems with uncertain nonlinear interactions: towards a distributed computing architecture

Large-scale dynamic systems are becoming highly pervasive in their occurrence with applications ranging from system biology, environment monitoring, sensor networks, and power systems. They are characterised by high dimensionality, complexity, and uncertainty in the node dynamic/interactions that require more and more computational demanding methods for their analysis and control design, as well as the network size and node system/interaction complexity increase. Therefore, it is a challenging problem to find scalable computational method for distributed control design of large-scale networks. In this paper, we investigate the robust distributed stabilisation problem of large-scale nonlinear multi-agent systems (briefly MASs) composed of non-identical (heterogeneous) linear dynamical systems coupled by uncertain nonlinear time-varying interconnections. By employing Lyapunov stability theory and linear matrix inequality (LMI) technique, new conditions are given for the distributed control design of large-scale MASs that can be easily solved by the toolbox of MATLAB. The stabilisability of each node dynamic is a sufficient assumption to design a global stabilising distributed control. The proposed approach improves some of the existing LMI-based results on MAS by both overcoming their computational limits and extending the applicative scenario to large-scale nonlinear heterogeneous MASs. Additionally, the proposed LMI conditions are further reduced in terms of computational requirement in the case of weakly heterogeneous MASs, which is a common scenario in real application where the network nodes and links are affected by parameter uncertainties. One of the main advantages of the proposed approach is to allow to move from a centralised towards a distributed computing architecture so that the expensive computation workload spent to solve LMIs may be shared among processors located at the networked nodes, thus increasing the scalability of the approach than the network size. Finally, a numerical example shows the applicability of the proposed method and its advantage in terms of computational complexity when compared with the existing approaches.     

Harmonic distortion monitoring for nonlinear loads using neural-network-method

Nowadays, harmonic distortion in electric power systems is a power quality problem that has been attracting significant attention of engineering and scientific community. In order to evaluate the total harmonic distortion caused by particular nonlinear loads in power systems, the harmonic current components estimation becomes a critical issue. This paper presents an efficient approach to distortion metering, based on artificial neural networks applied to harmonic content estimation of load currents in single-phase systems. The harmonic content is computed using the estimation of amplitudes and phases of the first five odd harmonic components, which are carried out considering the waveform variations of current drained by nonlinear loads, within previously known limits. The proposed online monitoring method requires low computational effort and does not demand a specific number of samples per period at a fixed sampling rate, resulting in a low cost harmonic tracking system. The results from neural networks harmonic identification method are compared to the truncated fast Fourier transform algorithm. Besides, simulation and experimental results are presented to validate the proposed approach.     

Artificial bee colony algorithm-neural networks for S-system models of biochemical networks approximation

High-throughput technologies nowadays allow for the acquisition of biological data. These temporal profiles carry topological and kinetic information regarding the biochemical network from which they were drawn. Retrieving this information requires systematic application of both experimental and computational methods. S-systems are nonlinear mathematical approximate models based on the power-law formalism and provide a general framework for the simulation of integrated biological systems exhibiting complex dynamics, such as genetic circuits, signal transduction, and metabolic networks. However, S-systems need lots of iterations to obtain convergent gene expression profiles. For this reason, this study constructed a substitutive approach using artificial neural networks (ANNs) based on the artificial bee colony (ABC) algorithm with learning and training processes. This was used to obtain models and prove that our model (called ABC-NN) certainly is another method to acquire convergent gene expressions, except for S-systems, supported by our testing results.     

Solution time reduction techniques of a stochastic dynamic programming approach for hazardous material route selection problem

We use a stochastic dynamic programming (SDP) approach to solve the problem of determining the optimal routing policies in a stochastic dynamic network. Due to its long time for solving SDP, we propose three techniques for pruning stochastic dynamic networks to expedite the process of obtaining optimal routing policies. The techniques include: (1) use of static upper/lower bounds, (2) pre-processing the stochastic dynamic networks by using the start time and origin location of the vehicle, and (3) a mix of pre-processing and upper/lower bounds. Our experiments show that while finding optimal routing policies in stochastic dynamic networks, the last two of the three strategies have a significant computational advantage over conventional SDP. Our main observation from these experiments was that the computational advantage of the pruning strategies that depend on the start time of the vehicle varies according to the time input to the problem. We present the results of this variation in the experiments section. We recommend that while comparing the computational performances of time-dependent techniques, it is very important to test the performance of such strategies at various time inputs.     

Optimal taxiway repair: A set-covering approach

This paper describes an approach for optimizing a key element of air base recovery after attack—the repair of craters on linear taxiway segments. Drawing upon the concept of a minimal cut set, familiar in reliability engineering, an algebraic representation of the problem is developed in the form of a weighted set covering problem. This supplants the use of complex logical algorithms for checking the feasibility of solutions postulated during enumerative solution of the repair minimization problem. It is demonstrated that the algebraic representation leads to enhanced computational efficiency. Also, a potential advantage is suggested for the algebraic approach in facilitating extensions of repair minimization to nonlinear taxiway segments, including intersections.This research was sponsored by the Air Force Contact No. F08635-82-C-0252.