On system state equipartitioning and semistability in network dynamical systems with arbitrary time-delays

In many applications involving multiagent systems, groups of agents are required to agree on certain quantities of interest. In particular, it is important to develop consensus protocols for networks of dynamic agents with directed information flow, switching network topologies, and possible system time-delays. In this paper, we use compartmental dynamical system models to characterize dynamic algorithms for linear and nonlinear networks of dynamic agents in the presence of inter-agent communication delays that possess a continuum of semistable equilibria, that is, protocol algorithms that guarantee convergence to Lyapunov stable equilibria. In addition, we show that the steady-state distribution of the dynamic network is uniform, leading to system state equipartitioning or consensus. These results extend the results in the literature on consensus protocols for linear balanced networks to linear and nonlinear unbalanced networks with time-delays.     

On biologically inspired predictions of the global financial crisis

Early-warning models provide means for ex ante identification of elevated risks that may lead to a financial crisis. This paper taps into the early-warning literature by introducing biologically inspired models for predicting systemic financial crises. We create three models: a conventional statistical model, a back-propagation neural network (NN) and a neuro-genetic (NG) model that uses a genetic algorithm for choosing the optimal NN configuration. The models are calibrated and evaluated in terms of usefulness for policymakers that incorporates preferences between type I and type II errors. Generally, model evaluations show that biologically inspired models outperform the statistical model. NG models are, however, shown not only to provide largest usefulness for policymakers as an early-warning model, but also in form of decreased expertise and labor needed for, and uncertainty caused by, manual calibration of an NN. For better generalization of data-driven models, we also advocate adopting to the early-warning literature a training scheme that includes validation data.     

Failure prediction in the Russian bank sector with logit and trait recognition models

The Russian banking sector experienced considerable turmoil in the late 1990s, especially around the Russian banking crisis in 1998. The question is what types of banks are vulnerable to shocks and whether or not bank-specific characteristics can be used to predict vulnerability to failures. In this study we employ a parametric logit model and a nonparametric trait recognition approach to predict failures among Russian commercial banks. We modify the trait recognition approach such that the default probabilities are calculated directly without preliminary classification of cells in the voting matrix as safe or unsafe. We test the predictive power of the models based on their prediction accuracy using holdout samples. All models performed better than the benchmark; the modified trait recognition approach outperformed logit and the traditional trait recognition approach in both the original and the holdout samples. As expected liquidity plays an important role in bank failure prediction, but also asset quality and capital adequacy turn out to be important determinants of failure.     

Bayesian inference for differential equations

Nonlinear dynamic systems such as biochemical pathways can be represented in abstract form using a number of modelling formalisms. In particular differential equations provide a highly expressive mathematical framework with which to model dynamic systems, and a very natural way to model the dynamics of a biochemical pathway in a deterministic manner is through the use of nonlinear ordinary or time delay differential equations. However if, for example, we consider a biochemical pathway the constituent chemical species and hence the pathway structure are seldom fully characterised. In addition it is often impossible to obtain values of the rates of activation or decay which form the free parameters of the mathematical model. The system model in many cases is therefore not fully characterised either in terms of structure or the values which parameters take. This uncertainty must be accounted for in a systematic manner when the model is used in simulation or predictive mode to safeguard against reaching conclusions about system characteristics that are unwarranted, or in making predictions that are unjustifiably optimistic given the uncertainty about the model. The Bayesian inferential methodology provides a coherent framework with which to characterise and propagate uncertainty in such mechanistic models and this paper provides an introduction to Bayesian methodology as applied to system models represented as differential equations.     

A Modeling Framework for Troubleshooting Automotive Systems

This article presents a novel framework for modeling the troubleshooting process for automotive systems such as trucks and buses. We describe how a diagnostic model of the troubleshooting process can be created using event-driven, nonstationary, dynamic Bayesian networks. Exact inference in such a model is in general not practically possible. Therefore, we evaluate different approximate methods for inference based on the Boyen–Koller algorithm. We identify relevant model classes that have particular structure such that inference can be made with linear time complexity. We also show how models created using expert knowledge can be tuned using statistical data. The proposed learning mechanism can use data that is collected from a heterogeneous fleet of modular vehicles that can consist of different components. The proposed framework is evaluated both theoretically and experimentally on an application example of a fuel injection system.     

Solving the Problem of Dynamic Adaptability of Artificial Intelligence Systems that Control Dynamic Technical Objects

This paper investigates the increase in the response speed and stability of artificial intelligence systems that control dynamic technical objects. The problem of calculating the optimal time of switching an artificial intelligence system between software classes by the criterion of the rigidity degree of the model of a control object is considered. The solution of this problem is proposed for the general case of the control object dynamics when the rigidity of the mathematical model can significantly change during functioning and it is necessary to dynamically determine the moment of transition from standard methods of numerical integration to specialized numerical methods intended for calculating rigid dynamic models.     

Fixed-structure Gaussian process model

This article describes a method for modelling non-linear dynamic systems from measurement data. The method merges the linear local model blending approach in the velocity-based linearisation form with Bayesian Gaussian process (GP) modelling. The new Fixed-Structure GP (FSGP) model has a predetermined linear model structure with varying and probabilistic parameters represented by GP models. These models have several advantages for the modelling of local model parameters as they give us adequate results, even with small data sets. Furthermore, they provide a measure of the confidence in the prediction of the varying parameters and information about the dependence of the parameters on individual inputs. The FSGP model can be applied for the extended local linear equivalence class of non-linear systems. The obtained non-linear system model can be, for example, used for control-system design. The proposed modelling method is illustrated with a simple example of non-linear system modelling for control design.     

The design of smooth switching control with application to V/STOL aircraft dynamics under input and output constraints

This paper presents a smooth switching gain‐scheduled control approach for linear parameter varying (LPV) system dynamics, indexed by a scalar varying parameter. The proposed approach is demonstrated by application to the planar vertical/short takeoff and landing (V/STOL) aircraft dynamics subject to input and output constraints. In the design of switching control, the switch logic determines the switching process between control laws. The usual switching logics use the instantaneous switching manner, which can cause discontinuous chattering control signal. By performing convex weightings between two individual control laws for neighboring subsystems, the proposed smooth switching gain‐scheduled control approach can provide improved performance but does not arouse control signal chattering. For the studied application, the nonlinear aircraft dynamics are represented in the form of LPV systems with parameter dependence on attitude angle. The resulting design is verified by the obtained relative stability and time response simulations. Copyright © 2011 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society     

A gap metric based multiple model approach for nonlinear switched systems

Many applications in chemical engineering often exhibit a switching character due to the presence of discrete modes in the course of their operation. First principles models of such systems constructed using process simulators are far too complex for use in online applications, especially in model-based control. For such systems, numerous control-relevant modeling approaches have been reported in the literature such as mixed logic dynamical (MLD) models [1] and piece wise affine (PWA) [2] models among others. These models describe the evolution of states in each discrete mode using linear equations. Fewer control-relevant models have been reported that address the nonlinear behavior of switched systems. To model nonlinear hybrid systems, Nandola and Bhartiya [3] proposed a multiple linear model approach wherein multiple linear models are used to describe the dynamic behavior in each mode of the hybrid system. However, no guidelines were provided to select the number of models necessary in each mode and their region of validity. In this work, we address these lacunae by presenting a systematic multiple model approach to describe nonlinear switched systems. The method involves a trajectory based linearization and employs a model bank with a set of local linear models for each discrete operational mode. The model bank is generated by linearizing the first principles model across a carefully designed trajectory based on accuracy of multi-step ahead predictions. The numerous models thus obtained are clustered using the gap metric as the distance measure and representative models are selected. The selected linear models are aggregated using Bayesian or Fuzzy approaches to obtain the global model for the nonlinear switched system. A simulation case study of spherical two-tank system and an experimental case study of a benchmark problem consisting of three tanks are used to validate the proposed modeling strategy.     

Complex Probabilistic Modeling with Recursive Relational Bayesian Networks

A number of representation systems have been proposed that extend the purely propositional Bayesian network paradigm with representation tools for some types of first-order probabilistic dependencies. Examples of such systems are dynamic Bayesian networks and systems for knowledge based model construction. We can identify the representation of probabilistic relational models as a common well-defined semantic core of such systems.Recursive relational Bayesian networks (RRBNs) are a framework for the representation of probabilistic relational models. A main design goal for RRBNs is to achieve greatest possible expressiveness with as few elementary syntactic constructs as possible. The advantage of such an approach is that a system based on a small number of elementary constructs will be much more amenable to a thorough mathematical investigation of its semantic and algorithmic properties than a system based on a larger number of high-level constructs. In this paper we show that with RRBNs we have achieved our goal, by showing, first, how to solve within that framework a number of non-trivial representation problems. In the second part of the paper we show how to construct from a RRBN and a specific query, a standard Bayesian network in which the answer to the query can be computed with standard inference algorithms. Here the simplicity of the underlying representation framework greatly facilitates the development of simple algorithms and correctness proofs. As a result we obtain a construction algorithm that even for RRBNs that represent models for complex first-order and statistical dependencies generates standard Bayesian networks of size polynomial in the size of the domain given in a specific application instance.     

Identification of structural systems by neural networks

A method based on the use of neural networks is developed for the identification of systems encountered in the field of structural dynamics. The methodology is applied to the identification of linear and nonlinear dynamic systems such as the damped Duffing oscillator and the Van der Pol equation. The “generalization” ability of the neural networks is used to predict the response of the identified systems under deterministic and stochastic excitations. It is shown that neural networks provide high fidelity models of unknown structural dynamic systems, which are used in applications such as structural control, health monitoring of structures, earthquake engineering, etc.     

Bayesian sparse solutions to linear inverse problems with non-stationary noise with Student-t priors

Bayesian approach has become a commonly used method for inverse problems arising in signal and image processing. One of the main advantages of the Bayesian approach is the possibility to propose unsupervised methods where the likelihood and prior model parameters can be estimated jointly with the main unknowns. In this paper, we propose to consider linear inverse problems in which the noise may be non-stationary and where we are looking for a sparse solution. To consider both of these requirements, we propose to use Student-t prior model both for the noise of the forward model and the unknown signal or image. The main interest of the Student-t prior model is its Infinite Gaussian Scale Mixture (IGSM) property. Using the resulted hierarchical prior models we obtain a joint posterior probability distribution of the unknowns of interest (input signal or image) and their associated hidden variables. To be able to propose practical methods, we use either a Joint Maximum A Posteriori (JMAP) estimator or an appropriate Variational Bayesian Approximation (VBA) technique to compute the Posterior Mean (PM) values. The proposed method is applied in many inverse problems such as deconvolution, image restoration and computed tomography. In this paper, we show only some results in signal deconvolution and in periodic components estimation of some biological signals related to circadian clock dynamics for cancer studies.     

Switching fuzzy controller design based on switching Lyapunov function for a class of nonlinear systems

This paper presents a switching fuzzy controller design for a class of nonlinear systems. A switching fuzzy model is employed to represent the dynamics of a nonlinear system. In our previous papers, we proposed the switching fuzzy model and a switching Lyapunov function and derived stability conditions for open-loop systems. In this paper, we design a switching fuzzy controller. We firstly show that switching fuzzy controller design conditions based on the switching Lyapunov function are given in terms of bilinear matrix inequalities, which is difficult to design the controller numerically. Then, we propose a new controller design approach utilizing an augmented system. By introducing the augmented system which consists of the switching fuzzy model and a stable linear system, the controller design conditions based on the switching Lyapunov function are given in terms of linear matrix inequalities (LMIs). Therefore, we can effectively design the switching fuzzy controller via LMI-based approach. A design example illustrates the utility of this approach. Moreover, we show that the approach proposed in this paper is available in the research area of piecewise linear control.     

Neural associative memory with optimal Bayesian learning

Neural associative memories are perceptron-like single-layer networks with fast synaptic learning typically storing discrete associations between pairs of neural activity patterns. Previous work optimized the memory capacity for various models of synaptic learning: linear Hopfield-type rules, the Willshaw model employing binary synapses, or the BCPNN rule of Lansner and Ekeberg, for example. Here I show that all of these previous models are limit cases of a general optimal model where synaptic learning is determined by probabilistic Bayesian considerations. Asymptotically, for large networks and very sparse neuron activity, the Bayesian model becomes identical to an inhibitory implementation of the Willshaw and BCPNN-type models. For less sparse patterns, the Bayesian model becomes identical to Hopfield-type networks employing the covariance rule. For intermediate sparseness or finite networks, the optimal Bayesian learning rule differs from the previous models and can significantly improve memory performance. I also provide a unified analytical framework to determine memory capacity at a given output noise level that links approaches based on mutual information, Hamming distance, and signal-to-noise ratio.     

基于稀疏学习的微电网负载建模

微电网由负载、储能系统和分布式电源互联集成到能源系统中, 微电网系统可以作为一个整体系统与电网并行运行或以孤岛模式运行. 负载建模是微电网运行和管理中的一个基本问题. 本文着重解决以下两个关键问题: 1)协调负载模型结构的合理性和简洁性; 2)负载模型参数的校准. 与常规负载建模方法不同, 本文提出了一类数据驱动建模方法以同时实现负载模型结构选择和参数校准. 具体地, 该方法从量测数据中稀疏学习静态负载模型和动态负载模型, 其关键方法分别来自于稀疏贝叶斯学习方法和交替方向方法, 即从一组备选非线性字典函数中稀疏学习最主要的非线性项以平衡数据拟合度并实现模型学习. 所提出的方法将机器学习与稀疏表示相结合, 旨在对负载模型从物理角度提供机理解释并向配电网系统操作员提供有关负载的动态信息. 在孤岛微电网测试系统中验证并评估了所提出的算法. 研究测例表明所提出算法从量测数据中实现负载稀疏学习的合理性和对于噪声的鲁棒性.     

Modelling uncertainty in social–natural interactions

Socio-ecological systems can be represented as a complex network of causal interactions. Modelling such systems requires methodologies that are able to take uncertainty into account. Due to their probabilistic nature, Bayesian networks are a powerful tool for representing complex systems where interactions between variables are subject to uncertainty. In this paper, we study the interactions between social and natural subsystems (land use and water flow components) using hybrid Bayesian networks based on the Mixture of Truncated Exponentials model. This study aims to provide a new methodology to model systemic change in a socio-ecological context. Two endogenous changes – agricultural intensification and the maintenance of traditional cropland – are proposed. Intensification of the agricultural practices leads to a rise in the rate of immigration to the area, as well as to greater water losses through evaporation. By contrast, maintenance of traditional cropland hardly changes the social structure, while increasing evapotranspiration rates and improving the control over runoff water. These results indicate that hybrid Bayesian networks are an excellent tool for modelling social–natural interactions.     

Analytic framework for blended multiple model systems using linear local models

In this paper it is shown that the dynamics of a conventional type of blended multiple model system are only weakly related to the local models from which it is formed. A novel class of velocity-based blended multiple model systems is proposed for which the dynamics are directly related to the local models. Indeed, the solution to the blended multiple model system, locally to a specific operating point, is approximated by the weighted linear combination of the solutions to the local models. Moreover, in contrast to conventional blended multiple model systems, the velocity-based blended multiple model systems employs linear local models, thereby providing a degree of continuity with established linear methods and, consequently, facilitating analysis and design.     

Disagreement and Antagonism in Signed Networks: A Survey

Signed networks refer to a class of network systems including not only cooperative but also antagonistic interactions among nodes. Due to the existence of antagonistic interactions in signed networks, the agreement of nodes may not be established,instead of which disagreement behaviors generally emerge. This paper reviews several different disagreement behaviors in signed networks under the single-integrator linear dynamics, where two classes of topologies, namely, the static topology and the dy...