Verification of approximate opacity for switched systems: A compositional approach

The security in information-flow has become a major concern for cyber–physical systems (CPSs). In this work, we focus on the analysis of an information-flow security property, called opacity. Opacity characterizes the plausible deniability of a system’s secret in the presence of a malicious outside intruder. We propose a methodology of checking a notion of opacity, called approximate opacity, for networks of discrete-time switched systems. Our framework relies on compositional constructions of finite abstractions for networks of switched systems and their approximate opacity-preserving simulation functions. Those functions characterize how close concrete networks and their finite abstractions are in terms of the satisfaction of approximate opacity. We show that such simulation functions can be obtained compositionally by assuming some small-gain type conditions and composing local simulation functions constructed for each switched subsystem separately. Additionally, assuming certain stability property of switched systems, we also provide a technique on constructing their finite abstractions together with the corresponding local simulation functions. Finally, we illustrate the effectiveness of our results through an example.     

On the Existence and Construction of Common Lyapunov Functions for Switched Discrete Systems

Under consideration is the problem of stability of switched discrete systems with the generalized homogeneous right-hand sides. The conditions are obtained for the existence of the common Lyapunov function, and a method for its construction is proposed in the form of a combination of the partial Lyapunov functions obtained for isolated subsystems. For a special case of linear three-dimensional systems, some algorithms are proposed for constructing common Lyapunov functions as quadratic and fourth degree forms. Some examples illustrate the effectiveness of the proposed approach.     

Functional regression modeling via regularized Gaussian basis expansions

We consider the problem of constructing functional regression models for scalar responses and functional predictors, using Gaussian basis functions along with the technique of regularization. An advantage of our regularized Gaussian basis expansions to functional data analysis is that it creates a much more flexible instrument for transforming each individual’s observations into functional form. In constructing functional regression models there remains the problem of how to determine the number of basis functions and an appropriate value of a regularization parameter. We present model selection criteria for evaluating models estimated by the method of regularization in the context of functional regression models. The proposed functional regression models are applied to Canadian temperature data. Monte Carlo simulations are conducted to examine the efficiency of our modeling strategies. The simulation results show that the proposed procedure performs well especially in terms of flexibility and stable estimates.     

On automorphisms of a distance-regular graph with intersection array {204, 175, 48, 1; 1, 12, 175, 204}

The research is focused on the question of proportional development in economic growth modeling. A multilevel dynamic optimization model is developed for the construction of balanced proportions for production factors and investments in a situation of changing prices. At the first level, models with production functions of different types are examined within the classical static optimization approach. It is shown that all these models possess the property of proportionality: in the solution of product maximization and cost minimization problems, production factor levels are directly proportional to each other with coefficients of proportionality depending on prices and elasticities of production functions. At the second level, proportional solutions of the first level are transferred to an economic growth model to solve the problem of dynamic optimization for the investments in production factors. Due to proportionality conditions and the homogeneity condition of degree 1 for the macroeconomic production functions, the original nonlinear dynamics is converted to a linear system of differential equations that describe the dynamics of production factors. In the conversion, all peculiarities of the nonlinear model are hidden in a time-dependent scale factor (total factor productivity) of the linear model, which is determined by proportions between prices and elasticities of the production functions. For a control problem with linear dynamics, analytic formulas are obtained for optimal development trajectories within the Pontryagin maximum principle for statements with finite and infinite horizons. It is shown that solutions of these two problems differ crucially from each other: in finite horizon problems the optimal investment strategy inevitably has the zero regime at the final stage, whereas the infinite horizon problem always has a strictly positive solution. A remarkable result of the proposed model consists in constructive analytical solutions for optimal investments in production factors, which depend on the price dynamics and other economic parameters such as elasticities of production functions, total factor productivity, and depreciation factors. This feature serves as a background for the productive fusion of optimization models for investments in production factors in the framework of a multilevel structure and provides a solid basis for constructing optimal trajectories of economic development.     

A new criterion to global exponential periodicity for discrete-time BAM neural network with infinite delays

The discrete-time bidirectional associative memory neural network with periodic coefficients and infinite delays is studied. And not by employing the continuation theorem of coincidence degree theory as other literatures, but by constructing suitable Liapunov function, using fixed point theorem and some analysis techniques, a sufficient criterion is obtained which ensures the existence and global exponential stability of periodic solution for the type of discrete-time BAM neural network. The obtained result is less restrictive to the BAM neural networks than previously known criteria. Furthermore, it can be applied to the BAM neural network which signal transfer functions are neither bounded nor differentiable. In addition, an example and its numerical simulation are given to illustrate the effectiveness of the obtained result.     

Estimates of reachable sets of multidimensional control systems with nonlinear interconnections

The paper is devoted to the problem of constructing external estimates for the reachable set of a multidimensional control system by means of vector estimators. A system is considered that permits a decomposition into several independent subsystems with simple structure (for example, linear subsystems), which are connected to each other by means of nonlinear interconnections. For each of the subsystems, an external estimate of the reachable set is assumed to be known; this estimate is representable in the form of a level set of some function satisfying a differential inequality. An estimate for the reachable set of the combined system is constructed with the use of estimates for subsystems. The method of deriving the estimates is based on constructing comparison systems for analogs of vector Lyapunov functions (value functions).     

Automated generation of LFT-based parametric uncertainty descriptions from generic aircraft models

A computer assisted modelling methodology is developed for the generation of linearized models with parametric uncertainties described by Linear Fractional Transformations (LFTs). The starting point of the uncertainty modelling is a class of generic nonlinear aircraft models with explicit parametric dependence used for simulation purposes. The proposed methodology integrates specialized software tools for object-oriented modelling, for simulation, and for numerical as well as symbolic computations. The methodology has many generic features being applicable to similar nonlinear model classes.     

A meta-heuristic approach for solving the Urban Network Design Problem

This paper proposes an optimisation model and a meta-heuristic algorithm for solving the urban network design problem. The problem consists in optimising the layout of an urban road network by designing directions of existing roads and signal settings at intersections. A non-linear constrained optimisation model for solving this problem is formulated, adopting a bi-level approach in order to reduce the complexity of solution methods and the computation times. A Scatter Search algorithm based on a random descent method is proposed and tested on a real dimension network. Initial results show that the proposed approach allows local optimal solutions to be obtained in reasonable computation times.     

A stage-structured predator-prey model with Beddington-DeAngelis functional response

In this paper, a stage-structured predator-prey model with Beddington-DeAngelis functional response is proposed and analyzed. It is assumed in the model that the individuals in each specie may belong to one of two classes: the immature and the mature, the age of maturity is represented by a time delay. By using the persistence theory for infinite dimensional systems, necessary and sufficient conditions for the permanence of the system are obtained. By constructing suitable Lyapunov functions and using an iterative technique, a set of easily verifiable sufficient conditions is also obtained for the local asymptotic stability and the global attractiveness of the positive equilibrium of the model.     

Optimization Models for Forest Road Upgrade Planning

Road blocking due to thawing or heavy rains annually contribute to a considerable loss in Swedish forestry. Companies are forced to build up large stocks of raw material (saw and pulp logs) in order to secure a continuous supply when access to the road network is uncertain. Storage outdoors leads to quality deterioration and monetary losses. Other related costs due to road blocking are road damage and longer haulage distances. One approach to reduce the losses due to road blocks is to upgrade the road network to a standard that guarantees accessibility. We consider the road upgrade problem from the perspective of Swedish forest companies with a planning horizon of about one decade. The objective is to minimize the combined upgrade and transportation costs. We present two mixed integer programming models, which are uncapacitated fixed charge network flow problems including multiple assortments, several time periods and a set of road classes. One model is based on arc flows and one on route flows. For a typical planning instance, the models become large and we propose how to improve solution performance through model strengthening. The models are tested in a case study for a major Swedish forest company.      

Performance analysis of an ISDN switch with distributed architecture: circuit switched calls

We have developed an approximate analytic model and a detailed simulation model to study the performance of an ISDN switch with distributed architecture. The analytic model treats the switch as a network of single server and infinite server queues with nonpreemptive priority service, general service times and batch arrivals. The simulation program is written in a distributed and modular way so as to simplify model development and debugging. Also extensive statistical techniques are employed for simulation output validation. It is observed that the analytic and the simulation models are in close agreement for the mean end-to-end delay and in moderately close agreement for the 95th percentile points of the end-to-end delay distribution. The comparisons between the analytic and the simulation models lead us to conjecture that the analytic model would be even more accurate for bigger systems with several hundred processors (where simulation models are too expensive to run). Even though the model assumes Poisson external call arrival process, it is shown that it may be applied with reasonable accuracy even when external call arrivals are non-Poisson. This is due to the fact that the composite message arrival process at a processor or transmission element tends to be close to Poisson even when the external call arrivals are non-Poisson.     

Nonintrusive reduced‐order modeling of parametrized time‐dependent partial differential equations

We propose a nonintrusive reduced‐order modeling method based on the notion of space‐time‐parameter proper orthogonal decomposition (POD) for approximating the solution of nonlinear parametrized time‐dependent partial differential equations. A two‐level POD method is introduced for constructing spatial and temporal basis functions with special properties such that the reduced‐order model satisfies the boundary and initial conditions by construction. A radial basis function approximation method is used to estimate the undetermined coefficients in the reduced‐order model without resorting to Galerkin projection. This nonintrusive approach enables the application of our approach to general problems with complicated nonlinearity terms. Numerical studies are presented for the parametrized Burgers' equation and a parametrized convection‐reaction‐diffusion problem. We demonstrate that our approach leads to reduced‐order models that accurately capture the behavior of the field variables as a function of the spatial coordinates, the parameter vector and time. © 2013 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 2013     

Existence and stability of periodic solutions of high-order Hopfield neural networks with impulses and delays

By using the continuation theorem of coincidence degree theory and constructing suitable Lyapunov functions, the global exponential stability and periodicity are investigated for a class of delayed high-order Hopfield neural networks (HHNNs) with impulses, which are new and complement previously known results. Finally, an example with numerical simulation is given to show the effectiveness of the proposed method and results. The numerical simulation shows that our models can occur in many forms of complexities including periodic oscillation and the Gui chaotic strange attractor.     

Rapid and modular prototyping-based Petri nets and distributed simulation for manufacturing systems

This paper presents an approach to simulate and implement by stepwise refinement the whole manufacturing system (MS) by means of distributed simulation. This approach is based on the use of different classes of Petri nets to model different levels of a manufacturing system. Furthermore these classes may match the abstraction levels of a high-level Petri net used to model the MS. Each level can be simulated on a processor or a cluster of processors which can communicate between themselves using a network. The main contribution is to give the opportunity to combine simulation, performance evaluation and emulation. The emulation means that a part of the system can be run in real time while the other part is simulated. Moreover based on the abstraction levels of high-level Petri nets, subsystems can be integrated step-by-step from the design stage to the implementation one, allowing inter-changeability between simulated components and real-time physical systems. This approach is achieved by defining a simulation engine which involves a local simulator, an emulator and an interface to the physical process. Criteria are defined to use an emulator or a local control software for a physical process as a logical process for the conservative distributed simulation.     

A Model for Evaluation of Transport Policies in Multimodal Networks with Road and Parking Capacity Constraints

This paper presents a model for evaluation of transport policies in multimodal networks with road and parking capacity constraints. The proposed model simultaneously considers choices of travelers on route, parking location and mode between auto and transit. In the proposed model, it is assumed that auto drivers make a simultaneous route and parking location choice in a user equilibrium manner, and the modal split between auto and transit follows a multinomial logit formulation. A mathematical programming model with capacity constraints on road link and parking facilities is proposed that generates optimality conditions equivalent to the requirements for multimodal network equilibrium. An augmented Lagrangian dual algorithm embedded by partial linearization approach is developed to solve the proposed model. Numerical results on two example networks are presented to illustrate the proposed methodology. The results show that the service level of transit, parking charges, road link and parking capacities, and addition of a new parking location may bring significant impacts on travelers’ behavior and network performance. In addition, transport policies may result in paradoxical phenomenon.     

Examples of entropy generating sequence

We introduce the notion of entropy generating sequence for infinite words and define its dimension when it exists. We construct an entropy generating sequence for each symbolic example constructed by Cassaigne such that the dimension of the sequence is the same as its topological entropy dimension. Hence the complexity can be measured via the dimension of an entropy generating sequence. Moreover, we construct a weakly mixing example with subexponential growth rate.     

Efficient simulation of discrete stochastic reaction systems with a splitting method

Stochastic reaction systems with discrete particle numbers are usually described by a continuous-time Markov process. Realizations of this process can be generated with the stochastic simulation algorithm, but simulating highly reactive systems is computationally costly because the computational work scales with the number of reaction events. We present a new approach which avoids this drawback and increases the efficiency considerably at the cost of a small approximation error. The approach is based on the fact that the time-dependent probability distribution associated to the Markov process is explicitly known for monomolecular, autocatalytic and certain catalytic reaction channels. More complicated reaction systems can often be decomposed into several parts some of which can be treated analytically. These subsystems are propagated in an alternating fashion similar to a splitting method for ordinary differential equations. We illustrate this approach by numerical examples and prove an error bound for the splitting error.