Stochastic Models to Mitigate Sparse Sensor Attacks in Continuous-Time Non-Linear Cyber-Physical Systems

Cyber-Physical Systems are very vulnerable to sparse sensor attacks.But current protection mechanisms employ linear and deterministic models which cannot detect attacks precisely.Therefore,in this paper,we propose a new non-linear generalized model to describe Cyber-Physical Systems.This model includes unknown multivariable discrete and continuous-time functions and different multiplicative noises to represent the evolution of physical processes and randomeffects in the physical and computationalworlds.Besides,the digitalization stage in hardware devices is represented too.Attackers and most critical sparse sensor attacks are described through a stochastic process.The reconstruction and protectionmechanisms are based on aweighted stochasticmodel.Error probability in data samples is estimated through different indicators commonly employed in non-linear dynamics(such as the Fourier transform,first-return maps,or the probability density function).A decision algorithm calculates the final reconstructed value considering the previous error probability.An experimental validation based on simulation tools and real deployments is also carried out.Both,the new technology performance and scalability are studied.Results prove that the proposed solution protects Cyber-Physical Systems against up to 92%of attacks and perturbations,with a computational delay below 2.5 s.The proposed model shows a linear complexity,as recursive or iterative structures are not employed,just algebraic and probabilistic functions.In conclusion,the new model and reconstructionmechanism can protect successfully Cyber-Physical Systems against sparse sensor attacks,even in dense or pervasive deployments and scenarios.

Numerical Experiments and Structural Transformation of Non-Linear Evolution in Ill-posed Systems

Numerical experiments on non-linear equations of the 1st-and 3rd-order derivatives have been carried out through structural analyses in the phase space according to the numerical instability of ill-posed systems,with changes of initial values and parameters,etc..The results show that the quantitative instability in an ill-posed system may reveal reversed transformation in system evolution by structural representation,and confirm A·Dauglas' theorem that "a non-linear equation does not satisfy the existence of the initial value in a linear well-posed system".

STATIONARITY OF A CLASS OF LARGE-SCALE DISCRETE-TIME STOCHASTIC SYSTEMS

Stationarity of a class of stochastically interconnecteil discrete-timesystems is analyzed by utilizins results from ergodic theory of general stateMarkov chains, incorporated with the so called large-scale system approach.

Periodic Solution for Stochastic Predator-Prey Systems with Nonlinear Harvesting and Impulses

In this paper, astochastic predator-prey systems with nonlinear harvesting and impulsive effect are investigated. Firstly, we show the existence and uniqueness of the global positive solution of the system. Secondly, by constructing appropriate Lyapunov function and using comparison theorem with an impulsive differential equation, we study that a positive periodic solution exists. Thirdly, we prove that system is globally attractive. Finally, numerical simulations are presented to show the feasibility of the obtained results.

The Average Power of a System under Random Excitation

The Taylor series expansion method is used to derive an approximation for theaverage total power of a non-linear system subjected to wide-band random excitation with zeromean value. The average dissipating power for non-linear systems subjected to randomexcitation is also discussed. The results of the derivation show that the average total power andthe average dissipating Power of a Systems are independent, of the dissipating force of the systemwhen excited by white noise. On the other hand, the average total energy is show,l to be inverselyproportional to damping,. The total power is dependent on both, the input and dissipating powerof the system.

Decentralised dynamic high-gain scaling-based output-feedback control of large-scale non-linear interconnected systems with delays

A general class of non-linear large-scale interconnected systems is considered,wherein each subsystem is comprised of a nominal part in a general strict-feedback-like structure and a set of appended dynamics.Parametric and functional uncertainties and time delays are allowed throughout the overall system structure including the nominal strictfeedback-like parts and appended dynamics of each subsystem as well as the non-linear subsystem interconnections.The controller design is based on the dual dynamic highgain scaling technique and provides a robust adaptive delay-independent globally stabilising decentralised output-feedback controller.The disturbance attenuation properties of the proposed output-feedback decentralised controller to an exogenous disturbance input are also analysed and specific conditions under which properties such as Input-toOutput-practical-Stability and asymptotic stabilisation are attained are also discussed.

A novel dynamic proportional-type iterative learning control design for non-linear systems

This paper presents a model-free adaptive iterative learning control(ILC)scheme called a proportional-type ILC scheme for non-linear systems.The obvious characteristic of the proposed ILC scheme is that we can easily finish the ILC task just utilising the Lipschitz constant of the system.In the proposed ILC scheme,the time-vary learning gain can be produced merely by input and output(I/O)measurements.Moreover,the convergence conclusion can be expressed by the ranges of the pseudo-partial derivative and the learning gain.In actual operation,a reasonable and useful convergence condition by a constant is also provided for selection.At last,the effectiveness of the proposed ILC scheme is shown by simulations.

Cooperative adaptive fuzzy control for a class of uncertain non-linear multi-agent systems with time delays

This paper studies the robust adaptive fuzzy cooperative tracking control problem for a class of uncertain non-linear multi-agent systems with multiple time delays and dead-zone non-linearities.First,based on the implicit function theorem,the non-affine form of the multi-agent system can be converted into the corresponding affine form.Then,using the local state information of neighbouring agents,a novel adaptive fuzzy cooperative tracking controller with the corresponding parameter-updated laws is designed based on undirected communication topologies.Furthermore,it is shown that all the closed-loop signals are bounded,and all follower nodes asymptotically tracking to the leader can be achieved in the presence of time-delayed perturbations and unknown dead-zone inputs.Finally,simulation results are given to demonstrate the effectiveness of the proposed adaptive control scheme.

Global stabilisation for a class of uncertain non-linear systems:a novel non-recursive design framework

In this paper,a novel global non-recursive stabilisation design framework is addressed for a class of inherent non-linear systems with the presence of system uncertainties and external nonvanishing disturbances.By virtue of the facility that the weighted homogeneity brings into the system synthesis procedure,a non-recursive design method is proposed to yield a globally effectiveness robust controller with its expression following a quasi-linear manner.By proceeding with a rigorous non-recursive stability analysis framework,which covers both global asymptotical and finite-time convergence cases,the common recursively treated derivative items in backsteppingbased methods are totally avoided.Inspired by the homogeneous domination technique,a scaling gain performed as a bandwidth factor is introduced into the original system and hence the robustness of the controlled system can be adjusted to meet the practical performance requirements.A numerical example and its control performance simulations are given to illustrate the effectiveness and simplicity of the proposed controller design framework.

THE MODEL VALIDATION OF DYNAMIC NEURAL NETWORKS

This paper investigates the problem of the model validation in identifying discrete-time-nonlinear dynamic systems by using neural networks with a single hidden layer.Based on the estimation theory,a synthetic error-index(SEI)criterion for the neural network models has been developed.By using the powerful training algorithm of recursive prediction error (RPE),two simulated non-linear systems are studied,and the results show that the synthetic error-index criterion can be used to verify the dynamic neural network models.Furthermore,the proposed technique is much simple in calculation than that of the effective correlation tests.Finally,some problems required by further study are discussed.

A Study on the Dynamic Performance of Hydroviscous Driyes

Gives a dynamic mathematical model of a typical type of multiple discs hydroviscous drive device which has been proved to be correct through tests.Utilizing the method of root-locus analysis the dynamic performance of this device is studied according to the model.Theoretical analysis and test re- suits show that the dynamic performance of the object of study can be greatly improved by speed negative feedback.

Liouville type theorems for Schrdinger systems

We study positive solutions to the following higher order SchrSdinger system with Dirichlet boundary conditions on a half space： where a is any even number between 0 and n. This PDE system is closely related to the integral system where G is the corresponding Green＇s function on the half space. More precisely, we show that every solution to （0.2） satisfies （0.1）, and we believe that the converse is also true. We establish a Liouville type theorem the non-existence of positive solutions to （0.2） under a very weak condition that u and v are only locally integrable. Some new ideas are involved in the proof, which can be applied to a system of more equations.

Robust adaptive passification and global stabilisation for uncertain switched nonlinear systems

In this paper,we focus on the problems of feedback passification and global stabilisation for a class of uncertain switched non-linear systems with parameter uncertainties and structural uncertainties.A state-dependent switching law and adaptive feedback controllers are designed to render the resulting closed-loop systems passive.The corresponding passivity-based adaptive stabilisation problems for these systems are solved.Finally,a numerical example is presented to illustrate the effectiveness of our method.

Basins of Attraction in the Copenhagen Problem Where the Primaries Are Magnetic Dipoles

We deal with the Copenhagen problem where the two big bodies of equal masses are also magnetic dipoles and we study some aspects of the dynamics of a charged particle which moves in the electromagnetic field produced by the primaries. We investigate the equilibrium positions of the particle and their parametric variations, as well as the basins of attraction for various numerical methods and various values of the parameter λ.

Quantization and Stable Attractors in a DissipativeOrbital Motion

We present a method for determining the motion of an electron in a hydrogen atom, which starts from a field Lagrangean foundation for non-conservative systems that can exhibit chaotic behavior. As a consequence, the problem of the formation of the atom becomes the problem of finding the possible stable orbital attractors and the associated transition paths through which the electron mechanical energy varies continuously until a stable energy state is reached.

Poly-contextural Logic： New Resource for Transdisciplinary Research in Sociology

A couple of decades ago natural phenomena began to be approached from a comprehensive and transdisciplinary point of view, as it was understood that living beings and their environments are not linear but complex. There is no doubt that this perspective of visualizing complexity and working inter- and trans-disciplinarily has to be applied. The reflection on the theoretical observation （i.e., meta-observation） involved in the concept of poly-contexturality is the framework in which a theory of complex systems is possible, which in turn enables an observation that oscillates （a concept of chaos theory） between models structured in a hierarchical order （normally linked to a logical-deductive formalization） and models structured in hetero-hierarchy. And this would allow this reflection to be done in a formalized language that does not follow either the principles of the Aristotelian logic or the postulates of the Kantian transcendental reflection. It is precisely this liberation from the dictates of mono-contextural logic what paves the way to an observation of complexity, in which one or the other language is used to model the states of things, such as the epistemological problems of molecular biology or the social systems. And-what is gaining relevance-it also paves the way to a true transdisciplinary meta-observation, since each discipline chooses its own contexture and only the use of poly-contexturality makes it possible to formulate transdisciplinary relationships within the framework of such meta-logic.

Generalized Coherent States for Position-Dependent Effective Mass Systems

A generalized scheme for the construction of coherent states in the context of position-dependent effective mass systems has been presented. This formalism is based on the ladder operators and associated algebra of the system which are obtained using the concepts of supersymmetric quantum mechanics and the property of shape invariance. In order to exemplify the general results and to analyze the properties of the coherent states, several examples have been considered.

Design and characterization of a multi-ring nested CMUT array for hydrophone

This paper presents the design,fabrication,packaging,and characterization of a high-performance CMUT array.The array,which features rectangular cells fabricated using a sacrificial release process,achieves a receiving sensitivity of-231.44 d B(re:1 V/μPa)with a 40 d B gain.Notably,the CMUT array exhibits a minimal sensitivity variation of just 0.87 d B across a temperature range of 0 to 60°C.Furthermore,the output voltage non-linearity at 1 k Hz is approximately 0.44%.These test results demonstrate that the reception performance of the 67-element CMUT array is superior to that of commercial transducers.The high performance and compact design of this CMUT array underscore its significant commercial potential for hydrophone applications.

The Multi-Step Differential Transform Method and Its Application to Determine the Solutions of Non-Linear Oscillators

In this paper,a reliable algorithm based on an adaptation of the standard differential transform method is presented,which is the multi-step differential transform method(MSDTM).The solutions of non-linear oscillators were obtained by MSDTM.Figurative comparisons between the MSDTM and the classical fourthorder Runge-Kutta method(RK4)reveal that the proposed technique is a promising tool to solve non-linear oscillators.

Identification of non-linear autoregressive models with exogenous inputs for room air temperature modelling

This paper proposes non-linear autoregressive models with exogenous inputs to model the air temperature ineach room of a Danish school building connected to the local district heating network. To obtain satisfactorymodels, the authors find it necessary to estimate the solar radiation effect as a function of the time of the dayusing a B-spline basis expansion. Furthermore, this paper proposes a method for estimating the valve positionof the radiator thermostats in each room using modified Hermite polynomials to ensure monotonicity of theestimated curve. The non-linearities require a modification in the estimation procedure: Some parametersare estimated in an outer optimisation, while the usual regression parameters are estimated in an inneroptimisation. The models are able to simulate the temperature 24 h ahead with a root-mean-square-errorof the predictions between 0.25℃ and 0.6℃. The models seem to capture the solar radiation gain in away aligned with expectations. The estimated thermostatic valve functions also seem to capture the importantvariations of the individual room heat inputs.