Linear Physical Systems Research Articles

Optimal control for linear cyber physical systems under replay attacks via time delay estimation approach

We mainly study the optimal control problem for linear cyber physical systems under replay attacks in this paper. The methodological research mainly relies on the following two starting points: (1) Promptly detect and estimate the malicious replay attack behaviours hampering normal system procedures; (2) Design a resilient optimal control strategy to ensure the system regularly works as much as possible. Specifically, the linear cyber physical system becomes a time delay system after the replay attack, and then an algorithm is designed to transform the system into a delay-free system and ensure its stability. Finally, a numerical simulation is employed to demonstrate the practicality and efficacy of the proposed approach.

Momentum and angular momentum reciprocity theorems for acoustic fields.

As a universal theorem applicable to linear physical systems, reciprocity theorems describe the reciprocity between the input and output of linear systems. As for the electromagnetic field, there have been detailed studies on the reciprocity theorems of energy, momentum, and angular momentum, which reveal the correlation between two electromagnetic field sources from different aspects. Based on the fundamentals of linear acoustic theory, the momentum-based and angular momentum-based reciprocity theorems for acoustic fields are derived. They indicate the correlation between two acoustic systems from the perspective of momentum and angular momentum, respectively. On this basis, a systematic summary and analogical study is also performed on various reciprocity theorems for acoustic and electromagnetic fields, which deepens our understanding of the reciprocity theorem as a universal law for linear physical fields. The results obtained in this work can further improve the reciprocity theory of linear acoustic systems, as well as provide theoretical guidance for practical applications, such as audio signal processing and acoustic measurement.

A unified methodology for the power efficiency analysis of physical systems

In this paper, the problem of power efficiency evaluation for n-ports physical systems is investigated. The efficiency analysis that we perform highlights the necessary and sufficient conditions for the system to be passive, and outlines the guidelines for the efficiency maps computation. After addressing the problem from a formal point of view, the analysis is deepened for the case of two-ports linear and nonlinear physical systems, and for the cases of three and four-ports linear systems. The efficiency analysis and the computation of the efficiency maps are addressed as a function of the power variables characterizing all the energetic ports of the considered systems. Furthermore, the salient properties of the efficiency are highlighted and discussed. The theoretical analysis which is developed is then applied to some physical systems of interest for industries and engineers working in the electromechanical, hydraulic and automotive fields: a DC electric motor driving an hydraulic pump for the two-ports systems class, a single-stage planetary gear set for the three-ports systems class, and a Ravigneaux planetary gear set for the four-ports systems class.

Information theory-based direct causality measure to assess cardiac fibrillation dynamics.

Understanding the mechanism sustaining cardiac fibrillation can facilitate the personalization of treatment. Granger causality analysis can be used to determine the existence of a hierarchical fibrillation mechanism that is more amenable to ablation treatment in cardiac time-series data. Conventional Granger causality based on linear predictability may fail if the assumption is not met or given sparsely sampled, high-dimensional data. More recently developed information theory-based causality measures could potentially provide a more accurate estimate of the nonlinear coupling. However, despite their successful application to linear and nonlinear physical systems, their use is not known in the clinical field. Partial mutual information from mixed embedding (PMIME) was implemented to identify the direct coupling of cardiac electrophysiology signals. We show that PMIME requires less data and is more robust to extrinsic confounding factors. The algorithms were then extended for efficient characterization of fibrillation organization and hierarchy using clinical high-dimensional data. We show that PMIME network measures correlate well with the spatio-temporal organization of fibrillation and demonstrated that hierarchical type of fibrillation and drivers could be identified in a subset of ventricular fibrillation patients, such that regions of high hierarchy are associated with high dominant frequency.

Convolução como um apelo da natureza

In this manuscript, we show in an educational way, how the operation known as convolution works. This is an important subject as it has a relevant physical appeal. At first, we will discuss the sampling concept where we will briefly focus on the decomposition of signals through a function known as impulse function. We address the impulse function and talk about the peculiarities of its representation in the discrete domain. We then talk about time signal shifts and address some very simple algorithms that deal with the pure convolution problem, without noise and without filters, in an elementary focus. We will deep-dive into the concept with the convolution integral culminating to the discussion with the Toeplitz matrix which is a key component of discrete convolution. It is worth mentioning that the methodology used in this work is simple and may offer the possibility to test a linear physical system for any input, a subject that is little treated in current literature. Finally, we conclude with some notes on the famous operation which has been used a long time for testing linear and time invariant physical systems, as it is very important in real applications in signals, telecommunication and image processing.

Universality of the amplitude shift in fast two-pulse collisions in weakly perturbed linear physical systems

We demonstrate the universal soliton-like behavior of the amplitude shifts in fast two-pulse collisions in perturbed linear physical systems with weak nonlinear dissipation. The behavior is demonstrated for linear optical waveguides with weak cubic loss and for systems described by linear diffusion–advection models with weak quadratic loss. We show by a perturbative calculation that in both systems, the expressions for the collision-induced amplitude shifts due to nonlinear loss have the same form as the expression obtained for a fast collision between solitons of the nonlinear Schrödinger equation in the presence of weak cubic loss. Moreover, we show that the expressions for the amplitude shifts are universal in the sense that they are independent of the details of the initial pulse shapes. We check the analytic predictions by extensive numerical simulations with the two perturbed linear evolution models with four major types of initial pulses corresponding to pulses with exponentially decreasing tails, two types of pulses with power-law decreasing tails, and pulses that are initially nonsmooth. In all cases, we observe a very good agreement between analytic predictions and numerical simulations. Thus, our study significantly generalizes the results of previous studies, which were limited to the special case of Gaussian-pulse collisions.

Transitivity of Commutativity for Linear Time-Varying Physical Systems

In this contribution, the transitivity property of commutative first-order linear time-varying systems with and without initial conditions is investigated. It is proven that transitivity property of first-order systems holds with and without initial conditions. On the base of impulse response function, transitivity of commutation property is formulated for any triplet of commutative linear time-varying relaxed systems. Transitivity proves are given for some special combinations of first and second-order linear time-varying systems which are initially relaxed.

Vulnerabilities of Control Systems in Internet of Things Applications

In this paper, we present some initial results about vulnerability of control systems that can be used in Internet of Things (IoT) applications. Up to our best knowledge, this paper is the first study about vulnerability of applied control systems in general, and especially in the IoT environment. The purpose of this paper is to examine fundamentals of linear control systems and consider vulnerability of its main features and concepts used in IoT applications under potential malicious attacks. We examine vulnerabilities of system stability, controllability, observability, design of feedback loops, and design and placement of sensors and controllers (actuators). The detailed study is limited to the most important vulnerability issues in time-invariant, unconstrained, deterministic, and linear physical systems. Several interesting and motivating examples are provided. We have outlined also some basic vulnerability studies for time-invariant nonlinear unconstrained systems, and indicate that such a study is particularly needed for distributed parameter systems that are very prone to outside physical and cyber-attacks.

Finite time attack detection and supervised secure state estimation for CPSs with malicious adversaries

In this paper, we investigate the finite time attack detection and secure state estimation problem for linear cyber physical systems (CPS) with s out of p sensors being attacked. By exploring the distinct properties of the undetectable and indistinguishable attacks to a CPS, novel explicit criteria on the detectability and distinguishability of the CPS under attack are proposed in terms of the r-resilient observability. This enables us to explicitly characterize the undetectable and/or indistinguishable attacks to the CPS. Then based on such characterization, we propose a finite time detector to solve the attack detection problem and a finite time alarm event driven supervised estimator to solve the secure state estimation problem, separately. Theoretical analysis shows that, the proposed detector and estimator can detect attacks and estimate the state within a prescribed finite time, respectively. Finally, some numerical simulations on an unmanned ground vehicle as an illustration of attack detection and secure state estimation is proposed to verify the effectiveness of the proposed schemes.

Soliton-like behavior in fast two-pulse collisions in weakly perturbed linear physical systems

We demonstrate that pulses of linear physical systems, weakly perturbed by nonlinear dissipation, exhibit soliton-like behavior in fast collisions. The behavior is demonstrated for linear waveguides with weak cubic loss and for systems described by linear diffusion-advection models with weak quadratic loss. We show that in both systems, the expressions for the collision-induced amplitude shifts due to the nonlinear loss have the same form as the expression for the amplitude shift in a fast collision between two optical solitons in the presence of weak cubic loss. Our analytic predictions are confirmed by numerical simulations with the corresponding coupled linear evolution models with weak nonlinear loss. These results open the way for studying dynamics of fast collisions between pulses of weakly perturbed linear physical systems in an arbitrary spatial dimension.

Passivity analysis of linear physical systems with internal energy sources modelled by bond graphs

Integrated dynamic systems such as mechatronic or control systems generally contain passive elements and internal energy sources that are appropriately modulated to perform the desired dynamic actions. The overall passivity of such systems is a useful property that relates to the stability and the safety of the system, in the sense that the maximum net amount of energy that the system can impart to the environment is limited by its initial state. In this paper, conditions under which a physical system containing internal modulated sources is globally passive are investigated using bond graph modelling techniques. For the class of systems under consideration, bond graph models include power bonds and active (signals) bonds modulating embedded energy sources, so that the continuity of power (or energy conservation) in the junction structure is not satisfied. For the purpose of the analysis, a so-called bond graph pseudo-junction structure is proposed as an alternative representation for linear time-invariant (LTI) bond graph models with internal modulated sources. The pseudo-junction structure highlights the existence of a multiport coupled resistive field involving the modulation gains of the internal sources and the parameters of dissipative elements, therefore implicitly realizing the balance of internal energy generation and dissipation. Moreover, it can be regarded as consisting of an inner structure which satisfies the continuity of power, and an outer structure in which a power scaling is performed in relation with the dissipative field. The associated multiport coupled resistive field constitutive equations can then be used to determine the passivity property of the overall system. The paper focuses on systems interconnected in cascade (with no loading effect) or in closed-loop configurations which are common in control systems.

Artificial Neural Network Approach for Dynamic Modelling of Heat Exchanger for Data Prediction

Objective: Artificial Neural Networks became a powerful tool for dynamic modelling of non linear physical systems and for prediction of specific parameters of complex systems. This work aims to model a heat exchanger using different neural networks and to investigate their performance in predicting its outlet temperature. Methods: In this work four different neural networks namely Elman Recurrent Neural Networks (ERNN), Time Delay Neural Networks (TDNN), Cascade Feed Forward Neural Networks (CFFNN) and Feed Forward Neural Networks (FFNN) are modelled for the prediction of the outlet liquid temperature of a saturated steam heat exchanger from its liquid flow rate. A benchmark dataset consisting of 4000 tuples is used to train, validate and test the performance of each neural network model. Findings: All the four ANN models are trained, validated and tested which predicted the outlet temperature of the Heat exchanger with acceptable accuracy and the Elman Recurrent Neural Network is found to have the best accuracy by having the lowest Mean Square Error (MSE) and best Regression due to its feedback connections. Applications: The Artificial Neural Network Models simulated, especially the Elman Neural Networks are good at prediction of operational parameters of a physical system and hence can be used in prediction and forecasting of operational parameters of engineering, medical, financial and environmental systems.Keywords: Artificial Neural Networks, Elman Recurrent Neural Network, Heat Exchanger, Prediction

Game-theoretic distributed control with information-theoretic security guarantees

This paper investigates the synthesis of distributed algorithms to solve a class of convex games. We first propose a distributed algorithm which enables abstract decision-makers and dynamically coupled linear physical systems to asymptotically identify a Nash equilibrium. By using secure multiparty computation, we then propose a distributed information-theoretically secure algorithm such that the convergence property is maintained and simultaneously the exchanged data of a decision-maker is kept private from semi-honest decision-makers.

An interictal EEG spectral metric for temporal lobe epilepsy lateralization

Visually-obvious abnormalities in the resting baseline EEG--slowing, spiking and high-frequency oscillations (HFOs)--are cardinal, though incompletely understood, features of the seizure onset zone in focal epilepsy. We hypothesized that evidence of cortical network dysfunction in temporal lobe epilepsy (TLE) would persist in the absence of visually-classifiable abnormalities in the baseline EEG recorded within the conventional passband, and that metrics of such dysfunction could serve as a lateralizing diagnostic in TLE. Epochs of resting EEG without significant abnormalities in light sleep over several days were compared between a group of 10 patients with proven TLE and 10 subjects without epilepsy. A novel laterality metric computed from the line length of normalized power spectra from the temporal channels was compared between the two groups. Significant group differences in spectral line length laterality metric were found between the TLE and control group. At the individual level, seven of 10 TLE patients had highly significant laterality metrics, all concordant with the known laterality of their disease. Detailed spectral analysis offers novel insight into TLE network behavior, independent of the orthodox abnormalities of EEG slowing, spikes or HFOs. The results may be deployed in a practical diagnostic manner, offer insight into the EEG manifestations of disordered cellular network architecture in TLE, and maybe understood through simple analogy with the theory of linear time-invariant physical systems.

Transient Excitation of Rectangular Resonators Through Electrically Small Circular Holes

In this paper, analytical solutions of response functions for rectangular resonators are investigated in time domain. Emphasis is placed on the study of electromagnetic field coupling to a 3-D cavity through a small circular aperture. The time-dependent parts of the resulting modal Green's functions exhibit typical behavior that is inherent in all resonating/oscillating linear physical systems: namely, they fulfill oscillating ordinary differential equations at any point of the considered resonator. Their solutions contain transient and steady-state parts. The transient parts of the response functions will become important for electromagnetic compatibility tests in particular of modern digital high-speed electronics.

A NEWTON METHOD FOR CYCLE DETERMINATION OF LINEAR PHYSICAL SYSTEMS WITH SWITCHES

The goal of this paper is to apply a newly developed Newton method for the cycle determination in the case of linear physical systems with switches. The difficulty consists in the fact that, in the general case, the dimension of the dynamics equation is different from one configuration of the system to another. The structural properties of the considered model of linear physical systems with switches can be used to simplify the cycle computation original scheme.

Model reduction in the physical domain

AbstractThis paper is concerned with obtaining physical-based low-order approximations of linear physical systems. Low-order models possess some advantages, including the reduction of computational difficulty and understanding of the physics of the original system in a simpler manner. Previously, a number of methods have been suggested to develop suitable low-order approximations. However, most of these approaches do not reflect the relation between the mathematical model and the physical subsystems. Specifically, these techniques do not indicate which of the physical subsystems should be retained or eliminated in the reduced-order model. The proposed model reduction method is based on identifying subsystem types of a physical system using the bond graph method. These subsystems are then removed or retained based on the information from the physical system decomposition procedures and partial fraction expansion residues to obtain a reduced-order model. The physical model reduction procedure is verified on...

Model reduction in the physical domain

This paper is concerned with obtaining physical-based low-order approximations of linear physical systems. Low-order models possess some advantages, including the reduction of computational difficulty and understanding of the physics of the original system in a simpler manner. Previously, a number of methods have been suggested to develop suitable low-order approximations. However, most of these approaches do not reflect the relation between the mathematical model and the physical subsystems. Specifically, these techniques do not indicate which of the physical subsystems should be retained or eliminated in the reduced-order model. The proposed model reduction method is based on identifying subsystem types of a physical system using the bond graph method. These subsystems are then removed or retained based on the information from the physical system decomposition procedures and partial fraction expansion residues to obtain a reduced-order model. The physical model reduction procedure is verified on physical linear systems.

A CLASS OF RATIONAL FUNCTION MATRICES WITH SOME PROPERTIES AND STRUCTURAL CONTROLLABILITY

In this paper, a definition of a class of rational function matrices called a type-1 matrix is given. Two illustrative examples show that the type-1 matrix can describe most of linear physical systems. It is proven that the type-1 matrix satisfies two properties that its characteristic polynomial in the ring F(z)[λ] has no nonzero constant eigenvalues or nonzero multiple factors in F(z)[λ]. The author present some controllability criteria of the linear systems whose characteristic polynomials have no nonzero multiple factors in F(z)[λ]. The applications of the type-1 matrix and system to structural controllability are indicated.

Controllability and reducibility conditions of a new system model

A new system model (a class of RFSs) (A, B) is proposed, where A=(G+D)-1C and B are, respectively, an n×n and an n×m matrix over the field F(ξ, z); D and C are two matrices over F(z), F(z) denotes the field of all rational functions in q independently variable parameters z1, …, zq, z=(z1,…,zq) q≥0; G=diag(0, G22), G22=diag(ξ1,…, ξn2), n2≤n, ξ=(ξ1,…,ξ2); F(ξ, z) is the field of all rational functions in q+n2 mutually independent parameters ξ1,…,ξn2, z1,…,zq. The model can describe most linear physical systems such as electrical networks and servo systems. The controllability condition of the system (A, B) and the reducibility condition of the nonzero part of the polynomial det(λI-A) are derived. An illustrative example is given.