Discrete-state Systems Research Articles

State Machines for Large Scale Computer Software and Systems

The behavior and architecture of large scale discrete state systems found in computer software and hardware can be specified and analyzed using a particular class of primitive recursive functions. This article begins with an illustration of the utility of the method via a number of small examples and then via longer specification and verification of the “Paxos” distributed consensus algorithm [ 26 ]. The “sequence maps” are then shown to provide an alternative representation of deterministic state machines and products of state machines. Distributed and composite systems, parallel and concurrent computation, and real-time behavior can all be specified naturally with these methods—which require neither extensions to the classical state machine model nor any axiomatic methods or other techniques from formal logic or other foundational methods. Compared to state diagrams or tables or the standard set-tuple-transition-maps, sequence maps are more concise and better suited to describing the behavior and compositional architecture of computer systems. Staying strictly within the boundaries of classical deterministic state machines anchors the methods to the algebraic structures of automata and makes the specifications faithful to engineering practice.

Real-time estimation of barycenter position for fuel cell distributed drive electric tractor based on derived UKF

ABSTRACT The FCDET is considered as a promising and advanced agricultural machinery due to its convenience and controllability. To enhance the control performance of the FCDET unit dynamic system, understanding the accurate position of the center of gravity (CoG) of the tractor unit in longitudinal motion and the operating environment is essential. In this paper, we proposed a real-time estimation method of CoG position of longitudinal motion for FCDET plowing and transportation conditions. CoG height and longitudinal axis distance distribution coefficients are used as state estimation variables, and the data obtained from displacement and velocity sensors are used as state observation variables, establishing a discrete system state space model and proving the observability. The proposed Derived UKF algorithm introduces the Sage-Husa adaptive noise equation within the Square-Root UKF framework to address the non-positive definite matrix problem. The research shows that the precise CoG longitudinal position effectively reflects changes in operational pavement load. The Derived UKF algorithm exhibits high state estimation accuracy in plowing and transportation conditions, with mean absolute errors of 14.2% and 5.0% of the state amplitude, respectively. This study supports the practical application of real-time state parameter estimation algorithms in controlling advanced agricultural machinery distributed drive systems.

Rational dimension of a basis of a regression model for adaptive short-term forecasting the state of a discrete nonstationary dynamic system

Relevance. Today, there are many methodologies for predicting power consumption of various objects. However, there is no a general methodology that is suitable for all types of energy systems, including the sectoral characteristics of small northern settlements and other objects with the stochastic nature of electricity consumption schedules. At the same time, during the development of problem-oriented forecasting methods, it is necessary to take into account computational and statistical features of forecasted time series to the maximum and apply them adequately. The mentioned circumstance prompts the creation of criteria-indicators that allow evaluating the quality of the applied model for solving the forecasting problem, correctness of its construction and correctness of applying a priori information about the object and its physical properties.Aim. Develop and apply the criteria-indicators, which allow evaluating the quality of the forecast regression model and the influence of the dimensionality of such model base on a forecasting error. Methods. The choice of rational dimensionality of the regression model basis for the adaptive forecasting problem is based on the known and developed criteria-indicators. The main provisions of such criteria-indicators were formulated, which provide an assessment of the quality of conditioning of an equivalent square matrix, the presence of uninformative elements of the matrix, and linear dependence of the columns. Results. Based on the analysis of criteria-indicators, the authors selected a rational dimension of the regression model basis for the problem of adaptive short-term forecasting of the state of discrete non-stationary dynamic systems. Conclusions. The authors have previously selected the most promising criteria-indicators and developed a normalized difference factor of diagonal predominance. This allows us to evaluate the influence of the basis size change on the regression model quality when building an approach of adaptive short-term forecasting of electricity consumption by autonomous power systems of small northern settlements on the basis of regression analysis methods. Based on the analysis of criteria-indicators the authors obtained information about the influence of the regression model basis dimension on the forecasting problem solution error. The authors stated the further stages of research to reduce this error. The paper introduces and describes one of the ways to improve the forecasting model quality. The dependence of the forecasting error on the size of the regression model basis were revealed; the criteria-indicators considered in the article were successfully applied. It is confirmed that the pre-selected and developed criteria-indicators make it possible, at the stage of compiling an equivalent square matrix and performing preliminary actions on it, to track changes within the matrix. The changes will lead to improvement in the solution of the problem of adaptive short-term forecasting.

Stability Indicators of Nonnegative Matrices: Parametric and Sparse Cases

Methods for the algorithmic construction of stability indicators of nonnegative matrices is described, and the application of these indicators to problems of modern mathematical biology and epidemiology is discussed. Specific features of such indicators when they are applied to problems about the parametric loss of stability of trivial equilibrium states of discrete dynamical systems are pointed out. Estimates of the efficiency of algorithms based on the proposed methods for the case of systems determined by sparse matrices are given. Examples of using the constructed algorithms for such systems are discussed.

Fluctuations of entropy production of a run-and-tumble particle.

Out-of-equilibrium systems continuously generate entropy, with its rate of production being a fingerprint of nonequilibrium conditions. In small-scale dissipative systems subject to thermal noise, fluctuations of entropy production are significant. Hitherto, mean and variance have been abundantly studied, even if higher moments might be important to fully characterize the system of interest. Here, we introduce a graphical method to compute any moment of entropy production for a generic discrete-state system. Then, we focus on a paradigmatic model of active particles, i.e., run-and-tumble dynamics, which resembles the motion observed in several micro-organisms. Employing our framework, we compute the first three cumulants of the entropy production for a discrete version of this model. We also compare our analytical results with numerical simulations. We find that as the number of states increases, the distribution of entropy production deviates from a Gaussian. Finally, we extend our framework to a continuous state-space run-and-tumble model, using an appropriate scaling of the transition rates. The approach presented here might help uncover the features of nonequilibrium fluctuations of any current in biological systems operating out-of-equilibrium.

Max-plus steady states in discrete event dynamic systems with inexact data

Max-plus steady states in discrete event dynamic systems with inexact data

Learning Physical Concepts in CPS: A Case Study with a Three-Tank System

Machine Learning (ML) has been implemented with great successes in recent decades, both in research and in practice. In the field of Cyber-Physical Systems (CPS), ML methods are already widely used, e.g. in anomaly detection, predictive maintenance or diagnosis use cases. However, Representation Learning (RepL), which learns general concepts from data and has been a major driver of improvements, is hardly utilized so far. To be useful for CPS, RepL methods would have to produce interpretable results, work without requiring much prior knowledge, and be applicable to typical CPS datasets, including e.g. noisy sensor signals and discrete system state changes. In this paper, we provide an overview of the current state of research regarding methods for learning physical concepts in time series data, which is the primary form of sensor data of CPS. We also analyze the most important methods from the current state of the art using the example of a three-tank system. Based on concrete implementations1, we discuss the advantages and disadvantages of the methods and show for which purpose and under which conditions they can be used for CPS.

On synthesizing tolerable and permissive controllers for labeled transition systems

Control systems should enforce a desired property for both expected/modeled situations as well as unexpected/unmodeled environmental situations. Existing methods focus on designing maximally permissive controllers to enforce the desired property only when the environment behaves as expected. However, these methods lack discussion on how the system behaves when the environment is perturbed. We propose an approach for analyzing discrete-state systems with respect to their permissiveness and tolerance against environmental perturbations. There is an inherent trade-off between permissiveness and tolerance that we capture via Pareto optimality conditions. We investigate this trade-off by defining Pareto optimality between permissiveness and tolerance for invariance properties. We show that memoryless controllers are sufficient to describe the Pareto front. We also study the problem of synthesizing Pareto optimal controllers that achieve a minimum level of tolerance and permissiveness.

Моделирование критерия прогноза потери устойчивости дискретных систем

The paper proposes a method for determining the estimated parameter of the stability state of discrete systems exposed to external influences. As a rule, the loss of stability of the first and second kind leads to a problematic operation process throughout the life cycle, or even the destruction of the system. Hence the requirements of a certain rigidity to the designed and operated systems in order to ensure their geometric immutability. At the same time, in practice, there are no naturally deformable systems from external influences. The paper sets and solves the problem of determining the stability parameter, with the help of which, even before the stage of loss of stability, it is possible to predict the future state of a discrete system, i.e. to predict whether it (the system) has sufficient internal properties to return to a stable position at any exit from the preliminary state of equilibrium due to the influence of external forces.

Toward relaxation asymmetry: Heating is faster than cooling

An asymmetry in thermal relaxation toward equilibrium has been uncovered for Langevin systems near stable minima [Phys. Rev. Lett. 125, 110602 (2020)]. It has been shown that, given the same degree of nonequilibrium of the initial distributions, relaxation from a lower temperature state (heating) is faster than that from a higher temperature state (cooling). In this study, we elucidate this relaxation asymmetry for discrete-state Markovian systems described by the master equation. We rigorously prove that heating is faster than cooling for arbitrary two-state systems, whereas for systems with more than two distinct energy levels, the relaxation asymmetry is no longer universal. Furthermore, for systems whose energy levels degenerate into two energy states, we find that there exist critical thresholds of the energy gap. Depending on the magnitude of the energy gap, heating can be faster or slower than cooling, irrespective of the transition rates between states. Our results clarify the relaxation asymmetry for discrete-state systems and reveal several hidden features inherent in thermal relaxation.

Novel data fusion strategy for human gait analysis using multiple kinect sensors

Human gait analysis using microsoft Kinect sensor is an intriguing area of research. Fusing multiple sensors’ data for clinical gait analysis using calibrated instruments helps in producing more accurate results. A novel technique for spatial calibration is proposed and implemented in this paper. This paper emphasizes on a novel technique of using five Kinect V2 sensors (four clients and one server) and data fusion methods to create unified skeletons for subject-wise gait analysis. These eradicate the problems of inaccurate skeleton poses caused due to occlusions or tracking failures from a single Kinect which otherwise remains a problem in most vision-based sensing systems. Two methods are compared for estimating states of discrete time linear systems. The first one is classical Kalman filtering, which gives accurate results when state disturbances are assumed to be Gaussian white noises and measurement noises and the statistical properties are procurable. Secondly, a Set-Membership filter is used which relies upon the principle of prediction and correction as well. A novel Set-Membership filtering approach is proposed where the measurement noise is modelled by multivariate Gaussian probability density function bounded by −1 to +1. Based on our observations of the linear frameworks joined with interval investigation, the two phases of the estimator are done in a productive way. Both the fusion techniques are tested on overground and treadmill data and the results are validated and compared with ground truth obtained using Qualisys motion capture systems. The proposed approach is also compared quantitatively with state-of-the-art methods.

Using Event-Based Method to Estimate Cybersecurity Equilibrium

Estimating the global state of a networked system is an important problem in many application domains. The classical approach to tackling this problem is the periodic (observation) method, which is inefficient because it often observes states at a very high frequency. This inefficiency has motivated the idea of event-based method, which leverages the evolution dynamics in question and makes observations only when some rules are triggered (i.e., only when certain conditions hold). This paper initiates the investigation of using the event-based method to estimate the equilibrium in the new application domain of cybersecurity, where equilibrium is an important metric that has no closed-form solutions. More specifically, the paper presents an event-based method for estimating cybersecurity equilibrium in the preventive and reactive cyber defense dynamics, which has been proven globally convergent. The presented study proves that the estimated equilibrium from our trigger rule i) indeed converges to the equilibrium of the dynamics and ii) is Zeno-free, which assures the usefulness of the event-based method. Numerical examples show that the event-based method can reduce 98% of the observation cost incurred by the periodic method. In order to use the event-based method in practice, this paper investigates how to bridge the gap between i) the continuous state in the dynamics model, which is dubbed probability-state because it measures the probability that a node is in the secure or compromised state, and ii) the discrete state that is often encountered in practice, dubbed sample-state because it is sampled from some nodes. This bridge may be of independent value because probability-state models have been widely used to approximate exponentially-many discrete state systems.

Development of buck power converter circuit with ANN RL algorithm intended for power industry

PurposeThis paper aims to deal with application of artificial intelligence for solving real time control complication adhered with the controlled operation of a buck power converter. This type of converter finds application for power conversion at various levels for the direct current-direct current power industry to step down the input voltage.Design/methodology/approachUse of ANN-RL (Artificial Neural Networks- Reinforcement Learning)-based control algorithm to control buck power converter shows robustness against parameter and load variation. Because of non-linearity instigated by element used for switching, control of this converter becomes an arduous control predicament. All the classical control techniques are based on an approximate linear model of the step down converter and these techniques fail to handle actual non-linearity.FindingsIn this paper, a reinforcement learning-based algorithm has been used to handle and control buck power converter output voltage, without approximating the model of converter. The non-linearity instigated in converter is subjected to state of switch. Model of buck power converter is defined as a multi-step decision problem so that it can be solved using mathematical model of Markov decision process (MDP) and, in turn, reinforcement learning can be implemented. As MDP model is available for a discrete state system so model of converter has to be discretized and then value iteration is applied and output is analyzed. Load regulation and integral time absolute error analysis is done to show efficacy of this technique.Originality/valueTo mitigate the effect of discretization function approximation using neural network is applied. MATrix LABoratory has been used for implementation and result indicates an improvement in the overall response.

Efficient Irreversible Monte Carlo Samplers

We present here two irreversible Markov chain Monte Carlo algorithms for general discrete state systems. One of the algorithms is based on the random-scan Gibbs sampler for discrete states and the other on its improved version, the Metropolized-Gibbs sampler. The algorithms we present incorporate the lifting framework with skewed detailed balance condition and construct irreversible Markov chains that satisfy the balance condition. We have applied our algorithms to 1D 4-state Potts model. The integrated autocorrelation times for magnetization and energy density indicate a reduction of the dynamical scaling exponent from z ≈ 1 to z ≈ 1/2. In addition, we have generalized an irreversible Metropolis-Hastings algorithm with skewed detailed balance, initially introduced by Turitsyn et al. [ Physica D 2011, 240, 410] for the mean field Ising model, to be now readily applicable to classical spin systems in general; application to 1D 4-state Potts model indicate a square root reduction of the mixing time at high temperatures.

Kalman Filter Finite Element Method for Real-Time Soft Tissue Modeling

Soft tissue modelling plays a significant role in surgery simulation as well as surgical procedure planning and training. However, it is a challenging research task to satisfy both physical realism and real-time simulation for soft tissue deformation. The finite element method (FEM) is a representative strategy for modelling of soft tissue deformation with highly physical realism. However, it suffers from expensive computations, unable to meet the requirement of real-time simulation. This paper proposes a novel method by combining FEM with the Kalman filter for real-time and accurate modelling of soft tissue deformation. The novelty of this method is that soft tissue deformation is formulated as a filtering identification process to online estimate soft tissue deformation from local measurement of displacement. To construct the discrete system state equation for filtering estimation, soft tissue deformation is discretised based on elastic theory in the space domain by FEM and is further discretised in the time domain by using the Wilson- $\theta $ implicit integration to solve the dynamic equilibrium equation of FEM deformation modelling. Subsequently, a Kalman filter is developed for online estimation and analysis of soft tissue deformation according to local measurement of displacement. Interactive tool-tissue interaction with haptic feedback is also achieved for surgery simulation. The presented method significantly improves the computational performance of the traditional FEM, but still maintains a similar level of accuracy. It not only achieves the real-time performance, but also exhibits the similar deformation behaviours as the traditional FEM and enables the use of large time steps to improve the simulation efficiency.

Entropy production in master equations and Fokker–Planck equations: facing the coarse-graining and recovering the information loss

Systems operating out of equilibrium exchange energy and matter with the environment, thus producing entropy in their surroundings. Since the entropy production depends on the current flowing throughout the system, its quantification is affected by the level of coarse-graining we adopt. In particular, it has been shown that the description of a system via a Fokker–Planck equation (FPE) lead to an underestimation of the entropy production with respect to the corresponding one in terms of microscopic transition rates. Moreover, such a correction can be derived exactly. Here we review this derivation, generalizing it when different prescriptions to derive the FPE from a Langevin equation are adopted. Then, some open problems about Gaussian transition rates and underdamped limit are discussed. In the second part of the manuscript we present a new approach to dealing with the discrepancy in entropy production due to the coarse graining by introducing enough microscopic variables to correctly estimate the entropy production within the FPE description. We show that any discrete state system can be described by making explicit the contribution of each microscopic current.

Classical breathers and quantum coherent states in discrete NLS systems

We present a comparison of quantum and “semiclassical” trajectories of coherent states that correspond to classical breather solutions of finite discrete nonlinear Schrödinger (DNLS) lattices. The main goal is to explain earlier numerical observations of recurrent return to the vicinity of initial coherent states corresponding to stable breathers that are also spatially localized. This effect can be considered as a quantum manifestation of classical spatial localization. We show that these phenomena are encoded in a simple expression for the distance between the quantum and semiclassical states that involves the basic frequencies of the classical and quantum systems, as well as the breather amplitude and quantum spectral decomposition of the system. A corollary is that recurrence phenomena are robust under perturbation of the initial conditions for stable breathers.

Disjunctive interaction in continuous time Bayesian networks

A continuous time Bayesian network is a probabilistic graphical model capable of describing discrete state systems that evolve in continuous time. Unfortunately, the number of parameters required for each node in the graph is exponential in the number of parents of the node, which can be prohibitively large for many real-world systems. To mitigate this problem, disjunctive interaction is proposed as a method for reducing the number of required parameters from exponential to linear. In this work, the relation between disjunctive interaction and standard parameterization techniques is explored both theoretically and experimentally. Experimental results demonstrate that inference over models with disjunctive interaction exhibits greater scalability with no degradation in accuracy.

A dynamic Bayesian network approach for prognosis computations on discrete state systems

The maintenance optimization of complex systems is a key question. One important objective is to be able to anticipate future maintenance actions required to optimize the logistic and future investments. That is why, over the past few years, the predictive maintenance approaches have been an expanding area of research. They rely on the concept of prognosis. Many papers have shown how dynamic Bayesian networks can be relevant to represent multicomponent complex systems and carry out reliability studies. The diagnosis and maintenance group from French institute of science and technology for transport, development and networks (IFSTTAR) developed a model (VirMaLab: Virtual Maintenance Laboratory) based on dynamic Bayesian networks in order to model a multicomponent system with its degradation dynamic and its diagnosis and maintenance processes. Its main purpose is to model a maintenance policy to be able to optimize the maintenance parameters due to the use of dynamic Bayesian networks. A discrete state-space system is considered, periodically observable through a diagnosis process. Such systems are common in railway or road infrastructure fields. This article presents a prognosis algorithm whose purpose is to compute the remaining useful life of the system and update this estimation each time a new diagnosis is available. Then, a representation of this algorithm is given as a dynamic Bayesian network in order to be next integrated into the Virtual Maintenance Laboratory model to include the set of predictive maintenance policies. Inference computation questions on the considered dynamic Bayesian networks will be discussed. Finally, an application on simulated data will be presented.

Prediction of States of Discrete Systems with Unknown Input of the Model Using Compensation

The problem of state prediction for linear dynamic systems with discrete time is considered in the presence of unknown input and inaccurately specified parameters in the model. An algorithm with compensation for the constant component and estimation of the unknown variable input component by the least squares method is suggested. Results of statistical simulation are presented. The algorithm can be used for solving problems of processing information obtained as a result of observations over physical processes.