State Space Of System Research Articles

On Filtering and Smoothing Algorithms for Linear State-Space Models Having Quantized Output Data

The problem of state estimation of a linear, dynamical state-space system where the output is subject to quantization is challenging and important in different areas of research, such as control systems, communications, and power systems. There are a number of methods and algorithms to deal with this state estimation problem. However, there is no consensus in the control and estimation community on (1) which methods are more suitable for a particular application and why, and (2) how these methods compare in terms of accuracy, computational cost, and user friendliness. In this paper, we provide a comprehensive overview of the state-of-the-art algorithms to deal with state estimation subject to quantized measurements, and an exhaustive comparison among them. The comparison analysis is performed in terms of the accuracy of the state estimation, dimensionality issues, hyperparameter selection, user friendliness, and computational cost. We consider classical approaches and a new development in the literature to obtain the filtering and smoothing distributions of the state conditioned to quantized data. The classical approaches include the extended Kalman filter/smoother, the quantized Kalman filter/smoother, the unscented Kalman filter/smoother, and the sequential Monte Carlo sampling method, also called particle filter/smoother, with its most relevant variants. We also consider a new approach based on the Gaussian sum filter/smoother. Extensive numerical simulations—including a practical application—are presented in order to analyze the accuracy of the state estimation and the computational cost.

A fault detection method based on the self-organizing fuzzy Luenberger for the generalized linear discrete time system with disturbances

A novel for an integrated fault and states estimator was proposed for the generalized linear discrete-time system with disturbances. The proposed scheme was based on a Self-Organizing fuzzy Luenberger system to estimate the states and approximate the fault information simultaneously for the generalized linear discrete-time system. For this purpose, a generalized linear discrete-time system with disturbances was transformed into an equivalent standard state-space system with disturbances and faults. Then, the faults and disturbances of generalized linear discrete-time system can be separated with the coordinate transform, meanwhile the Self-Organizing fuzzy Luenberger estimator was designed to obtain the accurate fault information. Based on the obtained fault information, the fault detection experiments were performed, and the fault feature parameters required for fault isolation were determined. Finally, the proposed strategy was applied for a direct current motor to demonstrate the effectiveness of the proposed approach.

Forecasting temperature of the Saudi Arabian Province of Makkah using a discrete state–space modeling approach

The maximum and minimum air temperature components (Tmax and Tmin) play a crucial role in science. This study proposes a discrete-time identified state-space modeling approach in which the temperature fluctuation was modelled as a state-space system with the temperature time series as inputs. We aim to provide a tool for projecting future scenarios of Tmax and Tmin. The current research employs a prediction-focused methodology to system identification, with the overarching goal of developing a realistic and dynamic system model. Data on the Tmin and Tmax recorded in the Saudi Arabian province of Makkah are used to test the accuracy and robustness of the proposed methodology. The proposed model was developed utilizing 120 years' (1901–2020) worth of historical monthly time series data on Tmax and Tmin. It was applied to anticipate future temperatures over the ensuing 60 years (up to 2080). For maximum temperature projections, the fit to the data or prediction focus was 87.04% and 85.14%, respectively for the identification (training) and validation phases of the model development. Akaike’s Final Prediction Error (FPE) and Mean Squared Error (MSE) values were observed to be 0.37 °C and 0.34 °C, respectively. The prediction focus during the identification and validation phases were 86.25% and 84.78%, respectively for the minimum temperature projection. The FPE and MSE values were 0.41 °C and 0.37 °C, respectively for this instance. The findings demonstrate that the recommended discrete state-space modeling approach may be utilized to predict temperature variations in the future.

Towards the Resolution of a Quantized Chaotic Phase-Space: The Interplay of Dynamics with Noise.

We outline formal and physical similarities between the quantum dynamics of open systems and the mesoscopic description of classical systems affected by weak noise. The main tool of our interest is the dissipative Wigner equation, which, for suitable timescales, becomes analogous to the Fokker-Planck equation describing classical advection and diffusion. This correspondence allows, in principle, to surmise a finite resolution, other than the Planck scale, for the quantized state space of the open system, particularly meaningful when the latter underlies chaotic classical dynamics. We provide representative examples of the quantum-stochastic parallel with noisy Hopf cycles and Van der Pol-type oscillators.

Inference and dynamic decision-making for deteriorating systems with probabilistic dependencies through Bayesian networks and deep reinforcement learning

In the context of modern engineering, environmental, and societal concerns, there is an increasing demand for methods able to identify rational management strategies for civil engineering systems, minimizing structural failure risks while optimally planning inspection and maintenance (I&M) processes. Most available methods simplify the I&M decision problem to the component level, often assuming statistical, structural, or cost independence among components, due to the computational complexity associated with global optimization methodologies under joint system-level state descriptions. In this paper, we propose an efficient algorithmic framework for inference and decision-making under uncertainty for engineering systems exposed to deteriorating environments, providing optimal management strategies directly at the system level. In our approach, the decision problem is formulated as a factored partially observable Markov decision process, whose dynamics are encoded in Bayesian network conditional structures. The methodology can handle environments under equal or general, unequal deterioration correlations among components, through Gaussian hierarchical structures and dynamic Bayesian networks, decoupling the originally joint system state space to component networks conditional on shared random variables. In terms of policy optimization, we adopt a deep decentralized multi-agent actor-critic (DDMAC) reinforcement learning approach, in which the policies are approximated by actor neural networks guided by a critic network. By including deterioration dependence in the simulated environment, and by formulating the cost model at the system level, DDMAC policies intrinsically consider the underlying system-effects. This is demonstrated through numerical experiments conducted for both a 9-out-of-10 system and a steel frame under fatigue deterioration. Results demonstrate that DDMAC policies offer substantial benefits when compared to state-of-the-art heuristic approaches. The inherent consideration of system-effects by DDMAC strategies is also interpreted based on the learned policies.

Sufficient Conditions for Observability in Electrocardiography Problem

The aim of this paper, is to study electrical cardiography problem. Thus, we construct the state space system of this model as mathematical model. Moreover, we present some definitions and results which is described some concepts of linear control system analysis related to this problem. More precisely, the sufficient conditions which characterize the observability notion of linear dynamical controlled system are presented and discussed. Finally, we prove that, the electrical cardiography model is completely observable system over finite time .

Extreme states and boundary representations of operator spaces in ternary rings of operators

This paper explores different notions of extreme states on operator systems and on operator spaces. We prove that boundary points of the generalized state space of an operator system in finite dimensions are precisely the restrictions of boundary representations of the generated [Formula: see text]-algebra. We study weak TRO-extreme states on operator spaces in ternary rings of operators as a non self-adjoint version of [Formula: see text]-extreme states on operator systems in [Formula: see text]-algebras. Rectangular boundary point for a rectangular matrix convex set is introduced and its connection with boundary representations of the associated operator space is established in finite dimensional setting. Also, we show that the set of all rectangular boundary points is the minimal spanning set for a compact rectangular matrix convex set in finite dimensions.

Sequential Monte Carlo: A Unified Review

Sequential Monte Carlo methods—also known as particle filters—offer approximate solutions to filtering problems for nonlinear state-space systems. These filtering problems are notoriously difficult to solve in general due to a lack of closed-form expressions and challenging expectation integrals. The essential idea behind particle filters is to employ Monte Carlo integration techniques in order to ameliorate both of these challenges. This article presents an intuitive introduction to the main particle filter ideas and then unifies three commonly employed particle filtering algorithms. This unified approach relies on a nonstandard presentation of the particle filter, which has the advantage of highlighting precisely where the differences between these algorithms stem from. Some relevant extensions and successful application domains of the particle filter are also presented.

IoT based dynamic Bayesian prediction of crop evapotranspiration in soilless cultivations

As water resources become scarce around the globe, a sustainable irrigation management is essential for increasing the crop use efficiency. Crop EvapoTranspiration (ET) is considered as one of the fundamental variables for correct irrigation management. Current ET prediction models adjust their system parameters: i) during time consuming training cycles; ii) by (destructive) leaf-area measurements; iii) only once during training for a particular meteorological scenario. These parameters are static. They cannot learn over time. On top of that, these models fail when some of the input variables are missing. To overcome these shortcomings, we follow an Internet of Things (IoT) approach to crop water use modeling and prediction for soilless cultivations. First, a stochastic crop coefficient confined to global radiation, Kr, is defined. Then, the evolution of Kr is modeled as state-space system with the daily temperature as input data, and global radiation and crop weight as measurement data. The latter data may also be missing at random. We derive a predictor for the posteriori probability of Kr and show that predicting crop ET via Kr it is immune to propagation of uncertainty over time due to erroneous weather forecasting. Our predictor is implemented in the cloud server of the IoT network. The sensor nodes, connected to a lightweight IoT client, supply our model with information in (soft) real-time. A web interface allows for visualization of the time series in real-time. To discuss Quality of Service (QoS) issues, we model the IoT network as synchronous data flow graph revealing its workflow and timings of the individual nodes.Sweet basil (Ocimum basilicum L.) is used to test the performance in four climatic environments and two different sampling methods: i) sample daily from the same environment in parallel; ii) sample daily from one environment and move on to the next in round robin fashion, emulating reuse of the same set of measurement equipment at a quarter of the costs. It turns out that in both cases, our Kr-based crop ET predictor outperforms the competing Baille technique. The performance of our IoT network is assessed by means of the QoS metrics response time, jitter, and availability.

A Generalized, Frequency Domain-Embedded, State Space Approach for Controller Synthesis

This paper develops a novel control synthesis approach for a wide class of practical systems. The control action is derived by inserting a compensator device in the forward path of the system that is to be controlled. The compensator design method is based on a state space system that is embedded in the frequency domain of the plant. It uses a nonlinear subspace that is the image of the compensator being used to determine the parameters of the compensator and modify system behavior. The coordinates of the state space system are taken as the compensator parameters. The method is capable of designing a compensator of arbitrary order to make the system comply with given stability performance requirements provided that these requirements can be geometrically interpreted in the frequency domain. The approach is developed and a proof of its ability to converge, if a solution exists, to the compensator tuning parameter set that satisfy the desired performance conditions is provided. A set of design examples are supplied to demonstrate the applicability of the approach to different types of linear, nonlinear, SISO and MIMO systems and system with delays.

Feasible-reachability of 1D and 2D state-space systems*

In this paper we define the property of feasible reachability both for 1D state-space systems evolving over Z and for 2D state-space systems evolving over Z2 described by Fornasini-Marchesini models. Feasible reachability consists in the reachability of the feasible subspaces associated with those systems. After characterizing these properties in terms of the system matrices, we compare them with behavioral controllability.

Sparse Multichannel Decomposition of Electrodermal Activity With Physiological Priors.

Goal: Inferring autonomous nervous system (ANS) activity is a challenging issue and has critical applications in stress regulation. Sweat secretions caused by ANS activity influence the electrical conductance of the skin. Therefore, the variations in skin conductance (SC) measurements reflect the sudomotor nerve activity (SMNA) and can be used to infer the underlying ANS activity. These variations are strongly correlated with emotional arousal as well as thermoregulation. However, accurately recovering ANS activity and the corresponding state-space system from a single channel signal is difficult due to artifacts introduced by measurement noise. To minimize the impact of noise on inferring ANS activity, we utilize multiple channels of SC data. Methods: We model skin conductance using a second-order differential equation incorporating a time-shifted sparse impulse train input in combination with independent cubic basis spline functions. Finally, we develop a block coordinate descent method for SC signal decomposition by employing a generalized cross-validation sparse recovery approach while including physiological priors. Results: We analyze the experimental data to validate the performance of the proposed algorithm. We demonstrate its capacity to recover the ANS activations, the underlying physiological system parameters, and both tonic and phasic components. Finally, we present an overview of the algorithm's comparative performance under varying conditions and configurations to substantiate its ability to accurately model ANS activity. Our results show that our algorithm performs better in terms of multiple metrics like noise performance, AUC score, the goodness of fit of reconstructed signal, and lower missing impulses compared with the single channel decomposition approach. Conclusion: In this study, we highlight the challenges and benefits of concurrent decomposition and deconvolution of multichannel SC signals.

Revisiting State Estimation for Linear Systems with State and/or Filter Equality Constraints*

This article revisits optimal state estimation, in the mean squared error matrix sense, for linear systems with state and/or filter subject to linear equality constraints (LECs). First, it is shown that the conventional Wiener filter (WF) form incorporates any LECs on the state, thus yielding a filter subject to the same LECs. Conversely, an optimal linear filter subject to LECs (or linear equality gain constraints) in general does not exist. Therefore, adding LECs on the WF or WF gain matrix either leaves unchanged or degrades the constrained WF performance w.r.t. the unconstrained WF. Since the Kalman filter (KF) and Kalman predictor (KP) are recursive WF forms for linear discrete state-space (LDSS) systems, the same results hold for both estimators, which is in contradiction with several existing results in the literature. Actually, even if these existing results are mathematically correct, however, they have been derived for unsuitable assumed LDSS models where the state is surprisingly not compliant with the assumed LECs. Indeed, it is shown that for suitable assumed state models, both standard KF and KP forms satisfy the assumed LECs, making any additional projection step superfluous.

An EM Algorithm for Lebesgue-sampled State-space Continuous-time System Identification*

This paper concerns the identification of continuous-time systems in state-space form that are subject to Lebesgue sampling. Contrary to equidistant (Riemann) sampling, Lebesgue sampling consists of taking measurements of a continuous-time signal whenever it crosses fixed and regularly partitioned thresholds. The knowledge of the intersample behavior of the output data is exploited in this work to derive an expectation-maximization (EM) algorithm for parameter estimation of the state-space and noise covariance matrices. For this purpose, we use the incremental discrete-time equivalent of the system, which leads to EM iterations of the continuous-time state-space matrices that can be computed by standard filtering and smoothing procedures. The effectiveness of the identification method is tested via Monte Carlo simulations.

GSM Filter: A Learning Model of Measurement Noise Distributions for Bayesian Filtering

In this paper, a new universal Bayesian filter with a Gaussian scale mixture (GSM) model, called the Gaussian scale mixture (GSM) filter, for adaptively learning any measurement noise distribution of a state space system is presented. It is demonstrated that the discrete measurement noise distribution of the system takes on a Gaussian sum form when described by a GSM model. It implies that, as the Gaussian sum model does, the GSM model can also be used to approximate any measurement distribution as closely as desired, whatever the probability density function (pdf) of the measurement noise is. If its covariance is known as a priori or can be estimated, it is found that the scale parameter and matrix of the GSM model at each time step can be achieved adaptively to make the following Bayesian inference much simpler. Further analyses show that the GSM model's auxiliary random variable and the system's state posterior at each time step can be inferred by a variational Bayesian (VB) approach adaptively. At each time step, the posterior distribution of system states shown is a Gaussian whatever the measurement noise pdf of the system is. As a result, the Bayesian filtering for nonlinear systems with any measurement noise pdf can be done by our GSM filter, almost as simple as the general Gaussian filters for filtering a nonlinear Gaussian system. Both simulations and experiments are conducted to verify the effectiveness and correctness of the analytical results. The results on the performances of our algorithms fully outperforming those of the existing state of the art Bayesian filters are given.

Subspace State-Space Identification of Nonlinear Dynamical System Using Deep Neural Network with a Bottleneck

This paper proposes a new type of subspace state-space system identification method for nonlinear dynamical systems, which generates a model consisting of a state estimator and a predictor that can be directly used for model predictive control (MPC). The main feature of the proposed method is that it uses a neural network with a bottleneck layer between the state estimator and predictor to represent the input-output dynamics, and it is proven that the state of the dynamical system can be extracted from the bottleneck layer based on the observability of the target system. The training of the network is shown to be a natural nonlinear extension of the subspace state-space system identification method established for linear dynamical systems. This correspondence provides interpretability and optimality to the resulting model based on linear control theory. The usefulness of the proposed method and the interpretability of the model are demonstrated through an illustrative example of MPC.

A Bayesian Filtering Method for Wiener State-Space Systems Utilizing a Piece-wise Linear Approximation

In this paper, we develop a filtering algorithm for Wiener systems written in state-space form which considers correlated noise sources. The output non-linearity is approximated by using a piece-wise linear function. The probability function of the output signal conditioned to the system state is written as a Gaussian mixture distribution. A Gaussian sum filter algorithm to obtain the a posteriori probability density function of the state given the current and past output is developed. The associated statistics of the system state are obtained. The benefits of our proposal are illustrated via numerical simulations.

A Numerically Robust Bayesian Filtering Algorithm for Gaussian Mixture Models

A Bayesian filtering algorithm is developed for a class of state-space systems that can be modelled via Gaussian mixtures. In general, the exact solution to this problem involves an exponential growth in the number of mixture terms and this is handled here by utilising a Gaussian mixture reduction step after both the time and measurement update steps. In addition, a numerically robust square-root implementation of the unified algorithm is presented and this algorithm is profiled on several simulated systems, including the state estimation for a challenging non-linear system.

Event-triggered dynamic output quantized control for 2-D switched systems

It is well known that designing mode-dependent event-triggered control (MDETC) brings challenging difficulties to theoretical analysis, especially for two-dimensional (2-D) switched systems. Therefore, for 2-D switched Fornasini–Marchesini local state-space (FMLSS) systems, this paper designs a MDETC to investigate global exponential stabilization almost surely (GES a.s.). A MDETC based on dynamic output quantization control scheme is designed, which not only has a wide range of practicability, but also greatly saves network bandwidth resources. By constructing mode-dependent Lyapunov functions that include two time directions, some novel sufficient conditions are provided such that the switched FMLSS system achieves GES a.s. Unlike most previous results, our results do not require each mode to be stable, not even after adding control. Finally, numerical experiments are provided to verify the validity of our main theoretical results.

Geometric structure of thermal cones.

The second law of thermodynamics imposes a fundamental asymmetry in the flow of events. The so-called thermodynamic arrow of time introduces an ordering that divides the system's state space into past, future, and incomparable regions. In this work, we analyze the structure of the resulting thermal cones, i.e., sets of states that a given state can thermodynamically evolve to (the future thermal cone) or evolve from (the past thermal cone). Specifically, for a d-dimensional classical state of a system interacting with a heat bath, we find explicit construction of the past thermal cone and the incomparable region. Moreover, we provide a detailed analysis of their behavior based on thermodynamic monotones given by the volumes of thermal cones. Results obtained apply also to other majorization-based resource theories (such as that of entanglement and coherence), since the partial ordering describing allowed state transformations is then the opposite of the thermodynamic order in the infinite temperature limit. Finally, we also generalize the construction of thermal cones to account for probabilistic transformations.