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ABSTRACT This study proposes a filtering based maximum likelihood generalized extended gradient algorithm for multivariable nonlinear systems with autoregressive moving average noises. The parameter estimates are obtained by minimizing the half squared residual measurement which can approach the true values. An auxiliary model is also established with the measurable information of the system, and the output of the auxiliary model is used to replace the unmeasurable variables of the system, so that the output of the auxiliary model approximates these unmeasurable variables, so as to obtain the consistent estimation of the system parameters. A maximum likelihood generalized extended gradient algorithm is derived for comparison and a numerical example is provided to show the effectiveness of the proposed method and the estimates converge to the actual values quickly. [ABSTRACT FROM AUTHOR]

Autoregressive Markov switching (ARMS) time series models are used to represent real-world signals whose dynamics may change over time. They have found application in many areas of the natural and social sciences, as well as in engineering. In general, inference in this kind of systems involves two problems: (a) detecting the number of distinct dynamical models that the signal may adopt and (b) estimating any unknown parameters in these models. In this paper, we introduce a new class of nonlinear ARMS time series models with delays that includes, among others, many systems resulting from the discretisation of stochastic delay differential equations (DDEs). Remarkably, this class includes cases in which the discretisation time grid is not necessarily aligned with the delays of the DDE, resulting in discrete-time ARMS models with real (non-integer) delays. The incorporation of real, possibly long, delays is a key departure compared to typical ARMS models in the literature. We describe methods for the maximum likelihood detection of the number of dynamical modes and the estimation of unknown parameters (including the possibly non-integer delays) and illustrate their application with a nonlinear ARMS model of El Niño–southern oscillation (ENSO) phenomenon. [ABSTRACT FROM AUTHOR]

The stability problem of Multiple n Inputs and Multiple n Outputs (MIMOn) cascade non-linear systems with random parameters is considered in this paper using the probability of stability estimation method. MIMOn cascade non-linear systems, particularly when the number of inputs and outputs exceeds three (n  > 3), exhibit a unique property: the appearance of spatial hyperchaos that can lead to system instability. To achieve desired spatial dynamics and prevent the occurrence of spatial hyperchaos, it is necessary to select the appropriate parameter values for these systems. Moreover, the optimal parameter values enable the attainment of the highest probability of stability for stochastic MIMOn systems. The research presents the results of stability analysis using tools such as bifurcation diagram, Lyapunov diagram and spatial phase portraits, generated through MATLAB M-files, with a specific focus on a stochastic MIMO5 system (five inputs and five outputs). [ABSTRACT FROM AUTHOR]

This article considers the parameter identification problems of stochastic systems which described by the finite impulse response moving average model. Since the system is disturbed by colored noise, we introduce the data filtering technique from a view point of improving the parameter estimation accuracy. The data filtering technique is to use a filter to filter the input and output data of the system disturbed by colored noise so as to improve the identification accuracy. By using the data filtering technique, this article proposes a filtering‐based recursive extended least squares (F‐RELS) algorithm. The convergence analysis indicates that the parameter estimates can converge to their true values. Compared with the recursive extended least squares algorithm, the proposed F‐RELS algorithm can obtain more accurate parameter estimation. Finally, a numerical simulation example is given to demonstrate the effectiveness of the proposed algorithms. [ABSTRACT FROM AUTHOR]

Summary: By using the collected batch data and the iterative search, and based on the filtering identification idea, this article investigates and proposes a filtered multi‐innovation generalized projection‐based iterative identification method, a filtered generalized gradient‐based iterative identification method, a filtered generalized least squares‐based iterative identification method, a filtered multi‐innovation generalized gradient‐based iterative identification method and a filtered multi‐innovation generalized least squares‐based iterative identification method for equation‐error autoregressive systems described by the equation‐error autoregressive models. These filtered generalized iterative identification methods can be extended to other linear and nonlinear scalar and multivariable stochastic systems with colored noises. [ABSTRACT FROM AUTHOR]

Mathematical models are a valuable tool for studying and predicting the spread of infectious agents. The accuracy of model simulations and predictions invariably depends on the specification of model parameters. Estimation of these parameters is therefore extremely important; however, while some parameters can be derived from observational studies, the values of others are difficult to measure. Instead, models can be coupled with inference algorithms (i.e., data assimilation methods, or statistical filters), which fit model simulations to existing observations and estimate unobserved model state variables and parameters. Ideally, these inference algorithms should find the best fitting solution for a given model and set of observations; however, as those estimated quantities are unobserved, it is typically uncertain whether the correct parameters have been identified. Further, it is unclear what 'correct' really means for abstract parameters defined based on specific model forms. In this work, we explored the problem of non-identifiability in a stochastic system which, when overlooked, can significantly impede model prediction. We used a network, agent-based model to simulate the transmission of Methicillin-resistant staphylococcus aureus (MRSA) within hospital settings and attempted to infer key model parameters using the Ensemble Adjustment Kalman Filter, an efficient Bayesian inference algorithm. We show that even though the inference method converged and that simulations using the estimated parameters produced an agreement with observations, the true parameters are not fully identifiable. While the model-inference system can exclude a substantial area of parameter space that is unlikely to contain the true parameters, the estimated parameter range still included multiple parameter combinations that can fit observations equally well. We show that analyzing synthetic trajectories can support or contradict claims of identifiability. While we perform this on a specific model system, this approach can be generalized for a variety of stochastic representations of partially observable systems. We also suggest data manipulations intended to improve identifiability that might be applicable in many systems of interest. [ABSTRACT FROM AUTHOR]

This paper proposes a new time-varying integer-valued autoregressive (TV-INAR) model with a state vector following a logistic regression structure. Since the autoregressive coefficient in the model is time-dependent, the Kalman-smoothed method is applicable. Some statistical properties of the model are established. To estimate the parameters of the model, a two-step estimation method is proposed. In the first step, the Kalman-smoothed estimation method, which is suitable for handling time-dependent systems and nonstationary stochastic processes, is utilized to estimate the time-varying parameters. In the second step, conditional least squares is used to estimate the parameter in the error term. This proposed method allows estimating the parameters in the nonlinear model and deriving the analytical solutions. The performance of the estimation method is evaluated through simulation studies. The model is then validated using actual time series data. [ABSTRACT FROM AUTHOR]

This paper considers the parameter estimation problem for bilinear stochastic systems with autoregressive moving average (ARMA) noise using the stochastic gradientmethod. First, the identification model is derived by eliminating the state variables. Based on the obtained identification model, a multi-innovation generalized extended stochastic gradient (MI-GESG) algorithm is proposed using the multi-innovation identification theory. Furthermore, to enhance the parameter estimation accuracy, a maximum likelihood based MI-GESG (ML-MI-GESG) algorithm is developed by using the maximum likelihood identification principle. Finally, an illustrative simulation example is provided to testify the proposed algorithms. The simulation results show the effectiveness of the proposed algorithms for identifying bilinear systems. [ABSTRACT FROM AUTHOR]

In this article, the problem of parameter estimation for a multiple‐input single‐output Hammerstein controlled autoregressive (MISO‐HCAR) model is solved. After establishing the identification model of MISO‐HCAR system, an improved adaptive moment estimation algorithm with decreasing weight (IADAM) is proposed. The improved algorithm transforms the nonlinear system identification problem into a parameter space optimization problem, according to the input and output data obtained from the system, and uses the parallel search ability of the IADAM algorithm to estimate all the parameters of the system simultaneously. Two numerical examples and the case study example of chemical continuously stirred tank reactor (CSTR) system show that the proposed IADAM algorithm with decreasing weight has better identification effect on the MISO‐HCAR model and CSTR system than the stochastic gradient descent (SGD) algorithm and the basic adaptive moment estimation (ADAM) algorithm, and the estimation accuracy and convergence speed are greatly improved. Thus, the IADAM can estimate the parameters of the MISO‐HCAR system and the CSTR system more effectively. [ABSTRACT FROM AUTHOR]

For equation‐error autoregressive moving average systems, that is, Box–Jenkins systems, this paper presents a filtered auxiliary model generalized extended stochastic gradient identification method, a filtered auxiliary model multi‐innovation generalized extended stochastic gradient identification method, a filtered auxiliary model recursive generalized extended gradient identification method, a filtered auxiliary model multi‐innovation recursive generalized extended gradient identification method, a filtered auxiliary model recursive generalized extended least squares identification method, and a filtered auxiliary model multi‐innovation recursive generalized extended least squares identification method by using the filtering identification idea and the auxiliary model identification idea. The proposed filtered auxiliary model recursive generalized extended identification methods can be generalized to other linear and nonlinear multivariable stochastic systems with colored noises. [ABSTRACT FROM AUTHOR]

A novel optimal control problem is considered for multiple input multiple output (MIMO) stochastic systems with mixed parameter drift, external disturbance and observation noise. The proposed controller can not only track and identify the drift parameters in finite time but, furthermore, drive the system to move towards the desired trajectory. However, there is a conflict between control and estimation, which makes the analytic solution unattainable in most situations. A dual control algorithm based on weight factor and innovation is, therefore, proposed. First, the innovation is added to the control goal by the appropriate weight and the Kalman filter is introduced to estimate and track the transformed drift parameters. The weight factor is used to adjust the degree of drift parameter estimation in order to achieve a balance between control and estimation. Then, the optimal control is derived by solving the modified optimization problem. In this strategy, the analytic solution of the control law can be obtained. The control law obtained in this paper is optimal because the estimation of drift parameters is integrated into the objective function rather than the suboptimal control law, which includes two parts of control and estimation in other studies. The proposed algorithm can achieve the best compromise between optimization and estatimation. Finally, the effectiveness of the algorithm is verified by numerical experiments in two different cases. [ABSTRACT FROM AUTHOR]

Summary: The uncertain parameters estimation problem for linear discrete‐time systems modeled in regression form and assuming an unknown but bounded description of the noise, is the main subject of this work. Particularly, zonotopic sets for bounding the parametric uncertainty are considered. Then, a zonotopic recursive least‐squares (ZRLS) estimator is proposed and compared with its stochastic counterpart (RLS), as well as with the set‐membership (SM) approach. Likewise, the parameter estimation problem is addressed from the Bayesian general framework to define the relationship between stochastic and deterministic approaches. Moreover, both ZRLS and SM applications applied to fault detection are assessed taking as a reference the minimum detectable fault in the worst case. Finally, a well‐known quadruple‐tank process is used to illustrate the estimation and fault detection results. [ABSTRACT FROM AUTHOR]

Polynomials are common algebraic structures, which are often used to approximate functions, such as probability distributions. This paper proposes to directly define polynomial distributions in order to describe stochastic properties of systems rather than to assume polynomials for only approximating known or empirically estimated distributions. Polynomial distributions offer great modeling flexibility and mathematical tractability. However, unlike canonical distributions, polynomial functions may have non-negative values in the intervals of support for some parameter values; their parameter numbers are usually much larger than for canonical distributions, and the interval of support must be finite. Hence, polynomial distributions are defined here assuming three forms of a polynomial function. Transformations and approximations of distributions and histograms by polynomial distributions are also considered. The key properties of the polynomial distributions are derived in closed form. A piecewise polynomial distribution construction is devised to ensure that it is non-negative over the support interval. A goodness-of-fit measure is proposed to determine the best order of the approximating polynomial. Numerical examples include the estimation of parameters of the polynomial distributions and generating polynomially distributed samples. [ABSTRACT FROM AUTHOR]

This paper presents a detailed investigation of a stochastic model that rules the spreading behavior of the measles virus while accounting for the white noises and the influence of immunizations. It is hypothesized that the perturbations of the model are nonlinear, and that a person may lose the resistance after vaccination, implying that vaccination might create temporary protection against the disease. Initially, the deterministic model is formulated, and then it has been expanded to a stochastic system, and it is well-founded that the stochastic model is both theoretically and practically viable by demonstrating that the model has a global solution, which is positive and stochastically confined. Next, we infer adequate criteria for the disease's elimination and permanence. Furthermore, the presence of a stationary distribution is examined by developing an appropriate Lyapunov function, wherein we noticed that the disease will persist for R 0 s > 1 and that the illness will vanish from the community when R 0 s < 1 . We tested the model against the accessible data of measles in Pakistan during the first ten months of 2019, using the conventional curve fitting methods and the values of the parameters were calculated accordingly. The values obtained were employed in running the model, and the conceptual findings of the research were evaluated by simulations and conclusions were made. Simulations imply that, in order to fully understand the dynamic behavior of measles epidemic, time-delay must be included in such analyses, and that advancements in every vaccine campaign are inevitable for the control of the disease. [ABSTRACT FROM AUTHOR]

Nonstationary stochastic systems in the Wiener-Kolmogorov sense have properties defined by their moments of probability, entropy, and distribution function. Filtering Theory, in general, describes indirectly, a stochastic system through the processes of parameter estimation and state identification. The objective of this article is to develop a Recursive Filter with an Exponential Kernel (RFEK) to reconstruct the response of a nonstationary stochastic system. To achieve this, first, a system viewed as a Black Box (BB) is analyzed. These systems are those whose internal dynamics are unknown, only their input-output is known from a set of responses measured with respect to a particular excitation. From these measurements and applying the proposed filter, a set of estimated parameters and identified states are obtained as a characterization of the system. Subsequently, a comparison is made between the filter output signal and the reference signal over time; that is, measuring their point-to-point convergence. The convergence of the stochastic reference makes it possible to indirectly observe its stability from a bounded estimation region. As a case study, bioelectric signals of the electroencephalographic (EEG) type are analyzed giving an improved approximation with respect to the Kalman filter results.

Model predictive control (MPC) is one of the most effective methods of dealing with constrained control problems. Nevertheless, the uncertainty of the control system poses many problems in its performance optimization. For high-precision servo systems, friction is typically the main factor in uncertainty affecting the accuracy of the system. Our work focuses on stochastic systems with unknown parameters and proposes a model predictive control strategy with machine learning characteristics that utilizes pre-estimated information to reduce uncertainty. Within this model, the parameters are obtained using the estimator. The uncertainty caused by the parameter estimation error in the system is parameterized, serving as a learning control component to reduce future uncertainty. Then, the estimated parameters and the current state of the system are used to predict the future p-step state. The control sequence is calculated under the MPC's rolling optimization mechanism. After the system output is obtained, the new parameter value at the next moment is re-estimated. Finally, MPC is carried out to realize the dual rolling optimization mechanism. In general, the proposed strategy optimizes the control objective while reducing the system uncertainty of the future parameter and achieving better system performance. Simulation results demonstrate the effectiveness of the algorithm. [ABSTRACT FROM AUTHOR]

The problem of estimating a parameter in the drift coefficient is addressed for N discretely observed independent and identically distributed stochastic differential equations (SDEs). This is done considering additional constraints, wherein only public data can be published and used for inference. The concept of local differential privacy (LDP) is formally introduced for a system of stochastic differential equations. The objective is to estimate the drift parameter by proposing a contrast function based on a pseudo-likelihood approach. A suitably scaled Laplace noise is incorporated to meet the privacy requirements. Our key findings encompass the derivation of explicit conditions tied to the privacy level. Under these conditions, we establish the consistency and asymptotic normality of the associated estimator. Notably, the convergence rate is intricately linked to the privacy level, and in some situations may be completely different from the case where privacy constraints are ignored. Our results hold true as the discretization step approaches zero and the number of processes N tends to infinity. [ABSTRACT FROM AUTHOR]

Featured Application: Potential applications of this work regard the parameter estimation and the resulting analyses of complex biochemical systems characterized by a stochastic behavior, which allows for elucidating the unknown underlying mechanisms. The parameter estimation (PE) of biochemical reactions is one of the most challenging tasks in systems biology given the pivotal role of these kinetic constants in driving the behavior of biochemical systems. PE is a non-convex, multi-modal, and non-separable optimization problem with an unknown fitness landscape; moreover, the quantities of the biochemical species appearing in the system can be low, making biological noise a non-negligible phenomenon and mandating the use of stochastic simulation. Finally, the values of the kinetic parameters typically follow a log-uniform distribution; thus, the optimal solutions are situated in the lowest orders of magnitude of the search space. In this work, we further elaborate on a novel approach to address the PE problem based on a combination of adaptive swarm intelligence and dilation functions (DFs). DFs require prior knowledge of the characteristics of the fitness landscape; therefore, we leverage an alternative solution to evolve optimal DFs. On top of this approach, we introduce surrogate Fourier modeling to simplify the PE, by producing a smoother version of the fitness landscape that excludes the high frequency components of the fitness function. Our results show that the PE exploiting evolved DFs has a performance comparable with that of the PE run with a custom DF. Moreover, surrogate Fourier modeling allows for improving the convergence speed. Finally, we discuss some open problems related to the scalability of our methodology. [ABSTRACT FROM AUTHOR]

This paper presents a new method for a comprehensive stabilization and backstepping control system design for a class of stochastic nonlinear systems. These types of systems are so abundant in practice that the control system designer must assume that random noise with a definite probability distribution affects the dynamics and observations of state variables. Stochastic control is intended to determine the time course of control variables so that the control target is achievable even with minimal cost. Since the mathematical equations of stochastic nonlinear systems are not always constant, not every model-based controller can be accurate. Therefore, in this paper, a type-3 fuzzy neural network is used to estimate the parameters of the backstepping control method. In the simulation, the proposed method is compared with the Type-1 fuzzy and RBFN methods. Results clearly show that the proposed method has a very good performance and can be used for any system in this class. [ABSTRACT FROM AUTHOR]

In this paper, we present some options to deal with the problem of parameter estimation in continuous-time stochastic systems under white, and coloured noise perturbations using classical methods. Least-squares method (LSM) is one of the most widely used estimation methods, in continuous and discrete time systems, but it presents a bias problem. The instrumental variable method (IV), even though is considered the best option when a noise is present in the system dynamics, cannot completely minimize its effect in continuous time. Here, we propose to combine these algorithms with two auxiliary techniques: the Kalman filter and the equivalent control. These techniques working in parallel with the LSM and IV estimation algorithm will reduce the bias, the noise effect in the estimated parameters, and are very easy to implement. The effectiveness of the proposed methods is illustrated in a numerical example. [ABSTRACT FROM AUTHOR]

Adaptive control has been successfully developed in deriving control law for stochastic systems with unknown parameters. The generation of reasonable control law depends on accurate parameter estimation. Recursive least square is widely used to estimate unknown parameters for stochastic systems; however, this approach only fits systems with Gaussian noises. In this paper, the adaptive quantile control is first proposed to cover the case where stochastic system noise follows sharp and thick tail distribution rather than Gaussian distribution. In the proposed approach, the system noise is modeled by the Asymmetric Laplace Distribution, and the unknown parameter is online estimated by our developed Bayesian quantile sum estimator, which combines recursive quantile estimations weighted by Bayesian posterior probabilities. With the real-time estimated parameter, the adaptive quantile control law is constructed based on the certainty equivalence principle. Our proposed estimator and controller are not computationally consuming and can be easily conducted in the Micro Controller Unit to fit practical applications. The comparison with some dominant controllers for the unknown stochastic system is conducted to verify the effectiveness of the adaptive quantile control. • Adaptive quantile control for the stochastic system with sharp and thick tail noise is proposed. • The sharp and thick tail noise is modeled by Asymmetric Laplace Distribution. • Bayesian quantile sum estimator combines different quantile estimated parameters weighted by Bayesian posterior probability. • The control law is based on the certainty equivalence principle. [ABSTRACT FROM AUTHOR]

Novel coronavirus has altered the socio-economic condition of the whole world through its devastating effects on the human population. Mathematical models and computation techniques may play an important role in understanding this epidemic and contribute a lot in policy making to control the infection in a more systematic and effective way. In this paper, we have proposed a deterministic mathematical model for the Covid-19 pandemic taking into account the different epidemiological status of individuals of a given geographical region and analyzed it with respect to the basic reproduction number. Uncertainty is obvious in the case of a growing epidemic and it multiplies if the disease etiology is unknown. Taking into account the uncertainty in the epidemiological parameters, we extended the deterministic system into a stochastic system through random parameter perturbations in three epidemiological parameters. Analyzing the model, we determined the disease persistence and eradication conditions. The asymptotic behavior of the stochastic solution around the coexistence equilibrium of the deterministic model was also presented. As a case study, we considered the Covid-19 pandemic of India and estimated the model parameters from the epidemic data. We demonstrated different analytical results and predicted the course of the epidemic. Our simulation results indicate that the epidemic in India may continue up to third week of July 2021 and the cumulative confirmed Covid-19 cases may vary from 12.13 × 10 6 to 13.41 × 10 6. Such results may be useful from management and policy development viewpoints. [ABSTRACT FROM AUTHOR]

Loss‐of‐control effectiveness is a common fault in the engineering field. In the existing adaptive fault‐tolerant control algorithms, observers and Lyapunov functions are often used to estimate fault parameters. However, they can only ensure the convergence of fault parameters as time goes to infinity. This leads to the fact that the controller can only play a better fault‐tolerant role in the steady‐state process, and cannot guarantee the system performance in the transient state. Therefore, a dual fault‐tolerant control (DFTC) algorithm is proposed for a class of stochastic systems with partial loss‐of‐control effectiveness. The algorithm introduces a fault‐tolerant objective on the basis of the control objective. By establishing a new objective function, the controller is forced to have the characteristics of active learning to improve the transient performance of the fault system. An example simulation verifies the validity of DFTC. The simulation results show that DFTC can drive the system to the desired output, especially when partial loss‐of‐control efficiency occurs in the system, it can learn the unknown parameters actively, quickly, and accurately, which is significantly better than the conventional control based on the certainty equivalence principle and improves the reliability of the system. [ABSTRACT FROM AUTHOR]

Today, induction motor (IM) is still the most popular electrical machine due to its robust and rare element-free structure, lower maintenance requirement, and cost-effective production. State estimation for this motor is the cornerstone for speed-sensorless control, fault-tolerant control, and fault diagnostics. Nonlinear Kalman filters, especially extended Kalman filters (EKFs), are the most preferred state and/or parameter estimation methods for IM. However, they require a stochastic system with complete process and measurement noise covariances for optimal estimations. These noise covariances, unknown or partially known in practice, vary under different operating conditions of the IM. To deal with this problem, various adaptive EKFs (AEKFs) have been proposed, which can compensate for the effect of varying noise covariances, but each approach has its own pitfalls. This article discusses the hybrid AEKF (HAEKF), which eliminates the problems of existing AEKFs. To demonstrate its effectiveness, the proposed HAEKF is compared qualitatively and quantitatively with existing AEKFs through simulation and experimental studies. Finally, improved estimation stability and performance are provided with the proposed HAEKF observer. [ABSTRACT FROM AUTHOR]

The partially observed linear Gaussian system of stochastic differential equations with low noise in observations is considered. The coefficients of this system are supposed to depend on some unknown parameter. The problem of estimation of these parameters is considered and the possibility of the approximation of the filtering equations is discussed. An estimators are used for estimation of the quadratic variation of the derivative of the limit of the observed process. Then this estimator is used for nonparametric estimation of the integral of the square of volatility of unobservable component. This estimator is also used for construction of method of moments estimators in the case where the drift in observable component and the volatility of the state component depend on some unknown parameter. Then this method of moments estimator and Fisher-score device allow us to introduce the One-step MLE-process and adaptive Kalman–Bucy filter. The asymptotic efficiency of the proposed filter is discussed. [ABSTRACT FROM AUTHOR]

This paper addresses the problem of reliability analysis of in-service identical systems when a limited number of lifetime data is available compared to censored ones. Lifetime (resp. censored) data characterise the life of failed (resp. non-failed) systems in the sample. Because, censored data induce biassed estimators of reliability model parameters, a methodology approach is proposed to overcome this inconvenience and improve the accuracy of the parameter estimation based on Bayesian inference methods. These methods combine, in an effective way, system’s life data and expert opinions learned from failure diagnosis of similar systems. Three Bayesian inference methods are considered: Classical Bayesian, Extended Bayesian and Bayesian Restoration Maximisation methods. Given a sample of lifetime data, simulated according to prior opinions of maintenance expert, a sensibility analysis of each Bayesian method is performed. Reliability analysis of critical subsystems of Diesel locomotives is established under the proposed methodology approach. The relevance of each Bayesian inference methods with respect to collected reliability data of critical subsystems and expert opinions is discussed. [ABSTRACT FROM PUBLISHER]

Purpose: This paper considers the complex stochastic systems such as supply chains, whose dynamics are controlled by an unknown parameter such as the arrival or service rates. The purpose of this paper is to provide a simulation-based estimator of the unknown parameter when only partially observed data on the underlying system is available. Design/methodology/approach: The proposed method treats the unknown parameter as a random variable and estimates the parameter by computing the conditional expectation of the random variable given the partially observed data. This study then express the conditional expectation as a weighted sum of reverse conditional probabilities using Bayes' rule. The reverse conditional probabilities are estimated using simulation. Findings: The simulation studies indicate that the proposed estimator converges to the true value of the conditional expectation as the computer time allocated to the simulation increases. The proposed estimator is computed within a few seconds in all of the numerical examples, which demonstrates its time efficiency. Originality/value: Most of the existing methods for estimating an unknown parameter require a significant amount of simulation, causing long computation delays. The proposed method requires a single simulation run for each candidate of the unknown parameter. Thus, it is designed to carry a significantly reduced computational burden. This feature will enable managers to use the proposed method when making real-time decisions. [ABSTRACT FROM AUTHOR]

Summary: For a dual‐rate sampled‐data stochastic system with additive colored noise, a dual‐rate identification model is obtained by using the polynomial transformation technique, which is suitable for the available dual‐rate measurement data. Based on the obtained model, a maximum likelihood least squares‐based iterative (ML‐LSI) algorithm is presented for identifying the parameters of the dual‐rate sampled‐data stochastic system. In order to improve the computation efficiency of the algorithm, the identification model of a dual‐rate sampled‐data stochastic system is divided into two subidentification models with smaller dimensions and fewer parameters, and a maximum likelihood hierarchical least squares‐based iterative (H‐ML‐LSI) algorithm is proposed for these subidentification models by using the hierarchical identification principle. The simulation results indicate that the proposed algorithms are effective for identifying dual‐rate sampled‐data stochastic systems and the H‐ML‐LSI algorithm has a higher computation efficiency than the ML‐LSI algorithm. [ABSTRACT FROM AUTHOR]

Summary: A robust adaptive parameter estimation method, based on the application of a full‐order filter capable of rejecting exogenous disturbances, is proposed in this article. A linear matrix inequality condition is proposed to synthesize the desired robust filter, assuming the presence of a known input control with constraints. The filter uses the output of the system to estimate the desired signal that will be employed in the adaptive estimation procedure and, to assure robustness to exogenous noise and unstructured uncertainties, the ℋ∞ guaranteed cost is minimized in the synthesis condition. The filtered signals are then applied to an adaptive procedure to estimate the unknown system's internal parameters, which is also proposed in this article. It is shown that lower values for the ℋ∞ guaranteed cost from the disturbance input to the error output of the filter imply more accurate estimations of the parameters. The efficiency of the proposed estimation technique is illustrated through a simulated model and a physical system has been considered to validate real‐time estimation. [ABSTRACT FROM AUTHOR]

Background: Extended Kalman filter (EKF) is one of the most preferred observers for state and parameter estimation of induction motor. To achieve optimal estimations, EKFs require a stochastic system with complete dynamic or measurement equation. However, those equations are partially known in practice and may vary depending on operating conditions, leading to a degradation in the estimation performance of conventional EKFs (CEKFs). Aim: To overcome this drawback, this paper proposes an adaptive fading EKF (AFEKF) observer that can compensate for the effect of the incomplete dynamic equation for the estimations of stator currents, rotor fluxes, rotor mechanical speed, and load torque. Materials & Methods: To show the superiority of AFEKF, its estimation performance is compared to that of CEKF in both simulations and real‐time experiments. Both observers have been implemented through the S‐Function block in Matlab/Simulink so that the same observer blocks can be used in both simulation and experimental studies. For real‐time implementations, a DS1104 controller board is used. In addition, the computational burdens of both CEKF and AFEKF are compared with real‐time experiments. Results and Discussion: The simulation and experimental studies indicate that the forgetting factor in AFKEF clearly improves the estimation performance of CEKF, especially in transient states. It also prevents the observer from diverging. Considering its advantages, the additional computational load that causes an increase in the computational load of about 4% can be ignored. Conclusion: The proposed AFEKF observer significantly improves the estimation performance and compensates for the effect of dynamic model inaccuracies. Its superiority has been validated by simulation and experimental studies. Finally, an observer with a better estimation performance has been proposed with a slight increase in computational load. [ABSTRACT FROM AUTHOR]

Considering the large‐scale development of renewable energy resources globally, control optimization of coal‐fired power plants is becoming increasingly crucial. The dynamics of the coordinated control system (CCS) must be studied prior to designing a controller. These dynamics of the subcritical units have been expressed through various modeling methods. However, in previous studies, ordinary differential equations (ODEs) have been primarily employed, which cannot reflect the uncertainties in the system. Therefore, a model with a greater accuracy should be observed to comprise uncorrelated residuals. In this study, the uncertainties in the calorific value of fired coal and combustion process were analyzed first. A normal distribution of disturbance was assumed in this process. The dynamics of the CCS were then described with stochastic differential equations (SDEs). Furthermore, a parameter estimation procedure was designed. The residual evaluation is employed to improve the model evaluation. After simulations, the SDE‐based model‐3 in this study elucidates the dynamics of the subcritical boiler‐turbine system better than the ODE‐based model and other SDE‐based models. The measured values can be regarded as a possible result of this model, rendering it a potential platform to employ stochastic model predictive control in CCS. [ABSTRACT FROM AUTHOR]

Parameter estimation is an important tool for modelling a real system. This study considers the parameter estimation problem of a multi‐input multi‐output state‐space system with unmeasurable states. By employing the negative gradient search and cutting down redundant parameter estimates, the authors derive a partially‐coupled generalised stochastic gradient (PC‐GSG) algorithm to estimate the parameters. Considering the unmeasurable states, they present a new state observer which replaces the unknown parameters with their estimates to generate state estimates. By combining the PC‐GSG algorithm and the new state observer, they obtain a state observer based partially‐coupled generalised stochastic gradient (SO‐PC‐GSG) algorithm to estimate the parameters and states. In order to eliminate the interference of the coloured noise and strengthen the performance of the SO‐PC‐GSG algorithm, they propose a state observer based filtering PC‐GSG algorithm by means of the data filtering technique. Finally, the effectiveness of the proposed algorithms is investigated in a simulation study. [ABSTRACT FROM AUTHOR]

Stochastic differential equations (SDEs) rapidly become one of the most well-known formats in which to express such diverse mathematical models under uncertainty such as financial models, neural systems, behavioral and neural responses, human reactions and behaviors. They belong to the main methods to describe randomness of a dynamical model today. In a financial system, different kinds of SDEs have been elaborated to model various financial assets. On the other hand, economists have conducted research on several empirical phenomena regarding the behaviour of individual investors, such as how their emotions and opinions influence their decisions. All those emotions and opinions are described by the word Sentiment. In finance, stochastic changes might occur according to investors' sentiment levels. In our study, we aim to represent the mutual effects between some financial process and investors' sentiment with constructing a coupled system of non-autonomous SDEs, evolving in time. These equations are hard to assess and solve. Therefore, we express them in a simplified manner by discretization and Multivariate Adaptive Regression Splines (MARS) model. MARS is a strong method for flexible regression and classification with interactive variables. Hereby, we treat time as another spatial variable. Eventually, we present a modern application with real-world data. This study finishes with a conclusion and an outlook towards future studies. [ABSTRACT FROM AUTHOR]

Summary: Joint estimation of states and time‐varying parameters of linear stochastic systems is of practical importance for fault diagnosis and fault tolerant control. The known fact is that measurements have outliers. They can significantly degrade the properties of linearly recursive algorithms, which are designed to work in presence of Gaussian noises. This article proposes two kinds of strategies for joint parameter‐state robust estimation of linear stochastic models in presence of all possible faults and non‐Gaussian noises. In the form of Theorem, joint robust algorithm for systems with sensor and component faults, as well as the algorithm for systems with parameter faults are proposed. Because of their good features in robust filtering, Masreliez‐Martin filter represents a cornerstone for realization of the proposed robust algorithms for joint state‐parameter estimation. The good features of proposed robust estimation algorithms, in relation to algorithms based on other widely‐used filters, are illustrated by simulation results. On the other side, intensive research in the field of mathematical modeling of pneumatic servo drives has shown that their mathematical models are nonlinear in which a lot of important details cannot be included in the model. Also, it has been well known that the nonlinear model can be approximated by a linear model with time‐varying parameters. Due to the abovementioned reasons, it can be assumed that the pneumatic cylinder model is a linear stochastic model with variable parameters. The good practical values of the proposed robust joint algorithm to identification of the pneumatic cylinder are illustrated by experimental results. [ABSTRACT FROM AUTHOR]

This work is about parameter estimation for a fast–slow stochastic system with non-Gaussian α-stable Lévy noise. When the observations are only available for slow components, a system parameter is estimated and the accuracy for this estimation is quantified by p-moment with p ∈ (1, α), with the help of a reduced system through a random slow manifold approximation. This method provides an advantage in computational complexity and cost due to the dimension reduction in stochastic systems. To numerically illustrate this method, and to corroborate that the parameter estimator based on the reduced slow system is a good approximation for the true parameter value of the original system, a prototypical example is present. [ABSTRACT FROM AUTHOR]

In this paper, a recursive hierarchical parametric estimation (RHPE) algorithm is proposed for stochastic nonlinear systems which can be described by Wiener‐Hammerstein (W‐H) mathematical models. The formulation of parameters estimation problem is based on the prediction error approach and the gradient techniques. The convergence analysis of the developed RHPE algorithm is derived using stochastic gradient‐based theory. Wiener‐Hammerstein hydraulic process is treated to prove the efficiency of the proposed approach. [ABSTRACT FROM AUTHOR]

This study considers the identification problems of multiple‐output non‐linear equation‐error moving average systems. There exist the product items of the parameters between the non‐linear and linear parts. To solve this difficulty, the key term separation technique is adopted. By using the model decomposition technique and the hierarchical identification principle, a maximum likelihood‐based recursive extended least‐squares estimation algorithm with reduced computational complexity is presented to estimate the parameters of the non‐linear part and the linear part interactively. The simulation results demonstrate the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

The present research has introduced a novel adaptive state-dependent impulsive observer (ASDIO) used to control diverse nonlinear systems with time-varying delay. This designed ASDIO is in conformity with the approach of extended pseudo-linearization for the purpose of parametrizing a nonlinear system with time-delay to a pseudo-linear time-delay structure having state-dependent coefficients. This technique makes the ASDIO applicable to nonlinear systems with distributed, multiple, and time-varying delays. The time-varying and delay-independent Lyapunov functional approach, coupled with the comparison method for impulsive systems, was used to confirm the stability of ASDIO. This new theorem affirmed the state and parameter estimation error to approach zero asymptotically through distinct and less-conservative adequate conditions with respect to practical linear matrix inequalities. Furthermore, the maximum impulse time was specified via the presented stability theorem. The ASDIO has also been offered for a special set of stochastic nonlinear systems with time-delay. An investigation of the asymptotic stability for the intended ASDIO was performed via a new theorem employing the comparison principle for stochastic impulsive systems. Accordingly, this observer was simulated on an epidemic system with time-delay nonlinear features to affirm its performance. • The ASDIO is applicable in a vast group of nonlinear systems with different time-delay types considering the extended pseudo-linearization approach. • The asymptotic convergence of the estimation error for both state and parameter to zero is guaranteed under explicit and less-conservative adequate conditions that are presented concerning feasible LMIs attributed to the comparison system theory. • The stability theorem determines an upper bound of time intervals between consecutive impulses, unlike existing methods where the minimum and maximum impulse intervals are regarded as known parameters. • The stability theorem contains the special case under Lipschitz condition and the general case of the sector bounded condition. Thus, less-conservative sufficient condition and LMIs with larger feasibility are generated. • The ASDIO can evaluate unknown parameters and states for a vast group of stochastic nonlinear time-delay systems under less-conservative adequate conditions stated regarding available LMIs. [ABSTRACT FROM AUTHOR]

Statistical process adjustment (SPA) is utilised prevalently in novel manufacturing scenarios. When quality characteristics rather than internal process variables are inspected for the purpose of quality control, data with different resolutions may be collected. This paper proposes a Bayesian framework for parameter estimation when only categorical observations are available. The proposed method incorporates categorical information recursively and updates parameter estimates in real time. Simulation results show that the framework is effective in utilising low-resolution information in parameter estimation, model building and process control. [ABSTRACT FROM AUTHOR]

We present the weighted-sum expression of quaternary parameter estimations via balancing surface bowing estimation errors. Expressions have been derived for both quaternary alloys AxByCzD and AxB1-xCyD1-y and applied to the band gaps of AlGaInAs, AlGaInP, InAsPSb, GaInAsP, and GaInAsSb. Approximation can be improved by fitting known data of quaternary alloys and maximum deviations are less than 20 meV with respect to the lattice-matched polynomial expressions. [ABSTRACT FROM AUTHOR]

We consider the joint state and parameter estimation for dynamical systems having both time-varying and time-invariant parameters. For systems with time-invariant parameters, it has previously been demonstrated that although nonlinear filters may be used for concurrent state and parameter estimation, employing the Markov Chain Monte Carlo (MCMC) algorithm for estimating time-invariant parameters with nested nonlinear filters for state estimation provides more reliable estimates. Following established methods for parameter estimation using filters, we augment the state vector to include the original system states in addition to the subset of the parameters that are known to vary in time. Conventionally, both time-varying and time-invariant parameters would be appended in the state vector, and thus for the purpose of estimation, both would free to vary in time. However, allowing parameters that are known to be time-invariant to change in time introduces non-physical dynamics into the original system. To avoid inducing artificial dynamics, the time-invariant parameters are estimated using MCMC. Furthermore, by estimating the time-invariant parameters by MCMC, the dimensionality of the augmented state is smaller and the nonlinearity in the ensuing state space model will tend to be weaker compared to the conventional approach. The time-varying parameters are perturbed by random noise processes, and the amplitude of the artificial noise is estimated alongside the time-invariant system parameters using MCMC. Estimating the noise strength in this procedure circumvents the need for manual tuning. We illustrate the above-described approach for a simple dynamical system in which some model parameters are time-varying, while the remaining parameters are time-invariant. We adopt the extended Kalman filter (EKF) for state estimation and the estimation of the time-varying system parameters, but reserve the task of estimating time-invariant parameters, including the model noise strength and the artificial noise strength associated with the time-varying parameter to the MCMC algorithm. • The concurrent estimation of time-varying and time-invariant parameters is presented • Nonlinear filters nested within MCMC permit robust time-varying parameter estimation • The framework is applied to an oscillator with a random forcing for damage detection [ABSTRACT FROM AUTHOR]

Compared with the systems with white noise disturbances, the parameter identification of the systems with colored noises (i.e., correlated noises) is more difficult. In this letter, we use the model transformation to study the identification problem for the systems with colored noises by using the filtering identification idea. The basic idea is to transform a system with colored noise into two identification models with white noises and then to propose a novel parameter estimation algorithms, which can generate more accurate parameter estimates than some related existing identification algorithm. The proposed method can be applied to other linear or nonlinear stochastic systems with different structures and colored disturbance noises. The provided simulation example tests the proposed algorithm. [ABSTRACT FROM AUTHOR]

To design and evaluate airborne networks (ANs), it is crucial to utilize random mobility models (RMMs) that capture the physical movement patterns of different aerial vehicles in real scenarios. Compared to expensive flight field tests, RMM-based modeling, simulation, and emulation is cost-effective with a large set of RMM-generated flight trajectories. Despite the importance of RMMs, we notice that most existing models focus on the 2-D movement, and do not consider the temporal and 3-D spatial correlation of aerial mobility patterns. In this paper, we propose a comprehensive 3-D smooth turn (ST) modeling framework for fixed-wing aircraft, which can serve as a design and evaluation foundation for future ANs. In the proposed framework, we develop two realistic 3-D ST RMMs that capture the diverse mobility patterns of fixed-wing aircraft, through coupling stochastic forcing with physical laws that govern the 3-D aerial maneuvers. We also develop two boundary models to determine the movement of aerial vehicles when they approach simulation boundaries. Moreover, we propose an approach to estimate the optimal 3-D ST RMMs, with which we can produce rich trajectory ensembles with statistical mobility patterns that match with the real trajectory data.

Summary: For many applications with multivariate data, random‐field models capturing departures from Gaussianity within realizations are appropriate. For this reason, we formulate a new class of multivariate non‐Gaussian models based on systems of stochastic partial differential equations with additive type G noise whose marginal covariance functions are of Matérn type. We consider four increasingly flexible constructions of the noise, where the first two are similar to existing copula‐based models. In contrast with these, the last two constructions can model non‐Gaussian spatial data without replicates. Computationally efficient methods for likelihood‐based parameter estimation and probabilistic prediction are proposed, and the flexibility of the models suggested is illustrated by numerical examples and two statistical applications. [ABSTRACT FROM AUTHOR]

This paper is concerned with the parameter estimation problem for partially observed mean-reversion type stochastic systems. The Girsanov transformation is used to simplify the equation because of the expression of the drift coefficient. The suboptimal estimation of the state is obtained by constructing the extended Kalman filtering equation. The likelihood function is provided based on state estimation equation. The strong consistency of the estimator is proved by applying maximal inequality for martingales, Borel-Cantelli lemma and uniform ergodic theorem. An example is given to verify the effectiveness of the estimation methods. [ABSTRACT FROM AUTHOR]

The estimation problem for stochastic parametric nonlinear dynamical models is recognized to be challenging. The main difficulty is the intractability of the likelihood function and the optimal one-step ahead predictor. In this paper, we present relatively simple prediction error methods based on non-stationary predictors that are linear in the outputs. They can be seen as extensions of the linear prediction error methods for the case where the hypothesized model is stochastic and nonlinear. The resulting estimators are defined by analytically tractable objective functions in several common cases. It is shown that, under certain identifiability and standard regularity conditions, the estimators are consistent and asymptotically normal. We discuss the relationship between the suggested estimators and those based on second-order equivalent models as well as the maximum likelihood method. The paper is concluded with a numerical simulation example as well as a real-data benchmark problem. [ABSTRACT FROM AUTHOR]

This paper considers the parameter estimation problem of stochastic systems (i.e., controlled autoregressive systems) by adopting the projection method and the hierarchical identification principle. To improve the performance of the projection identification algorithm, a generalized projection algorithm is proposed by introducing a data window length. By means of the hierarchical identification principle, we divide the system into two fictitious subsystems and derive a two-stage generalized projection identification algorithm. The simulation example tests the effectiveness of the proposed identification algorithms. [ABSTRACT FROM AUTHOR]