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Minimum variance (MV) benchmark is a quantification that is widely applied to compare actual performance of a control loop against its optimal performance. For linear systems, MV benchmark has been well studied, and several well-practiced techniques have been proposed to evaluate the performance of the systems. However, these techniques may not provide satisfactory performance in some situations. For instance, the operational data sampled from a multi-model system does not satisfy stationary conditions that are required for conventional methods. As a result, linear MV benchmark techniques cannot be applied. One possible approach to design MV controller for a multi-model system is to segregate, and label the data using a dynamic clustering method. Then, the MV benchmark can be determined by the multi-model MV control. In this paper, a support vector regression based method is proposed in which all three steps of dynamic clustering, model identification and MV controller design are performed simultaneously through a data driven approach. In addition, a new support vector-based clustering method is proposed by which the data are clustered in residual space of the process model. The optimality and convergence of the proposed algorithm are studied. The proposed multi-model MV controller design technique is demonstrated through a simulated continuous stirred-tank reactor (CSTR) example, which is operated in varying conditions. • SVR based minimum variance controller is proposed. • Three steps of clustering, identification and controller design are performed simultaneously. • Multi-mode MV controller is designed. • Data driven approach is proposed. • The optimality and convergence are studied. [ABSTRACT FROM AUTHOR]

The dual neural extended Kalman filter (DNEKF) is proposed in this article to compensate for model inaccuracies and violations of noise assumption in the EKF-based multirate sensor fusion. The DNEKF employs two neural networks to improve process state and output predictions through simultaneous state and parameter estimations using state vector augmentation. Taking advantage of frequent but less accurate measurements and infrequent but more accurate measurements provides a multirate parameter update strategy for neural networks training in the proposed approach. Two numerical examples and one industrial application demonstrate the effectiveness of the proposed method to compensate for inadequate process knowledge to improve multirate sensor fusion performance. [ABSTRACT FROM AUTHOR]

Summary: This paper is concerned with distributed data‐driven observer design problem. The existing data‐driven observers rely on a common assumption that all the information about the system, and the calculations based upon this information are centralized. Therefore the resulting algorithms cannot be applied to the distributed systems in which each local observer receives only a part of the output signal. On the other hand, traditional model‐based distributed state estimation methods generally assume that the processes are decomposed according to the known process models, while in data‐driven approaches there is no such information available. The main goal of this paper is to extend the centralized data‐driven observer design approach to the distributed framework. The stability of the proposed data‐driven distributed observer is also proved analytically. A quadruple‐tank process is simulated to demonstrate the performance of the proposed scheme. [ABSTRACT FROM AUTHOR]

In distributed control systems, a local regulator does not have complete knowledge of the whole system. Therefore, some information is transmitted between local regulators through communication lines. The delays in communication lines are not negligible and they can make the closed‐loop system unstable or impose a limit on the achievable control performance. Due to the process and communication delays, controllers cannot reject all disturbances. Although there has been a plethora of literature available for assessing the control performance in the presence of process time delay, no similar study has been conducted for distributed control systems in the presence of communication delays. In order to address this problem, a new solution for performance assessment of distributed control systems, which takes communication delays into account, is proposed here. Further, the corresponding minimum variance controller is also derived under the distributed control framework with communication delays. [ABSTRACT FROM AUTHOR]

In the traditional formulation of Gaussian Process Regression (GPR), the input data is assumed to be noise-free. However, this assumption is not always realistic in many practical problems. A new robust GPR model is introduced in this paper where the input and output are both corrupted by noise. To address this problem, the output noise is modelled using a mixture of two Gaussian distributions to account for both regular and outlying noises and the input noise is assumed to be an independently and identically distributed (i.i.d.) Gaussian noise. A learning scheme based on the Errors-In-Variables (EIV) model and the Expectation Maximization (EM) algorithm is proposed to derive a new Gaussian Process model whose kernel function is dependent on hyper-parameters describing both the input and output noises. The first and second moments of the predictive distribution are obtained based on the learned hyper-parameters through the proposed algorithm. Simulation examples as well as an industrial case study presented here demonstrate the effectiveness of the proposed method and its superiority to other existing methods. • A new robust GP model with input noise is proposed. • The input and output noises are Gaussian and mixture of two Gaussian distributions, respectively. • Using two different approaches, the GP prior is approximated. • A learning scheme based on the Errors-In-Variables (EIV) model and the Expectation Maximization (EM) algorithm is proposed. • The first and second moments of the predictive distribution are obtained. [ABSTRACT FROM AUTHOR]

Prediction is an essential part of predictive control and is widely applied in control engineering. In a distributed control system configuration, there are signal transmissions between local subsystems. Communication delays impose a limit on the achievable prediction performance. Even though there is a plethora of literatures available for multiple step ahead prediction under the centralised framework, they are traditional techniques that cannot be applied to the distributed framework due to the interactions between the different subsystems and communication delays that have not been taken into account. In this study, a technique for determining the distributed multiple step ahead prediction is proposed which is optimal in sense of the lowest total prediction error variance. The proposed approach is useful for designing optimal controllers or assessing the performance of the implemented control loop while the controller structure has the distributed framework. [ABSTRACT FROM AUTHOR]

To assess the performance of a control loop based on the minimum variance (MV) benchmark, we need to calculate MV lower bound (MVLB). Even though there is a plethora of literature available for calculating MVLB for the linear systems, these methods are not suitable for non‐linear systems. Furthermore, almost all of the real‐world applications have been encountered with input variance constraints. These constraints limit controllers' abilities in decreasing the output variability. Therefore, existing MVLB computation methods, which do not account for input constraints, are not realistic when applied to constrained systems. The authors propose a novel approach to estimate MVLB by employing properties of dual Lagrangian functions to address these issues simultaneously in this study. Furthermore, to design the constrained non‐linear MV controller (MVC), they propose to use the recurrent neural network for accommodating non‐linearities and the input constraints. Then, control loop stability, optimality with respect to MVLB as well as the global convergence of the proposed controller are analytically proved for convex‐non‐linear systems with input constraints. The proposed control strategy is verified through simulations performed on a non‐linear quadruple‐tank system. The results indicate that the proposed design provides satisfactory results in decreasing output variance while satisfying the constraints. [ABSTRACT FROM AUTHOR]

Designing nonlinear optimal controllers such as Minimum Variance Controller (MVC) has many difficulties. Main difficulties are 1) in order to design controller; the explicit relations between outputs and inputs must be executable. This relation is defined as implicitly in the nonlinear models; 2) learning controller is a high dimensional-multimodal optimization task and search space can be extremely rugged and has many local minima. In this paper, in order to overcome these disadvantages, the model-free optimal controller scheme is utilized. In a model-free controller, as the system model is not available, the gradient of the cost function cannot be executed. Instead, in this paper, a relation between gradient of the controller with gradient of the system model is derived by inverse lemma. The controller structure is selected to be neural network. Then, the gradient based PSO (GPSO) is proposed to be a learning controller. GPSO has both advantages of global searching and convergence properties. The application of the methodology to the empirical CSTR model indicates that this approach gives very credible estimates of the controller. The simulation results indicate that the proposed method can be more accurate than existing methods. [ABSTRACT FROM AUTHOR]

This paper presents a control strategy for achieving a robust minimum variance controller (MVC) by modelling uncertainty using a type-2 fuzzy set and satisfying H∞ norm specifications. In this paper, an MVC is designed considering three types of structural, parametric and algorithmic uncertainties. Thus, an interval type-2 fuzzy set is utilized. This paper utilizes one method to construct interval type-2 fuzzy set models by the uncertain interval data and model error modelling approach. In addition, a sufficient condition is developed that guarantees the stability and robustness of the controller. The design of a robust generalized MVC by the identified model is presented. Finally, an experimental test is used to clarify the effectiveness of the proposed control scheme. The proposed method (omitting uncertainty of the linear model) considerably decreases output variance from 0.15 to 0.0018. [ABSTRACT FROM AUTHOR]

Many real-world applications require minimization of a cost function. This function is the criterion that figures out optimally. In the control engineering, this criterion is used in the design of optimal controllers. Cost function optimization has difficulties including calculating gradient function and lack of information about the system and the control loop. In this article, for the first time, gradient memetic evolutionary programming is proposed for minimization of non-convex cost functions that have been defined in control engineering. Moreover, stability and convergence of the proposed algorithm are proved. Besides, it is modified to be used in online optimization. To achieve this, the sign of the gradient function is utilized. For calculating the sign of the gradient, there is no need to know the cost-function's shape. The gradient functions are estimated by the algorithm. The proposed algorithm is used to design a PI controller for nonlinear benchmark system CSTR (Continuous Stirred Tank Reactor) by online and offline approaches. [ABSTRACT FROM AUTHOR]

Photocatalytic oxidation (PCO)-based air filters are gaining attention owing to their capacity for indoor pollutant removal. This review summarized the application of ultraviolet-photocatalytic oxidation (UV-PCO) in heating, ventilation, and air conditioning (HVAC) systems, including the modeling studies, reactor designs, the influence of operational conditions, with emphasis on the common issue of byproduct generation, and the resulting indoor byproduct exposure levels. As a result, the concentrations of the typical byproducts for the most challenging pollutants were relatively low, except for the PCO of ethanol. Hence, UV-PCO is not recommended for buildings with high ethanol concentrations. Based on the formation of the formaldehyde, a new exposure-based evaluation standard for UV-PCO was developed to evaluate the feasibility of integrating UV-PCO reactors into an HVAC system. Then, applying the newly developed evaluation standard on a developed database (data size: 174) from the literature, 32.5% of the cases were identified as suitable for HVAC system applications in residential and commercial buildings, and all cases could be used for industrial buildings. Finally, a case study was conducted to develop a support vector machine (SVM) classification model with good accuracy, and challenging compound types, inlet concentrations, and air velocity were found to be the main parameters affecting the applicability of UV-PCO. [Display omitted] • Concentrations of the typical byproducts for the most challenging compounds are relatively low except for the PCO of ethanol. • Integrating UV-PCO reactors into HVAC systems requires case by case evaluation due to the byproduct formation. • A novel approach was proposed to evaluate the health impact of PCO in the case of formaldehyde removal/generation. • A SVM model was developed to classify PCO applications into different buildings. [ABSTRACT FROM AUTHOR]

We propose amethod to improve the performance of evolutionary algorithms (EA). The proposed approach defines operatorswhich can modify the performance of EA, including Levy distribution function as a strategy parameters adaptation, calculating mean point for finding proper region of breeding offspring, and shifting strategy parameters to change the sequence of these parameters. Thereafter, a set of benchmark cost functions is utilized to compare the results of the proposedmethod with some other well-known algorithms. It is shown that the speed and accuracy of EA are increased accordingly. Finally, this method is exploited to optimize fuzzy control of truck backer-upper system. [ABSTRACT FROM AUTHOR]

This paper deals with the control performance assessment of distributed networked control systems in the presence of communication delays. The best achievable steady-state performance of distributed networked control systems in the framework of distributed linear quadratic Gaussian (LQG) control is presented where communication delays serve as the most fundamental performance limitation. In the proposed distributed LQG control design, distributed controllers and distributed observers are designed simultaneously without using separation principle. And the non-applicability of separation principle is investigated and demonstrated in distributed networked control with communication delays. In order to handle time-varying communication delays, we propose to use lower and upper bounds to characterize the range of the best achievable control performance with respect to the range of the communication delays. The obtained results can be used to evaluate the potential performance improvement of an existing distributed networked control system. The proposed approach is illustrated through a numerical example. [ABSTRACT FROM AUTHOR]

One of the indices for evaluating the performance of control systems based on the routine operation data is the Hurst index. It is shown that the Hurst index value is very close to that of the minimum variance index which measures the performance of a control loop in terms of minimum variance benchmark. The advantage of Hurst index over minimum variance index is that it does not require the system model and its parameters. The Hurst index is based on the Hurst exponent, which measures the time series correlations. This paper analytically scrutinizes the effect of parameters and dynamics of a stochastic control system on the output Hurst exponent, which helps better comprehend the Hurst index and its relationship with the minimum variance index. For this purpose, the control system output is modeled as an Autoregressive Moving Average (ARMA) process, and the relationship between the parameters of the ARMA process and the output Hurst exponent is examined. Furthermore, the characteristics of the autocorrelation function of a signal under minimum variance conditions are extracted. This paper also proposes a new technique for estimating the Hurst exponent of control signals based on the autocorrelation function. Simulation examples illustrate the efficiency of the proposed approaches. • A new technique for estimating the Hurst exponent of control signals. • The effect of control system parameters and dynamics on the output Hurst exponent. • The relationship between parameters of an ARMA process and the output Hurst exponent. • Why can the Hurst index be used to estimate the minimum variance index? • How can the autocorrelation function quickly show the minimum variance conditions? [ABSTRACT FROM AUTHOR]

In this study, a generalised minimum variance control (GMVC) method using the projection-based recurrent neural network (PRNN) is proposed to minimise the error variance in the output of the non-linear plant. One the main drawbacks of the conventional GMVC approaches is the lack of a systematic procedure to deal with the input constraints. In this study, the PRNN is employed for incorporating the input constraints to the minimum variance index. This network is based on the optimality conditions of a constrained problem and is designed using projection theorem. To formulate the proposed approach, by considering an ARMAX model of the system and converting the cost function to a quadratic programming problem, the dynamics and output equations of the PRNN is obtained. The stability and global convergence of the PRNN is analytically shown. Moreover, suitable conditions for the weighting matrices of the cost function are determined to ensure the closed-loop stability. The proposed control method is applied to the non-linear quadruple tank and a comparative analysis between MVC, GMVC and the proposed approach is performed. [ABSTRACT FROM AUTHOR]

In this study, a generalised minimum variance control (GMVC) method using the projection‐based recurrent neural network (PRNN) is proposed to minimise the error variance in the output of the non‐linear plant. One the main drawbacks of the conventional GMVC approaches is the lack of a systematic procedure to deal with the input constraints. In this study, the PRNN is employed for incorporating the input constraints to the minimum variance index. This network is based on the optimality conditions of a constrained problem and is designed using projection theorem. To formulate the proposed approach, by considering an ARMAX model of the system and converting the cost function to a quadratic programming problem, the dynamics and output equations of the PRNN is obtained. The stability and global convergence of the PRNN is analytically shown. Moreover, suitable conditions for the weighting matrices of the cost function are determined to ensure the closed‐loop stability. The proposed control method is applied to the non‐linear quadruple tank and a comparative analysis between MVC, GMVC and the proposed approach is performed. [ABSTRACT FROM AUTHOR]

• Addressing the control performance assessment problem using Hurst index. • Examining crossover phenomena in estimating the Hurst exponent of control signals. • Modifying the Hurst index based on the crossover phenomena. • Estimating the minimum variance index using routine operation data of the system. This paper proposes a new Hurst exponent-based method to evaluate the performance of control loops by estimating Minimum Variance Index (MVI). Incorrect estimation of time delays dramatically affects MVI-based performance assessment accuracy. The main advantage of the proposed method over existing methods is that it only requires routine operation data, without any need for prior information of the system model parameters and time delays. Hence, this method is more suitable to be applied on various industrial control processes. Recently, crossover phenomena have been reported in the graphs used to estimate the Hurst exponent of different control signals, which complicate deciding the Hurst exponents values. To address this problem, the crossover phenomenon is investigated for control signals, then the Hurst index is modified based on it. The proposed method is successfully used to assess performance of various types of control loops such as the cascade loop and verified through simulation results. [ABSTRACT FROM AUTHOR]