Stochastic Distribution Control Research Articles

Reducing Urban Traffic Congestion Using Deep Learning and Model Predictive Control.

This article proposes a deep learning (DL)-based control algorithm-DL velocity-based model predictive control (VMPC)-for reducing traffic congestion with slowly time-varying traffic signal controls. This control algorithm consists of system identification using DL and traffic signal control using VMPC. For the training process of DL, we established a modeling error entropy loss as the criteria inspired by the theory of stochastic distribution control (SDC) originated by the fourth author. Simulation results show that the proposed algorithm can reduce traffic congestion with a slowly varying traffic signal control input. Results of an ablation study demonstrate that this algorithm compares favorably to other model-based controllers in terms of prediction error, signal varying speed, and control effectiveness.

States estimation and resilient control for non-Gaussian stochastic distribution control system under sensor attacks

This paper studies states estimation and resilient control schemes based on model predictive control (MPC) algorithm for a class of Takagi–Sugeno (T–S) fuzzy stochastic distribution control (SDC) system subjected to sparse sensor attacks. Firstly, a T–S fuzzy model is used to approximate the dynamics of a non-Gaussian SDC system, where the outputs of the system is the output probability density functions (PDFs). Secondly, in order to estimate the states and attacks in the system, a fuzzy Luenberger observer is designed. In addition, based on the estimated states and attacks, the designed MPC resilient control method achieves a satisfied tracking performance. Finally, the feasibility of the estimation algorithm and resilient controller are verified by simulation.

Optimized Distributed Cooperative Control for Islanded Microgrid Based on Dragonfly Algorithm

This study introduces novel stochastic distributed cooperative control (SDCC) in the context of island microgrids (MGs). A proportional resonant (PR) controller and virtual impedance droop control in stationary reference frames are employed in cooperation with distributed averaging secondary control optimized by the dragonfly algorithm (DA). The suggested approach demonstrates the capability to achieve mean-square synchronization for the voltage and frequency restoration of distributed generators (DGs) to ensure efficient active power sharing. Therefore, a sparse communication network has been used to avoid data congestion and reduce the need for extensive communication and information exchange. The proposed system offers an instinctive compromise between voltage regulation and reactive power sharing. A conventional centralized secondary control with PR droop control is simulated for performance evaluation and comparison purposes. In this study, empirical evidence is demonstrated to support the MG’s ability to confront communication failure and its ability to work reliably during plug-and-play operations.

Fault‐tolerant control design for stochastic distribution control systems based on k‐step fault estimation

AbstractA novel scheme of fault‐tolerant control (FTC) and fault estimation (FE) for the stochastic distribution control (SDC) system with disturbance is investigated. The output probability density function (PDF) is modelled by the weight vector of the B‐spline neural network with the given basis function, and control of output probability density function can be converted to control of the weight vector of the B‐spline neural network. A k‐step fault estimation algorithm aiming at enhancing the accuracy of fault estimation is first applied to the stochastic distribution control system. Subsequently, a dynamic output feedback fault‐tolerant control algorithm is constructed by using the k‐step fault estimation information to guarantee that the target weight vector can be still approximated by the output weight vector in case of actuator fault. A simulation example is used to confirm the availability of the presented method.

Fault isolation and fault‐tolerant control for nonlinear stochastic distribution control systems with multiplicative faults

AbstractIn this paper, a fault isolation, diagnosis and fault tolerant control algorithm is proposed for nonlinear multiple multiplicative faults stochastic distribution control systems employing Takagi–Sugeno fuzzy system. To obtain the detailed fault information, a fault detection algorithm is introduced to discover the fault occurrence time. Then a fault isolation observer is built to produce the residual, and the error system is separated to subsystems affected only by disturbance and multiplicative faults. Moreover, a fault estimation scheme is presented to obtain the fault magnitude information. When faults occur, the system output probability density function will deviate from the desired distribution. So the model predictive control fault tolerant control scheme is needed to minimize the impact of faults as much as possible to make sure that the post fault output probability density function track the desired probability density function. The validity of the designed algorithm is demonstrated through a simulation example, where the fault tolerant control algorithm ensures that the system output probability density function still track the given output probability density function despite the complex case of multiple multiplicative faults occurring simultaneously.

A stochastic distributed control approach for load restoration of networked microgrids with mobile energy storage systems

In response to extreme events, substantial research efforts have focused on developing load restoration strategies for networked microgrids (MGs). However, existing distributed control approaches only consider independent time periods, which cannot capture the time-coupled flexibility of storage units. Additionally, mobile energy storage systems (MESSs) have been deployed for resilience enhancement due to their advantages in mobility and flexibility. However, existing research on networked MGs utilizes simplistic energy management approaches for MG modeling without detailed network structures, which cannot capture the mobility of MESSs. To address these issues, this paper proposes a three-stage stochastic distributed control approach based on rolling optimization to enhance the resilience of networked MGs with MESSs. Specifically, a stochastic linearized OPF is formulated in the first stage to capture the flexibility of MESSs and uncertainties, while a consensus algorithm is utilized in the second stage to calculate the power exchange among MGs. Finally, a detailed non-linear AC OPF algorithm is employed in the third stage to capture technical constraints relating to stability properties towards accurate optimization results. Case studies considering load distinction, multiple line outages, and limited generation resources are developed to demonstrate the effectiveness of the proposed distributed control approach in accurate and timely decision-making.

Recent Advances in Non-Gaussian Stochastic Systems Control Theory and Its Applications

Survey/review study Recent Advances in Non-Gaussian Stochastic Systems Control Theory and Its Applications Qichun Zhang 1, and Yuyang Zhou 2,* 1 Department of Computer Science, University of Bradford, Bradford BD7 1DP, United Kingdom 2 School of Computing, Engineering and the Built Environment, Edinburgh Napier University, Edinburgh EH10 5DT, United Kingdom * Correspondence: y.zhou@napier.ac.uk Received: 24 October 2022 Accepted: 18 November 2022 Published: 22 December 2022 Abstract: Non-Gaussian randomness widely exists in complex dynamical systems, in which the traditional mean-variance index cannot fully reflect the systematic characteristics. To improve the performance of control design subjected to non-Gaussian noises, stochastic distribution control (SDC) theory was proposed in the 1990s, where the output probability density function (PDF) has been investigated as an additional system variable. Following this framework, SDC has been extended to other research subjects in control systems such as filter design, fault diagnosis, and so on. It shows that SDC supplies an important solution to enhance the accuracy of system design, which is further beneficial to almost all the topics subject to non-Gaussian randomness. Meanwhile, the theoretical results of the SDC have been applied to several practical industrial applications. As data science raises based on the development of industrial artificial intelligence, SDC has been further developed recently focusing on data-driven design and multi-agent systems. To explore the new challenges with the evolution of SDC, e.g. unknown system models, unknown noise distributions, strong non-stationary transient dynamics, stability analysis and industrial applications, this survey summarises the most recent published results in the last 5 years of SDC work in terms of modelling, control, filtering, fault diagnosis, and industrial applications. Based on the technical analysis, potential future work is discussed in the end.

Concurrent multiscale topology optimisation towards design and additive manufacturing of bio-mimicking porous structures

ABSTRACT This paper presents a novel multiscale explicit topology optimisation approach for concurrently optimizing the structure at the macro level and the bio-mimicking porous infillings at the micro level. Solid bar components with cross-section control at the macro level and sphere components at the micro level are constructed as the minimal control units to replace the manipulation of material distribution at each grid. The overlapping, moving and morphing of bar components provide the ability to generate flexible structural shapes at the macro level. Using the inspiration of the turtle shell (carapace), the sphere components are designed to move, overlap, and resize inside the bar to sufficiently mimic both the regular and irregular porous features. Classical beam designs, lattice structure designs and unit cell designs are illustrated as numerical examples to demonstrate the functionalities and correctness of the proposed method. As a result, the stochastic pores distribution and porosity control can be validated. The abilities of optimising lattice structure at truss-level and single unit cell level are demonstrated. Moreover, the samples are fabricated by selective laser melting (SLM) technology and then scanned with the X-ray micro-computed tomography (micro-CT) technique to further examine the manufacturability.

Boundedness analysis of stochastic distributed delay-coupled systems on networks driven by G-Brownian motion

The present article is devoted to discuss the pth moment exponential ultimate boundedness for a class of stochastic distributed delay-coupled systems on networks driven by G-Brownian motion. By combining the method of proof by contradiction with Lyapunov method and graph theory, some sufficient condition for both the Lyapunov-type theorem and the coefficients-type theorem are proposed to ensure the pth moment exponential ultimate boundedness of the considered systems. As applications, the boundedness criteria are applied to stochastic distributed delay-coupled neural networks and stochastic distributed delay-coupled control systems in the framework of G-Brownian motion.

Optimal power‐constrained control of distributed systems with information constraints

AbstractThis paper is concerned with a special case of stochastic distributed optimal control, where the objective is to design a structurally constrained controller for a system subject to state and input power constraints. The structural constraints are induced by the directed communication between local controllers over a strongly connected graph. Based on the information structure present, that is, who knows what and when, we provide a control synthesis with the optimal control law consisting of two parts: one that is based on the common information between the subsystems and one that uses more localized information. The developed method is applicable to an arbitrary number of physically interconnected subsystems.

Survey on stochastic distribution systems: A full probability density function control theory with potential applications

AbstractComplex systems seen either in general engineering practice or economics are subjected to ever increased uncertainties that are mostly represented as random variables or parameters, and the characteristics of random variables are represented by their probability density functions (PDFs). Controlling their PDFs means to shape their stochastic distributions and in general it would provide a full treatment for system analysis and operational control and optimization. This leads to the development of stochastic distribution control (SDC) systems theory in the past decades, where the original aim of the controller design is to realize a shape control of the distributions of certain random variables in their PDFs sense for some engineering processes. Indeed, once the PDFs of these random variables or parameters are used to describe their distribution characters, the control task is to obtain control signals so that the output PDFs of stochastic systems are made to follow their target PDFs. The subject of SDC was initially originated for non‐Gaussian stochastic control systems design but has found a wide spectrum of applications in general systems in terms of data‐driven modeling, analysis, signal processing (filtering), data mining via multivariable statistics, decision‐making (optimization) for systems subjected to uncertainties and even in economics. In this context, SDC constitutes an effective primer tool for complex system analysis, control and operational optimizations. In this review paper, a detailed survey of the developments on the research of SDC systems will be made together with their wide spectrum applications and future perspectives.

Ramp metering control under stochastic capacity in a connected environment: A dynamic bargaining game theory approach

This paper presents a dynamic predictive and cooperative ramp metering approach that considers stochastic breakdowns at merging bottlenecks. A stochastic microscopic model is used to estimate traffic state parameters based on speed, location, and travel time information from connected vehicles. Traffic state predictions are obtained on a lane by lane basis using an adaptive Kalman filter (AKF) that fuses fixed detector measurements with the model; the AKF then produces multiple step ahead predictions. The ramp metering problem in this paper is modeled as a stochastic distributed model predictive control (SDMPC) approach. The SDMPC problem is solved based on a bargaining game approach where each controller, a player in the game, receives traffic state and control decision information from other controllers to solve the local optimization problem based on expected local costs and constraints. The performance of the proposed model is evaluated for three aspects of efficiency: short-term and long-term equity and effectiveness compared to multiple control scenarios. The outcomes indicate that the proposed cooperative model with stochastic capacity considerations outperforms the deterministic capacity-based models in regard to effectiveness and equity properties. However, the centralized approach performs slightly better in respect to system-wide efficiency.

Stochastic Distribution Controller for Wind Turbines with Doubly Fed Induction Generator

The major purpose of this work is to design the controllers for controlling thevariable speed, variable pitch wind turbine (WT) with doubly fed inductiongenerator (DFIG). Vector control strategy is adopted for controlling theDFIG active and reactive power. Generator torque is control to provide theregulated real power with minimum fluctuation. The fixed gain proportional-integral (PI) controller designed to the converter of rotor side and gridside has limited operating range and inherent overshoot. Gain schedulingPI controller is designed to minimize the overshoot and fluctuation existsin proportional-integral controller. Since DFIG based wind energy conver-sion system (WECS) works in uncertain wind speed, stochastic distributioncontrol (SDC) method is proposed to control the probability distributionfunction (PDF) of DFIG based WECS. It copes with nonlinearities in theWECS and contiguous variations at operating point and provides satisfactoryperformance for the whole operating region. It improves the performancetogether with power quality of generated electric power thereby maximizing the lifespan of installation and ensures secure and acceptable operation of theDFIG based WECS.

Distributed stochastic model predictive control for cyber–physical systems with multiple state delays and probabilistic saturation constraints

In this paper, a stochastic distributed model predictive control (DMPC) architecture is investigated for cyber–physical systems subject to probabilistic input saturations. We present a systematic approach to design the stochastic DMPC by extending the deterministic DMPC. The input saturation constraints are relaxed and characterized by a Bernoulli-distributed white sequence, which can provide a trade-off between the satisfaction of input saturations and control performance. The probabilistic input constraints are transformed into a convex hull of linear feedback laws, therefore, can make the controller design less conservative. Then, the optimization problem of the stochastic DMPC is designed and cast into solving an online optimization problem. The probabilistic input saturations are dealt with a distributed fashion by developing an iterative algorithm of the DMPC. The recursive feasibility and closed-loop stability subject to probabilistic input saturations are given. Finally, a numerical example and an industrial electric heater system are used to demonstrate the effectiveness of the proposed approach.

Fault diagnosis and fault-tolerant control for T-S fuzzy time-varying delay stochastic distribution systems with actuator and sensor faults

ABSTRACT The problem of fault diagnosis (FD) and fault-tolerant control (FTC) for a class of nonlinear time-varying delay stochastic distribution control (SDC) systems with actuator and sensor faults is investigated in this paper. The Takagi–Sugeno (T-S) model is used to approximate the nonlinear dynamics. The B-spline function is used to approximate the output probability density function (PDF) of the system. According to the output equivalence principle and Laplace transformation, an augmented state vector is designed to solve the time-varying delay problem. An augmented state adaptive diagnosis observer is proposed to estimate the system state, actuator and sensor faults simultaneously. A new fault-tolerant control algorithm is designed based on the PI control strategy to compensate sensor fault and actuator faults simultaneously. The sensor fault is compensated through the information obtained by the observer. The PI controller can compensate for the influence of the actuator fault, and the output PDF of system can still track the desired PDF when fault occurs. Simulation results are provided to show the effectiveness of the proposed method.

A Novel Data-based Stochastic Distribution Control for Non-Gaussian Stochastic Systems

This article presents a novel data-based approach to investigate the non-Gaussian stochastic distribution control problem. As the motivation of this article, the existing methods have been summarised regarding to the drawbacks, for example, neural network weights training for unknown stochastic distribution and so on. To overcome these disadvantages, a new transformation for dynamic probability density function is given by kernel density estimation using interpolation. Based upon this transformation, a representative model has been developed while the stochastic distribution control problem has been transformed into an optimization problem. Then, data-based direct optimization and identification-based indirect optimization have been proposed. In addition, the convergences of the presented algorithms are analysed and the effectiveness of these algorithms has been evaluated by numerical examples. In summary, the contributions of this article are as follows: 1) a new data-based probability density function transformation is given; 2) the optimization algorithms are given based on the presented model; and 3) a new research framework is demonstrated as the potential extensions to the existing stochastic distribution control.

Stochastic distributed model predictive control of microgrid with uncertain PV power prediction

This paper is concerned with a stochastic distributed Model Predictive Control (MPC) technique for power management of a photovoltaic (PV) generators-installed microgrid. The photovoltaic power sup...

Fault isolation and fault-tolerant control for Takagi-Sugeno fuzzy time-varying delay stochastic distribution systems

A fault isolation, estimation, and fault-tolerant control (FTC) scheme for nonlinear time-varying delay stochastic distribution control systems was presented in this paper. The Takagi-Sugeno fuzzy model was adopted to approach the nonlinear dynamics of time-varying delay systems. According to the output equivalence principle and Laplace transformation, an augmented state vector was given to solve the time-varying delay problem. When multiple actuator faults and interference occur simultaneously, fault detection, isolation and fault estimation was designed to obtained the fault information. To decouple faults and obtain the value and location information of the fault, the system was separated into two parts through the designed multiple conversion matrices, in which one subsystem was only affected by one actuator fault. This has simplified the design of fault isolation and estimation. A adaptive observer for fault estimation was given. Then, fault information such as the time, location, and size was determined. The observer gain matrices were calculated using linear matrix inequality (LMI). When a fault was detected and diagnosed, a FTC algorithm was devised using the proportional-integral control scheme to compensate the fault as much as possible. It has been shown that even if multiple faults actuator occurred simultaneously, the FTC controller still ensured the output probability density function of the system traced the desired probability density function when a fault occurred. Finally, the expected results were obtained through the simulation example, which confirmed the effectiveness of the method.

Modeling and Control Using Stochastic Distribution Control Theory for Intersection Traffic Flow

This work investigated stochastic distribution control theory-based traffic signal optimization to achieve a smooth and uniform flow of vehicles through signalized intersections. In this context, the static and linear dynamic stochastic distribution models were developed to express the relationship between the signal timing and the traffic queue length together with its probability density function. Two stochastic distribution control algorithms were designed to control the signal timing at intersections such that the probability density function of the traffic queue of each intersection road segment is made as narrow and as small as possible. Also, a recursive input-output traffic queue estimation model was proposed, which is data-driven and dynamic in nature, to calculate real-time traffic queue length using traffic signal timings and loop-detector data. The control algorithms were evaluated for a one-signal corridor, two-signal corridor, and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$2 \times 2$ </tex-math></inline-formula> network of signalized intersections. MATLAB simulation examples are provided to demonstrate the use of the proposed algorithms and comparison to the existing widely-used semi-actuated control has been made. Desired results were obtained.

Fault Diagnosis and Fault Tolerant Control for T–S Fuzzy Stochastic Distribution Systems Subject to Sensor and Actuator Faults

The problem of fault diagnosis (FD) and fault tolerant control for a class of Takagi–Sugeno (T–S) fuzzy stochastic distribution control systems subject to sensor and actuator faults is discussed in this article. First, fuzzy logic models are used to approximate the output probability density function (PDF). Next, an adaptive augmented state/FD observer is proposed to estimate the system state, sensor and the actuator faults simultaneously. New expected weights based on the sensor fault estimation information and a PI-type fuzzy feedback fault tolerant controller are designed to compensate the effect of sensor fault and actuator fault simultaneously. When the sensor fault occurs, the expected objective is redesigned to compensate the sensor fault. Meanwhile, the PI controller can compensate the effect of actuator fault, and the output PDF of the system can still track the desired PDF after the fault occurs. Finally, an example of quality distribution control in chemical reaction process is given to confirm the effectiveness of the algorithm.