A Survey of the Probability Density Function Control for Stochastic Dynamic Systems

Probability density function (PDF) control strategy investigates the controller design approaches in order to to realise a desirable distributions shape control of the random variables for the stochastic processes. Different from the existing stochastic optimisation and control methods, the most important problem of PDF control is to establish the evolution of the PDF expressions of the system variables. Once the relationship between the control input and the output PDF is formulated, the control objective can be described as obtaining the control input signals which would adjust the system output PDFs to follow the pre-specified target PDFs. This paper summarises the recent research results of the PDF control while the controller design approaches can be categorised into three groups: 1) system model-based direct evolution PDF control; 2) model-based distribution-transformation PDF control methods and 3) databased PDF control. In addition, minimum entropy control, PDF-based filter design, fault diagnosis and probabilistic decoupling design are also introduced briefly as extended applications in theory sense

PMAC:Probabilistic Multimodality Adaptive Control

This paper develops a probabilistic multimodal adaptive control approach for systems that are characterised by temporal multimodality where the system dynamics are subject to abrupt mode switching at arbitrary times. In this framework, the control objective is redefined such that it utilises the complete probability distribution of the system dynamics. The derived probabilistic control law is thus of a dual type that incorporates the functional uncertainty of the controlled system. A multi-modal density model with prediction error-dependent mixing coefficients is introduced to effect the mode switching. This approach can deal with arbitrary noise distributions, nonlinear plant dynamics and arbitrary mode switching. For the affine systems focussed upon for illustration in this paper the approach has global stability. The theoretical architecture constructs are verified by validation on a simulation example

Dual adaptive dynamic control of mobile robots using neural networks

This paper proposes two novel dual adaptive neural control schemes for the dynamic control of nonholonomic mobile robots. The two schemes are developed in discrete time, and the robot's nonlinear dynamic functions are assumed to be unknown. Gaussian radial basis function and sigmoidal multilayer perceptron neural networks are used for function approximation. In each scheme, the unknown network parameters are estimated stochastically in real time, and no preliminary offline neural network training is used. In contrast to other adaptive techniques hitherto proposed in the literature on mobile robots, the dual control laws presented in this paper do not rely on the heuristic certainty equivalence property but account for the uncertainty in the estimates. This results in a major improvement in tracking performance, despite the plant uncertainty and unmodeled dynamics. Monte Carlo simulation and statistical hypothesis testing are used to illustrate the effectiveness of the two proposed stochastic controllers as applied to the trajectory-tracking problem of a differentially driven wheeled mobile robot.peer-reviewe

Comparative Analysis of Different Classes of On-line State Estimators for Aerodynamics Angles and True Airspeed Sensors for Applications to the Sensor Failure Problem

Throughout aviation history, there have been numerous incidents due to sensor failure that have caused a range of issues from loss of control of the aircraft to crashes resulting in loss of human life. Although there are many hardware-based solutions to this problem, the threat of control hardware failure still exists. This work investigates the efficacy of implementing neural networks (NN) and Kalman filters (KF) to solve the accommodation portion of the sensor failure detection, identification, and accommodation (SFDIA) problem through on-line real-time estimation of specific aircraft dynamic parameters. The implementation of on-line estimation architectures into the aircraft flight control system provides multiple advantages such as cost effectiveness and drastic decrease in weight. The multilayer perceptron (MLP) NN, extended minimal resource allocation (neural) network (EMRAN), extended KF (EKF), and unscented KF (UKF) have been evaluated in this effort for the purpose of providing analytical redundancy (AR) for estimating the parameter of the ‘failed’ sensor in lieu of physical redundancy. Each NN-based and KF-based estimator was compared using preset criteria including estimation accuracy, time to perform, and complexity of the model. The overall results have shown that the NN-based sensor failure accommodation (SFA) schemes outperform the KF-based SFA schemes with no undetected faults nor false alarms and significantly smaller estimation errors. More specifically, the EMRAN-based neural estimator has the best performance of all four schemes followed by the MLP NN, UKF, and EKF, respectively. This research shows the great potential of analytical redundancy-based approaches as opposed to physical or hardware redundancy to improved aviation safety for preventing future crashes due to sensor failures

An introductory survey of probability density function control

YesProbability density function (PDF) control strategy investigates the controller design approaches where the random variables for the stochastic processes were adjusted to follow the desirable distributions. In other words, the shape of the system PDF can be regulated by controller design.Different from the existing stochastic optimization and control methods, the most important problem of PDF control is to establish the evolution of the PDF expressions of the system variables. Once the relationship between the control input and the output PDF is formulated, the control objective can be described as obtaining the control input signals which would adjust the system output PDFs to follow the pre-specified target PDFs. Motivated by the development of data-driven control and the state of the art PDF-based applications, this paper summarizes the recent research results of the PDF control while the controller design approaches can be categorized into three groups: (1) system model-based direct evolution PDF control; (2) model-based distribution-transformation PDF control methods and (3) data-based PDF control. In addition, minimum entropy control, PDF-based filter design, fault diagnosis and probabilistic decoupling design are also introduced briefly as extended applications in theory sense.De Montfort University - DMU HEIF’18 project, Natural Science Foundation of Shanxi Province [grant number 201701D221112], National Natural Science Foundation of China [grant numbers 61503271 and 61603136

Application of Conventional Feedforward and Deep Neural Networks to Power Distribution System State Estimation and State Forecasting

Classical neural networks such as feedforward multilayer perceptron models (MLPs) are well established as universal approximators and as such, show promise in applications such as static state estimation in power transmission systems. This research investigates the application of conventional neural networks (MLPs) and deep learning based models such as convolutional neural networks (CNNs) and long short-term memory networks (LSTMs) to mitigate challenges in power distribution system state estimation and forecasting based upon conventional analytic methods. The ability of MLPs to perform regression to perform power system state estimation will be investigated. MLPs are considered based upon their promise to learn complex functional mapping between datasets with many features. CNNs and LSTMs are considered based upon their promise to perform time-series forecasting by learning the autocorrelation of the dataset being predicted. The performance of MLPs will be presented in terms of root-mean-square error (RMSE) between actual and predicted voltage magnitude and voltage phase angles and training execution time for distribution system state estimation (DSSE). The performance of CNNs, and LSTMs will be presented in terms of RMSE between actual and predicted real power demand and execution time when performing distribution system state forecasting (DSSF). Additionally, Bayesian Optimization with Gaussian Processes are used to optimize MLPs for regression. An IEEE standard 34-bus test system is used to illustrate the proposed conventional neural network and deep learning methods and their effectiveness to perform power system state estimation and power system state forecasting respectively

Multidimensional prognostics for rotating machinery: A review

open access articleDetermining prognosis for rotating machinery could potentially reduce maintenance costs and improve safety and avail- ability. Complex rotating machines are usually equipped with multiple sensors, which enable the development of multidi- mensional prognostic models. By considering the possible synergy among different sensor signals, multivariate models may provide more accurate prognosis than those using single-source information. Consequently, numerous research papers focusing on the theoretical considerations and practical implementations of multivariate prognostic models have been published in the last decade. However, only a limited number of review papers have been written on the subject. This article focuses on multidimensional prognostic models that have been applied to predict the failures of rotating machinery with multiple sensors. The theory and basic functioning of these techniques, their relative merits and draw- backs and how these models have been used to predict the remnant life of a machine are discussed in detail. Furthermore, this article summarizes the rotating machines to which these models have been applied and discusses future research challenges. The authors also provide seven evaluation criteria that can be used to compare the reviewed techniques. By reviewing the models reported in the literature, this article provides a guide for researchers considering prognosis options for multi-sensor rotating equipment