We explore in this chapter questions of existence and uniqueness for solutions to stochastic differential equations and offer a study of their properties. This endeavor is really a study of diffusion processes. Loosely speaking, the term diffusion is attributed to a Markov process which has continuous sample paths and can be characterized in terms of its infinitesimal generator.

Stochastic Differential Equations

Correspondence Panagiotis Christofides, Department of Chemical and Biomolecular Engineering, University of California, Los Angeles, CA. Email: pdc@seas.ucla.edu Abstract This article focuses on the design of model predictive control (MPC) systems for nonlinear processes that utilize an ensemble of recurrent neural network (RNN) models to predict nonlinear dynamics. Specifically, RNN models are initially developed based on a data set generated from extensive open-loop simulations within a desired process operation region to capture process dynamics with a sufficiently small modeling error between the RNN model and the actual nonlinear process model. Subsequently, Lyapunov-based MPC (LMPC) that utilizes RNN models as the prediction model is developed to achieve closed-loop state boundedness and convergence to the origin. Additionally, machine learning ensemble regression modeling tools are employed in the formulation of LMPC to improve prediction accuracy of RNN models and overall closed-loop performance while parallel computing is utilized to reduce computation time. Computational implementation of the method and application to a chemical reactor example is discussed in the second article of this series.

Machine learning-based predictive control of nonlinear processes. Part I: Theory

In the past decades, with the rapid development of modern technologies, a special kind of fault, the intermittent fault (IF) has become a serious threat to system securities. Although fruitful research results have been obtained for fault diagnosis, most of them are concerned with permanent faults. Furthermore, up to now, there has been no overview on the diagnosis techniques for IFs in dynamic systems. In fact, IFs are common in a variety of fields, whereas their research is far from mature and many open issues still remain to be solved. Therefore, in this overview, our main objective is to attract direct attentions from more researchers and engineers into the fascinating area of IF diagnosis. In this paper, the concept, research background, challenges and research motivations of IFs are introduced. Then, current research into diagnostics of IFs is reviewed, along with discussions on their strengths, limitations, and future directions.

Review on Diagnosis Techniques for Intermittent Faults in Dynamic Systems

Recently, to ensure the reliability and safety of high-speed trains, detection and diagnosis of faults (FDD) in traction systems have become an active issue in the transportation area over the past two decades. Among these FDD methods, data-driven designs, that can be directly implemented without a logical or mathematical description of traction systems, have received special attention because of their overwhelming advantages. Based on the existing data-driven FDD methods for traction systems in high-speed trains, the first objective of this paper is to systematically review and categorize most of the mainstream methods. By analyzing the characteristic of observations from sensors equipped in traction systems, great challenges which may prevent successful FDD implementations on practical high-speed trains are then summarized in detail. Benefiting from theoretical developments of data-driven FDD strategies, instructive perspectives on this topic are further elaborately conceived by the integration of model-based FDD issues, system identification techniques, and new machine learning tools, which provide several promising solutions to FDD strategies for traction systems in high-speed trains. 

Data-Driven Fault Diagnosis for Traction Systems in High-Speed Trains: A Survey, Challenges, and Perspectives

Distributed filtering based on Cauchy-kernel-based maximum correntropy subject to randomly occurring cyber-attacks

Control Lyapunov-Barrier function-based model predictive control of nonlinear systems

Since industrial control systems are usually integrated with numerous physical devices, the security of control systems plays an important role in safe operation of industrial chemical processes. However, due to the use of a large number of control actuators and measurement sensors and the increasing use of wireless communication, control systems are becoming increasingly vulnerable to cyber-attacks, which may spread rapidly and may cause severe industrial incidents. To mitigate the impact of cyber-attacks in chemical processes, this work integrates a neural network (NN)-based detection method and a Lyapunov-based model predictive controller for a class of nonlinear systems. A chemical process example is used to illustrate the application of the proposed NN-based detection and LMPC methods to handle cyber-attacks.

https://www.mdpi.com/2227-7390/6/10/173/pdf

Junfeng Zhang

Papers

Control Lyapunov-Barrier function-based model predictive control of nonlinear systems

Detecting and Handling Cyber-Attacks in Model Predictive Control of Chemical Processes

Detection of intermittent faults based on an optimally weighted moving average T2 control chart with stationary observations

Fault detection based on robust characteristic dimensionality reduction

Economic model predictive control of stochastic nonlinear systems