The purpose of this paper is to provide a comprehensive presentation and interpretation of the Ensemble Kalman Filter (EnKF) and its numerical implementation. The EnKF has a large user group, and numerous publications have discussed applications and theoretical aspects of it. This paper reviews the important results from these studies and also presents new ideas and alternative interpretations which further explain the success of the EnKF. In addition to providing the theoretical framework needed for using the EnKF, there is also a focus on the algorithmic formulation and optimal numerical implementation. A program listing is given for some of the key subroutines. The paper also touches upon specific issues such as the use of nonlinear measurements, in situ profiles of temperature and salinity, and data which are available with high frequency in time. An ensemble based optimal interpolation (EnOI) scheme is presented as a cost-effective approach which may serve as an alternative to the EnKF in some applications. A fairly extensive discussion is devoted to the use of time correlated model errors and the estimation of model bias.

The Ensemble Kalman Filter: Theoretical formulation and practical implementation

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

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Analysis Synthesis And Design Of Chemical Processes

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Stable Adaptive Systems

Model-based predictive control (MPC) describes a set of advanced control methods, which make use of a process model to predict the future behavior of the controlled system. By solving a—potentially constrained—optimization problem, MPC determines the control law implicitly. This shifts the effort for the design of a controller towards modeling of the to-be-controlled process. Since such models are available in many fields of engineering, the initial hurdle for applying control is deceased with MPC. Its implicit formulation maintains the physical understanding of the system parameters facilitating the tuning of the controller. Model-based predictive control (MPC) can even control systems, which cannot be controlled by conventional feedback controllers. With most of the theory laid out, it is time for a concise summary of it and an application-driven survey. This review article should serve as such. While in the beginnings of MPC, several widely noticed review paper have been published, a comprehensive overview on the latest developments, and on applications, is missing today. This article reviews the current state of the art including theory, historic evolution, and practical considerations to create intuitive understanding. We lay special attention on applications in order to demonstrate what is already possible today. Furthermore, we provide detailed discussion on implantation details in general and strategies to cope with the computational burden—still a major factor in the design of MPC. Besides key methods in the development of MPC, this review points to the future trends emphasizing why they are the next logical steps in MPC.

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Review on model predictive control: an engineering perspective

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

CFD modeling and control of a steam methane reforming reactor

Machine-learning-based predictive control of nonlinear processes. Part II: Computational implementation

Process structure-based recurrent neural network modeling for model predictive control of nonlinear processes

We present a machine learning-based predictive control scheme that integrates an online update of the recurrent neural network (RNN) models to capture process nonlinear dynamics in the presence of ...

Zhe Wu

Papers

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

CFD modeling and control of a steam methane reforming reactor

Machine-learning-based predictive control of nonlinear processes. Part II: Computational implementation

Process structure-based recurrent neural network modeling for model predictive control of nonlinear processes

Real-Time Adaptive Machine-Learning-Based Predictive Control of Nonlinear Processes