Statistical machine-learning–based predictive control of uncertain nonlinear processes

In this study, we present machine-learning–based predictive control schemes for nonlinear processes subject to disturbances, and establish closed-loop system stability properties using statistical machine learning theory. Specifically, we derive a generalization error bound via Rademacher complexity method for the recurrent neural networks (RNN) that are developed to capture the dynamics of the nominal system. Then, the RNN models are incorporated in Lyapunov-based model predictive controllers, under which we study closed-loop stability properties for the nonlinear systems subject to two types of disturbances: bounded disturbances and stochastic disturbances with unbounded variation. A chemical reactor example is used to demonstrate the implementation and evaluate the performance of the proposed approach.     

Dynamic output feedback covariance control of stochastic dissipative partial differential equations

In this work, we develop a method for dynamic output feedback covariance control of the state covariance of linear dissipative stochastic partial differential equations (PDEs) using spatially distributed control actuation and sensing with noise. Such stochastic PDEs arise naturally in the modeling of surface height profile evolution in thin film growth and sputtering processes. We begin with the formulation of the stochastic PDE into a system of infinite stochastic ordinary differential equations (ODEs) by using modal decomposition. A finite-dimensional approximation is then obtained to capture the dominant mode contribution to the surface roughness profile (i.e., the covariance of the surface height profile). Subsequently, a state feedback controller and a Kalman-Bucy filter are designed on the basis of the finite-dimensional approximation. The dynamic output feedback covariance controller is subsequently obtained by combining the state feedback controller and the state estimator. The steady-state expected surface covariance under the dynamic output feedback controller is then estimated on the basis of the closed-loop finite-dimensional system. An analysis is performed to obtain a theoretical estimate of the expected surface covariance of the closed-loop infinite-dimensional system. Applications of the linear dynamic output feedback controller to both the linearized and the nonlinear stochastic Kuramoto-Sivashinsky equations (KSEs) are presented. Finally, nonlinear state feedback controller and nonlinear output feedback controller designs are also presented and applied to the nonlinear stochastic KSE.     

Handling sensor malfunctions in control of particulate processes

This work focuses on feedback control of particulate processes in the presence of sensor data losses. Two typical particulate process examples, a continuous crystallizer and a batch protein crystallizer, modeled by population balance models (PBMs), are considered. In the case of the continuous crystallizer, a Lyapunov-based nonlinear output feedback controller is first designed on the basis of an approximate moment model and is shown to stabilize an open-loop unstable steady-state of the PBM in the presence of input constraints. Then, the problem of modeling sensor data losses is investigated and the robustness of the nonlinear controller with respect to data losses is extensively investigated through simulations. In the case of the batch crystallizer, a predictive controller is first designed to obtain a desired crystal size distribution at the end of the batch while satisfying state and input constraints. Subsequently, we point out how the constraints in the predictive controller can be modified as a means of achieving constraint satisfaction in the closed-loop system in the presence of sensor data losses.     

Optimal control of diffusion-convection-reaction processes using reduced-order models

Two approaches for optimal control of diffusion-convection-reaction processes based on reduced-order models are presented. The approaches differ in the way spatial discretization is carried out to compute a reduced-order model suitable for controller design. In the first approach, the partial differential equation (PDE) that describes the process is first discretized in space and time using the finite difference method to derive a large number of recursive algebraic equations, which are written in the form of a discrete-time state-space model with sparse state, input and output matrices. Snapshots based on this high-dimensional state-space model are generated to calculate empirical eigenfunctions using proper orthogonal decomposition. The Galerkin projection with the computed empirical eigenfunctions as basis functions is then directly applied to the high-dimensional state-space model to derive a reduced-order model. In the second approach, a continuous-time finite-dimensional state-space model is constructed directly from the PDE through application of orthogonal collocation on finite elements in the spatial domain. The dimension of the derived state-space model can be further reduced using standard model reduction techniques. In both cases, optimal controllers are designed based on the low-order state-space models using discrete-time and continuous-time linear quadratic regulator (LQR) techniques. The effectiveness of the proposed methods are illustrated through applications to a diffusion-convection process and a diffusion-convection-reaction process.     

Predictive control of crystal size distribution in protein crystallization

This work focuses on the modelling, simulation and control of a batch protein crystallization process that is used to produce the crystals of tetragonal hen egg-white (HEW) lysozyme. First, a model is presented that describes the formation of protein crystals via nucleation and growth. Existing experimental data are used to develop empirical models of the nucleation and growth mechanisms of the tetragonal HEW lysozyme crystal. The developed growth and nucleation rate expressions are used within a population balance model to simulate the batch crystallization process. Then, model reduction techniques are used to derive a reduced-order moments model for the purpose of controller design. Online measurements of the solute concentration and reactor temperature are assumed to be available, and a Luenberger-type observer is used to estimate the moments of the crystal size distribution based on the available measurements. A predictive controller, which uses the available state estimates, is designed to achieve the objective of maximizing the volume-averaged crystal size while respecting constraints on the manipulated input variables (which reflect physical limitations of control actuators) and on the process state variables (which reflect performance considerations). Simulation results demonstrate that the proposed predictive controller is able to increase the volume-averaged crystal size by 30% and 8.5% compared to constant temperature control (CTC) and constant supersaturation control (CSC) strategies, respectively, while reducing the number of fine crystals produced. Furthermore, a comparison of the crystal size distributions (CSDs) indicates that the product achieved by the proposed predictive control strategy has larger total volume and lower polydispersity compared to the CTC and CSC strategies. Finally, the robustness of the proposed method (achieved due to the presence of feedback) with respect to plant-model mismatch is demonstrated. The proposed method is demonstrated to successfully achieve the task of maximizing the volume-averaged crystal size in the presence of plant-model mismatch, and is found to be robust in comparison to open-loop optimal control strategies.     

Optical characterization of varnish films by spectroscopic ellipsometry for application in artwork conservation

The specific aim of this paper is to measure the optical constants of fresh varnish layers up to a thickness of 10 mum by spectroscopic ellipsometry. It is the first time that this technique has been used in artwork conservation and it may prove very promising due to its nondestructive character. Samples of fresh dammar varnish (natural resin) and Paraloid B72 (synthetic resin) applied on glass and carbon black acrylic paint were analyzed. Both varnishes were considered as perfect dielectrics, and the real part of their refractive index was described by the Cauchy model: n (lambda) = A + B/lambda(2) + C/lambda(4). The Cauchy coefficients for dammar varnish and Paraloid B72 were then determined for layers of known thickness. The ellipsometric data were fitted to a model, which includes a mixed varnish-air layer. The optical properties of this layer were calculated by the Bruggeman effective medium approximation. In the case of carbon black acrylic paint, another mixed layer (paint-varnish) was added to the model. The results are very close to the values given in the literature. Given the measurement reproducibility, the results show that ellipsometry can discriminate between dammar varnish and Paraloid B72. This is very important in artwork conservation studies, because it has been done by time-consuming, destructive techniques up to now. Future work includes measurements of other types of natural and synthetic varnishes, in an attempt to introduce a nondestructive method for picture varnish identification and aging studies.     

Intermittent sensor fault detection for stochastic LTV systems with parameter uncertainty and limited resolution

ABSTRACT

This paper considers the detection problem of intermittent sensor faults in stochastic linear time-varying systems with both parameter uncertainty and limited resolution. By introducing the soft measurement model, a state estimator is designed whose upper bound of estimation error covariance is obtained and minimised at each time step. Based on it, the residual is generated and its relationship with the fault is analysed quantitatively. Then the evaluation function and corresponding detection threshold is given. Our proposed method is recursive and therefore suitable for real-time online applications. At last, two simulation studies are carried out to illustrate the validity of our proposed method.     

Economic model predictive control of stochastic nonlinear systems

This work focuses on the design of stochastic Lyapunov‐based economic model predictive control (SLEMPC) systems for a broad class of stochastic nonlinear systems with input constraints. Under the assumption of stabilizability of the origin of the stochastic nonlinear system via a stochastic Lyapunov‐based control law, an economic model predictive controller is proposed that utilizes suitable constraints based on the stochastic Lyapunov‐based controller to ensure economic optimality, feasibility and stability in probability in a well‐characterized region of the state‐space surrounding the origin. A chemical process example is used to illustrate the application of the approach and demonstrate its economic benefits with respect to an EMPC scheme that treats the disturbances in a deterministic, bounded manner. © 2018 American Institute of Chemical Engineers AIChE J, 64: 3312–3322, 2018     

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

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.