Panagiotis D. Christofides


5532-F Boelter Hall

(310) 794-1015






Research Interests
Our research interests are in the general areas of control, dynamics and optimization including both theory and applications, computational process modeling and simulation, and applied mathematics.  The central objective of our research is the development of novel methods for the systematic and rigorous solution of complex process control and systems engineering problems. Our group has pioneered the development of nonlinear model-based control methods for broad classes of nonlinear, hybrid and distributed parameter processes and has demonstrated their successful application to complex industrial processes.
Our research team is part of the UCLA Center for Systems, Dynamics and Control and of the Process Systems Engineering Group Our research work is carried out in collaboration with experimental groups and major industrial companies. The following research directions are being pursued: 

Statistical machine learning in process modeling and control
The goal of this research is to employ and further develop the methodological framework of generalized error bounds from machine learning theory  for the development and verification of machine learning (ML) models with specific theoretical accuracy guarantees and integrate these models into model predictive control (MPC) system design for nonlinear chemical processes. This research focuses on the following broad objectives: a) the development of generalized probabilistic error bounds for ML models accounting for the impact of the number of neurons and layers on accuracy and guiding network structure selection and training, b) the design of model predictive control schemes that incorporate ML models that are computationally-efficient and ensure desired closed-loop stability, performance, robustness and operational safety properties, and c) the development of a methodology for on-line adaptation of ML models in MPC to capture changing process dynamics and model uncertainty using real-time noisy data. The machine learning modeling and control methods are tested using large-scale process simulators incorporating industrial-data informed parameters and noise, and an experimental electrochemical reactor system at UCLA ((in collaboration with Professor C. Morales-Guio)) employed to convert carbon dioxide to liquid fuels.

Process operational safety and cybersecurity
This work focuses on the development of rigorous, yet practical, methods for the design of optimization-based control systems that improve process operational safety and cybersecurity for broad classes of nonlinear processes. The research addresses two key directions: a) the design of novel model predictive control systems that explicitly account for operational safety considerations and ensure simultaneous closed-loop stability and safety, and b) the design of integrated machine-learning-based detection and control systems that can improve process cybersecurity by efficiently detecting and mitigating the impact of intelligent cyber-attacks. The methods are being tested using large-scale chemical process network simulators and industrial data.

Networked, distributed and economic model predictive control  of nonlinear processes
Process control systems traditionally utilize dedicated, point-to-point wired communication links to measurement sensors and control actuators, to regulate process variables at desired values. While this paradigm to process control has been successful, we are currently witnessing an augmentation of the existing, dedicated control networks, with additional networked (wired and/or wireless) actuator/sensor devices which have become cheap and easy-to-install the last few years. Such an augmentation in sensor information and networked-based availability of data has the potential to be transformative in the sense of dramatically improving the ability of the control systems to further optimize process performance and fault-tolerance. However, augmenting dedicated, local control networks with real-time wired/wireless sensor and actuator networks challenges many of the assumptions in traditional process  control and monitoring methods dealing with dynamical systems linked through ideal channels with flawless, synchronous communication. In the context of designing process control systems which utilize sensor and actuator networks, key fundamental issues that need to be addressed include the use of asynchronous and delayed measurements in the control system as well as the occurrence of network malfunctions due to field interference and device power losses. To address these fundamental problems, our research currently focuses on the development of the theory and algorithms needed for the design of networked and distributed  predictive control systems accounting explicitly for asynchronous and delayed measurements and random network malfunctions. In this direction, the integration of economic optimization and feedback control in the context of economic model predictive control is currently investigated in our group.

Multiscale computational fluid dynamics modeling, control and optimization of multiscale process systems
Interest in the control and optimization of multiscale (deterministic/stochastic) process systems has been triggered by the need to achieve tight feedback control of complex processes, such as deposition and sputtering of thin films in semiconductor manufacturing and solar-cell systems, which are characterized by highly coupled phenomena occurring at disparate time and length scales. We develop general methods for multiscale computational fluid dynamics modeling, reduced-order modeling and feedback controller synthesis for multiscale systems that efficiently address coupled macroscopic and microscopic (e.g., thin film roughness, height-height correlation and porosity) objectives, and illustrate their application to thin-film growth and sputtering processes of industrial interest. Specifically, we develop: a) multiscale computational fluid dynamics modeling archtectures that allow to build accurate models of industrial processes, b) detailed microscopic modeling approacheswith emphasis on the theory and implementation of efficient kinetic Monte Carlo simulation, c) methods for stochastic model construction and parameter estimation, and d) methods for optimization, predictive and covariance controller design using stochastic partial differential equation models.

Control of nonlinear and hybrid process networks
Chemical process networks are inherently nonlinear and cannot be effectively controlled and monitored with conventional control and estimation schemes which are developed on the basis of linear or linearized process models. To enhance our ability to operate chemical process networks, our research focuses on: a) the development of a rigorous and practical framework for nonlinear model-based control of chemical processes that explicitly accounts for the presence of uncertainty in the process model, and constraints and time-delays in the control actuators and measurement sensors, b) the development of nonlinear state estimation algorithms for process monitoring, and c) the development of a comprehensive framework for nonlinear model-based feedback control of hybrid nonlinear processes (i.e., processes with combined continuous dynamics and discrete events) and large-scale process networks with significant interactions. The theoretical studies are coupled with applications to complex process networks used in the chemical and petroleum industry.

Model reduction, optimization and control of nonlinear distributed parameter systems
Distributed parameter systems (DPS) like integro-differential equations and partial differential equations arise naturally in the mathematical modeling of particulate and transport-reaction processes.  The main feature of DPS is that they are characterized by infinite dimensional dynamic behavior.  Therefore, it is impossible to perform dynamical analysis, optimization and design, and synthesize practically-implementable controllers for particulate and transport-reaction processes based on full distributed parameter models.  The objectives of this research are:   a) the development of model reduction methods for the derivation of low-order systems that accurately reproduce the solution and dynamics of a DPS, b) the development of optimization algorithms and the synthesis of nonlinear controllers, which are guaranteed to work for the DPS, based on the low-order approximations, and c) the development of a general framework for integrated optimal design and control of DPS. 
The theoretical results are applied to particulate processes like continuous and batch crystallization and aerosol production for particle size distribution control, as well as to transport-reaction processes used in advanced materials and semiconductor processing including crystal growth, rapid thermal processing, and plasma-assisted chemical vapor deposition and etching.

Fault-tolerant control and monitoring
Increased process automation tends to increase the vulnerability of the
process to faults (e.g., defects/malfunctions in process equipment, sensors and actuators, failures in the controllers or in the control loops) potentially causing a host of safety, environmental and economic problems. Many recent incidents are chilling examples of faults that turned into disasters. Management of abnormal situations is a major challenge in the chemical and process industries since abnormal situations account annually at least for
$10 billion in lost revenue in the US alone. We work on the development of model-based based and data-based process monitoring methods which utilize information from sensor networks to achieve quick and accurate
fault detection and isolation, as well as we develop fault-tolerant control re-configuration strategies  that achieve continuous, safe and economically-optimal process operation in the event of faults.

Water and energy system modeling and control
In this  direction, our research (in collaboration with Professor Y. Cohen) focuses on the modeling, analysis and control of water processing and distribution systems with particular emphasis on real-time fault diagnosis and control of water desalination plants for energy-optimal operation. This research covers both development of user-friendly software tools for the practical implementation of UCLA-developed algorithms and applications to experimental systems and pilot plants as well as the efficient integration of water systems with renewable-energy systems.

Modeling and control of particulate systems
Advances in on-line particle size and shape distribution measurement including laser absorption scattering and probe sampling techniques provide the means for achieving real-time model-based feedback control of fine particle synthesis and processing. We develop a systematic multiscale approach to real-time control of processes involved in the synthesis (e.g.,  crystallizers, aerosol reactors) and processing (e.g., thermal spray processing of nanostructured coatings using nanosized powders) of fine particles. We address the development of low-order approximations of multiscale models linking macroscopic scale (e.g., thermal spray process) and microscopic scale (e.g., evolution of coating microstructure) and the integration of models, measurements and control theory to develop real-time feedback control systems.  Recent work in the broader area of particle technology also focuses on the development of a computational framework for controlling crystal size and shape in protein crystallization.

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