Overview

My research is focused on five areas: 1) nonlinear systems and controls; 2) stochastic control and optimization; 3) data-driven control and optimization; 4) uncertainty quantification; 5) modeling and control of partial differential equations (PDEs) described systems.

Problems & challenges

Contribution & impacts

Nonlinear Systems and Controls

Almost all practical systems are inherently nonlinear. Due to complex operating circumstances and material or structural limits of the plants, these nonlinear systems suffer from actuator and sensor faults, model uncertainties, external disturbances, system constraints, and partial measurements. Handling these problems is beyond the capability of many existing control methodologies. To address these concerns, we develop new algorithms by combining control theory, optimization theory, probability theory, and machine learning. Our goal is to enhance the safety and efficiency of practical systems and to meet the quality specifications and environmental regulations. We plan to extend our theoretical results into diverse real-world applications and foster our collaborations with multidisciplinary research teams, including but not limited to autonomous systems, energy systems, and mechatronic systems.

Stochastic Control and Optimization

In many practical control applications, e.g., thermal regulation and HVAC control in buildings, load frequency control (LFC) of power systems with renewable energies, system uncertainties are of stochastic nature. In these cases, stochastic control and optimization is a preferred choice because it evaluates system constraints and control objectives in a probabilistic sense and allows for constraint violation at a prescribed probabilistic threshold. Specifically, we first capture the statistics (probability distribution) of the model uncertainty by using Monte Carlo (MC), Kalman Filter (KF), and Bayesian methods; then we incorporate the statistics into system dynamics and chance constraints; finally we formulate a tractable finite-horizon constrained optimization problem.

Data-driven Control and Optimization

We plan to build the fundamental connection between control theory and machine learning. Control and machine learning are two high-impact research areas, both are important for managing complex systems in many fields. Although control theory lays rigorous mathematical foundations with well-established frameworks for complex systems, the application of existing control methodologies is limited to situations where high-fidelity models of the underlying systems are available. Although machine learning is becoming more popular in diverse areas, it lacks of theoretical analysis. Hence, these two research areas are complements to each other. Our research focuses on overcoming these limitations by leveraging control theory and machine learning.

Uncertainty Quantification

Uncertainty quantification is widely relevant to almost all the disciplines. Some typical applications include load forecasting and weather forecasting. Our research focuses on capturing/characterizing the uncertainty by employing statistical and machine learning tools, and then we perform estimation, prediction/forecasting, and control tasks.

Modeling and Control Framework for Partial Differential Equations (PDEs) Described Systems

We plan to develop a universal, easily understood modeling and control framework for general PDEs described systems. Many industrial processes are described by PDEs, including heat conduction, fluid flow, chemical reactor processes, and mechanical vibrations. Due to the infinite-dimensional nature of PDEs, direct computation, analysis, and control on them are time-consuming and difficult, so it necessitates the development of modeling and control framework to address these challenges. Our research focuses on learning unknown system dynamics and neural control policies by employing controls, optimization, and deep neural networks.