ºìÐÓÊÓƵ

Topic

On Switched Control Systems and Model Predictive Control under Uncertainty: Theory and Applications

Department of Mechanical Engineering

Date & location

• Wednesday, April 30, 2025

• 10:00 A.M.

• Virtual Defence

Reviewers

Supervisory Committee

• Dr. Yang Shi, Department of Mechanical Engineering, University of Victoria (Supervisor)

• Dr. Daniela Constantinescu, Department of Mechanical Engineering, UVic (Member)

• Dr. Xiaodai Dong, Department of Electrical and Computer Engineering, UVic (Outside Member) 

External Examiner

• Dr. Ya-Jun Pan, Department of Mechanical Engineering, Dalhousie University 

Chair of Oral Examination

• Dr. Sang Nam, Gustavson School of Business, UVic

   

Abstract

Hybrid systems are a widely applied class of dynamic systems, leveraging both continuous and discrete variables to characterize practical physical processes, including discrete variables like switches and logic, as well as continuous variables like position and velocity. As a powerful tool to model a variety of control systems, it has been widely applied in control system design and utilized in a large number of practical applications, such as aerospace, industrial electronics, and biomedical engineering. Since the seminal work published in Automatica in 1999 by Prof. Bemporad (Professor of Control Systems, IMT School for Advanced Studies Lucca, Italy), more and more control scientists and engineers have been increasingly devoted to studying the fundamental theories and applications of hybrid systems. Along with this historical research road, this dissertation focuses on:

• Theories: Stability and stabilization (Chapter 3), robustness (Chapter 4), data driven model predictive control (MPC) (Chapter 5)
• Applications: Path planning and obstacle avoidance (Chapter 6), mobile communication networks, and hydrogen refueling station optimization (Chapter 7)

In the following, a brief introduction will be given.

In Chapter 1, a brief introduction to a class of hybrid systems is provided, including their stability and stabilization methods, as well as a typical case, i.e., switched systems. Moreover, a comprehensive review of MPC variants designed for handling uncertain hybrid systems is also presented.

In Chapter 2, preliminary concepts and notations are introduced, providing the foundational understanding required for the subsequent chapters.

In Chapter 3, an asynchronous stabilization of discrete-time switched linear systems under dwell-time constraints is presented. This research investigates the stability and control of systems that switch between different modes in an asynchronous manner, and a novel convex stability criterion is developed, facilitating efficient control design.

Following that, in Chapter 4, from a more practical perspective for stabilizing switched systems, a new control strategy is provided to minimize the error between nominal and disturbed states by employing ellipsoidal techniques and demonstrates how system stability can be maintained despite disturbances.

In Chapter 5, a lightweight data-driven approach is developed to construct a novel data-driven MPC framework to control an unknown linear system. The proposed theories ensure two of the most critical properties in MPC frameworks: system stability and recursive feasibility, even under significant uncertainties.

Then, Chapter 6 is devoted to the scenario-based MPC for path planning and obstacle avoidance with chance constraints. This work provides solutions for dealing with uncertainties in real-time decision-making under safety-critical conditions.

In Chapter 7, a representative application is presented, demonstrating how the fundamental theories developed in previous chapters can address practical requirements. The application involves modeling the hydrogen refueling processes as hybrid systems and leveraging MPC to optimize energy costs while satisfying safety constraints (e.g., temperature and pressure).

Finally, the conclusion and future works of the dissertation are presented in Chapter 8.