Convex and distributed safety analysis and design for control systems

Wang, H

Thesis

Convex and distributed safety analysis and design for control systems

Abstract:: Our future will increasingly be filled with intelligent autonomous systems such as autonomous cars, robots, and power devices. As these systems are deployed in the real world, especially within human reach, there is an increasing need to provide safety guarantees, such as collision avoidance for moving robots and current/voltage protection for power devices. However, verifying and designing safe control systems is challenging due to the inherent nonconvexity in optimization and poor scalability with the system dimension. This thesis addresses these challenges from different aspects, using advanced convex optimization techniques.

A prevalent technique for designing safe control systems is the use of control barrier functions (CBFs). Analogous to control Lyapunov functions (CLFs), which certify stability, CBFs are certificate functions for safety. However, co-designing a candidate CBF and a feedback controller is NP-hard, even for linear systems. This thesis addresses this difficulty by proposing novel convex co-design programs. We parameterize the CBF and feedback controller with certain functional bases to obtain a convex reformulation of the nominal nonconvex problem. The proposed convex program co-designs a CBF and a feedback controller efficiently. We further investigate more complex settings such as systems with nonlinear dynamics, input constraints, mixed-relative degrees, and model uncertainty. Convex conditions are proposed for each setting and we demonstrate great flexibility in being incorporated into the proposed convex program.

Another challenge arises from large-scale multi-agent systems (MASs) which have linearly growing dimensionality of state-space models with the number of agents. We propose a novel distributed control design algorithm for parallel computation with a guaranteed sublinear convergence rate. To facilitate computational implementation, we propose terminating the algorithm before convergence, providing probabilistic results for safety guarantees.

We then consider simultaneously ensuring safety and stability for control systems. This problem is arduous due to the potential conflict between a CBF and a CLF in the state space. We address this difficulty by co-designing these certificate functions that satisfy the relaxed compatibility conditions, and proposing a new control design framework. The designed controller guarantees safety, local stability, and is locally Lipschitz continuous.

Actions

Email

Email this record

Send the bibliographic details of this record to your email address.

Your Email
Please enter the email address that the record information will be sent to.

-
Your message (optional)
Please add any additional information to be included within the email.
Share
Cite

Cite this record

APA Style

Wang, H. (2024). Convex and distributed safety analysis and design for control systems [PhD thesis]. University of Oxford.

MLA Style

Wang, H. Convex and Distributed Safety Analysis and Design for Control Systems. 2024. University of Oxford, PhD thesis.

Chicago Style

Wang, H. 2024. “Convex and Distributed Safety Analysis and Design for Control Systems.” PhD thesis, University of Oxford.
Print