UC Berkeley

Model predictive control (MPC) and control barrier functions (CBFs) have been widely adopted in autonomous systems research for their ability to rigorously enforce safety constraints. In many controls and planning applications, these constraints depend on the optimality of a lower-level optimization problem. This dissertation uses tools from differentiable convex optimization to address challenges in enforcing such implicit safety constraints for two applications: collision avoidance for convex sets and hierarchical MPC. The dissertation is composed of three parts. In Part I, we consider enforcing distance-based safety constraints for convex sets using CBFs. Using duality theory, we smoothly and nonconservatively reformulate distance-based discrete-time CBF constraints for polytopes, enabling robot navigation in tight environments. For continuous-time dynamical systems, we use sensitivity analysis to enforce CBF constraints for state-dependent convex sets and guarantee strong safety for the closed-loop system. In Part II, we aim to enforce distance-based collision avoidance constraints in trajectory optimization by treating the distance between convex sets as a black-box, differentiable function. First, we propose a state-of-the-art algorithm for computing a growth distance metric between convex sets. Then, we introduce a novel algorithm to compute the optimal solution derivatives for the growth distance problem and demonstrate its application to convex set collision avoidance using nonlinear MPC. In Part III, we focus on hierarchical MPC problems, where the upper-level system solves its MPC problem subject to lower-level convex MPC optimality constraints. We consider a specific class of hierarchical MPC problems in which the upper-level system provides additional incentives to the lower-level systems to influence their outputs. We solve the problem by proposing a dual gradient descent-based incentive coordination algorithm and demonstrate its application to dynamic electricity price control for large-scale electric vehicle charging.