SE PhD Prospectus Defense of Wei Xiao

TITLE: OPTIMAL CONTROL AND LEARNING METHODS FOR SAFETY-CRITICAL AUTONOMOUS SYSTEMS

ABSTRACT: Optimal control of autonomous systems is a fundamental and challenging problem, especially when many stringent safety constraints and tight control limitations are involved such that problem solutions can easily become infeasible. This work focuses on optimal and online control for safety critical systems, and employs machine learning techniques to improve the problem solution feasibility.

An important class of autonomous system arises in new transportation systems based on Connected and Automated Vehicles (CAVs). This work first focuses on decentralized optimal merging control of CAVs arriving from two roads where the objective is to jointly minimize the travel time and energy consumption of each CAV. The solution guarantees that all the constraints are always satisfied, both at the merging point and everywhere within a control zone which precedes it. In order to improve computational efficiency of the optimal solutions, this work provides simple-to-check conditions on whether constraints become active or not in the control zone. With nonlinear dynamics and complicated objectives, the merging problem is reformulated to a sequence of quadratic programs (QPs) that are solved on line with the Control Barrier Function (CBF) method. When unconstrained optimal solutions are available, they are used as references for these online QPs.

This thesis prospectus also extends CBFs to high order CBFs (HOCBFs) that can be used for arbitrary relative degree constraints. First, a notion of high order barrier functions (HOBFs) is introduced, and their satisfaction of Lyapunov-like conditions implies the forward invariance of the intersection of a series of sets. Then the HOCBFs are proposed, and any control input that satisfies the HOCBF constraint also renders this intersection set forward invariant. Optimal control problems with constraints are reformulated by HOCBFs and control Lyapunov functions (CLFs) to online QPs. A promising and simple penalty method to address the conflict between HOCBF constraints and control limitations is proposed. Based on the penalty method, this work puts forward a framework that helps a system to safely and automatically explore an unknown environment with long term feasibility and high computational efficiency.

While computationally efficient, the formulation of online QPs can easily be infeasible: the set of constraints in the QPs are likely to become empty for stringent safety constraints and control limitations. Machine learning techniques can significantly improve the feasibility of such problems in an unknown environment. This work also proposes a methodology that arbitrarily assigns a location to a type of unsafe set, samples the state space of the system in the proximity of the safety set, and learns a differentiable classifier that is then added to the set of initial constraints. Finally, a feedback training algorithm that recursively improves the classification accuracy and decreases the infeasibility rate is also introduced.

COMMITTEE: ADVISORS/CHAIR Christos Cassandras, SE/ECE and Calin A. Belta, SE/ME; Yannis Paschalidis, SE/ECE/BME; Sean B. Andersson, SE/ME