Hybrid Systems and Control

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Cyber-physical systems (CPS) are physical engineering systems controlled by computer-based algorithms. Such systems are increasingly penetrating our lives: unmanned air vehicles (UAVs) executing search and rescue missions, autonomous cars navigating through busy traffic, and surgical robots performing life-saving operations---these are just a few examples of how integrations of advanced control algorithms with physical systems can lead to important applications. Many cyber-physical systems, including the above motivating applications, are safety-critical: their failure can lead to catastrophic consequences. For example, the Ariane 5 rocket, which took the European Space Agency 10 years and $7 billions to produce, crashed in less than 1 minute due to a small error in the numerical software design. The recent failures of Tesla's AutoPilot that caused multiple fatal accidents is another warning sign that we still significantly lack confidence in trusting automated machines. The increasingly pervasive use of machine learning algorithms also raises the fundamentally important question of AI trust in control of safety-critical CPS. Indeed, how to affordably build and efficiently certify CPS as safe, reliable, and trustworthy remains a fundamental challenge in both academia and industry. Motivated by these challenges, this research aims to advance the-state-of-the-art of mathematical control theory and design methods for safety-critical cyber-physical systems (CPS). The long-term goal is to systematically develop validated computational methods for robust design of CPS and translate them into practice. The short-term objectives over the next five years are to: (O1) explore the theoretical limits of validated computation and formal methods for control of CPS; (O2) design efficient algorithms for robust control synthesis for CPS from rigorous specifications; (O3) exploit the synergies of control theory, learning, and optimization for safety-critical control of CPS.