Implementing solutions to complex dynamic optimization problems is limited by the fact that these solutions must often satisfy hard safety constraints at all times. A prime example arises in optimizing the operation of autonomous vehicles which must, above all else, guarantee safety. Obtaining such solutions incurs a high computational cost, which limits them to models with simple linear dynamics, simple objective functions, and ignoring noise. Control Barrier Functions (CBFs) may be used for safety-critical control overcoming such limitations at the expense of sub-optimal performance. We present a real-time control framework that combines trajectories generated through optimal control with the computationally efficient CBF method providing safety guarantees. A tractable optimal solution is first obtained for a linear or linearized system with few or no constraints. Next, this solution is optimally tracked while using CBFs to guarantee the satisfaction of all state and control constraints. This Optimal Control and CBF (OCBF) framework is applied to autonomous vehicles in transportation systems where the objective is to jointly minimize the travel time and energy consumption for each vehicle subject to speed, acceleration, and speed-dependent safety constraints.

We will also present some recent new results showing that this framework can be robust to the behavior of human-driven vehicles despite their uncontrollable and unpredictable behaviors.

About Dr. Christos Cassandras

Christos G. Cassandras is a Distinguished Professor of Engineering at Boston University. He is Head of the Division of Systems Engineering, Professor of Electrical and Computer Engineering, and co-founder of Boston University’s Center for Information and Systems Engineering (CISE). He received a B.S. degree from Yale University, M.S.E.E from Stanford University, and S.M. and Ph.D. degrees from Harvard University. In 1982-84 he was with ITP Boston, Inc. where he worked on the design of automated manufacturing systems. In 1984-1996 he was a faculty member at the Department of Electrical and Computer Engineering, University of Massachusetts/Amherst. He specializes in the areas of discrete event and hybrid systems, cooperative control, stochastic optimization, and computer simulation, with applications to computer and sensor networks, manufacturing systems, and transportation systems. He has published over 500 refereed papers in these areas, and seven books. He has guest-edited several technical journal issues and serves on several journal Editorial Boards. In addition to his academic activities, he has worked extensively with industrial organizations on various systems integration projects and the development of decision-support software. He has most recently collaborated with MathWorks, Inc. in the development of the discrete event and hybrid system simulator SimEvents.