Boundary Control for Stability and Invariance of Traffic Flow Dynamics: A Convex Optimization Approach

In this letter we propose an optimization-based boundary controller for traffic flow dynamics capable of achieving both stability and invariance conditions. The approach is based on the definition of Boundary Control Barrier Functionals, from which sets of invariance-preserving boundary controllers are derived. In combination with sets of stabilizing controllers, we reformulate the problem as a convex optimization program solved at each point in time to synthesize the boundary control inputs. We derive sufficient conditions for the existence of optimal controllers that ensure both stability and invariance.