Network congestion alleviation using adjoint hybrid control: Application to highways

Abstract

This paper derives an optimization-based control methodology for networks of switched and hybrid systems in which each mode is governed by a partial differential equation (PDE). We pose the continuous controller synthesis problem as an optimization program with PDEs in the constraints. The proposed algorithm relies on an explicit formulation of the gradient of the cost function, obtained via the adjoint of the PDE operator. First, we show how to use the result of the optimization to synthesize on/off control strategies. Then, we generalize the method to optimal switching control of hybrid systems over PDEs: the system is allowed to switch from one mode (or PDE) to another at times which we synthesize to minimize a given cost. We derive an explicit expression of the gradient of the cost with respect to the switching times. We implement our techniques on a highway congestion control problem using Performance Measurement System (PeMS) data for the California 1210 for a 9 mile long strip with 26 on-ramps (controllable with red/green metering lights) and off-ramp's (uncontrollable). © Springer-Verlag 2004.