Optimal and Feedback Control for Hyperbolic Conservation Laws

This dissertation studies hyperbolic partial differential equations for Conservation Laws motivated by traffic control problems. New traffic models for multi-directional flow in two dimensions are derived and their properties studied. Control models are proposed where the control variable is a multiplicative term in the flux function. Control models are also proposed for relaxation type systems of hyperbolic PDEs. Existence of optimal control for the case of constant controls is presented. Unbounded and bounded feedback control designs are proposed. These include advective, diffusive, and advective-diffusive controls. Existence result for the bounded advective control is derived. Performance of the relaxation model using bounded advective control is analyzed. Finally simulations using Godunov scheme are performed on unbounded and bounded feedback advective controls.