Bilateral Boundary Control of Moving Shockwave in LWR Model of Congested Traffic

We develop backstepping state feedback control to stabilize a moving shockwave in freeway segment under bilateral boundary actuations of traffic flow. A shockwave, consisting light upstream the and heavy downstream, is usually caused by changes local road situations. The density discontinuity travels drivers caught experience transitions from free congested traffic. Boundary design this paper brings front static setpoint position, hindering propagation congestion. dynamics are described with Lighthill-Whitham-Richard (LWR) model, leading system two first-order hyperbolic partial differential equations (PDEs). Each represents spatial domain segregated interface. By Rankine-Hugoniot condition, interface position driven flux thus governed PDE dependent ordinary equation (ODE). For PDE-ODE coupled system. objective both states ODE shock values. Using delay representation method, we predictor controllers cooperatively compensate state-dependent input delays ODE. From Lyapunov stability analysis, show closed-loop $H^1$ norm. performance demonstrated numerical simulation.