Freeway ramp metering: an LPV set theoretical analysis

Paper in proceeding, 2011

The paper contributes to the set theoretic analysis of freeway traffic flow control by ramp metering. From the generic and discrete time non-linear second-order macroscopic dynamics of freeway, first, an equivalent, quasi Linear Parameter Varying (LPV) representation is derived by steady-state centering and factorization. Second, a polytopic LPV model form is obtained from the quasi reformulation of the non-linear problem statement. The latter polytopic LPV form is then used for the computation and analysis of distur- bance invariant sets. This framework is able to characterize constrained sets of states which can be reached by pure ramp metering control input signal respectively becomes invariant under the effect of other measured and unmeasured inputs. The application of disturbance invariant set theory clearly quantifies the set of states being invariant under the polytopic LPV dynamics and other physical constraints regardless to the open- and closed-loop nature of the system. The proposed idea is fully based on the analysis of the (transformed) non-linear macroscopic system and aims at filling the gap between the traffic modelling and quantitative freeway ramp metering.