Stochastic Models of the Traffic System Sample Clauses

Stochastic Models of the Traffic System. We start with uncertain continuous-time parameterized models of the form x˙ = fρ(x, u, w) (1) X U ∈ P · where x ∈ X ⊆ Rn are states, u ∈ U ⊂ Rm are control inputs, w ∈ Rd is a Gaussian-distributed disturbance vector, w ∼ N (0, Σρ), where Σρ is positive definite, and ρ are fixed model parameters. Our system model fρ( ) is as- sumed to be C1 continuous, and the sets and to be compact. We work from a decomposition of our system model as a coupling of N closed-loop parame- terized traffic vehicle models, plus one additional system capturing the physics model for the ego vehicle:   x˙0       x˙1  x˙ = . fego(x0, u) .      f1,ρ (x, w1)  =