非線性理論第八講ppt課件(編輯修改稿)
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【文章內(nèi)容簡(jiǎn)介】 ls ? a differential equation 221( ) ( )( ( ) )( ) ( ) ( ) , 2 , 3 , ,iiii i id x t d x ta A x td t d tx t x t x t i N???? ? ?????? ? ? ?Models: The definition of traffic jam A simple definition about traffic jams (Konishi et al, 1999) Definition 1. Assume that characteristic polynomial d(s) is stable. If H?norm of G(s) is greater than 1, that is where G(s) is the transfer function between the (i1)th vehicle velocity disturbance and the ith vehicle velocity disturbance, then traffic jam occurs in the OV traffic model. 10??????)(s u p)(),(??jGsGThe traffic jam never occurs , ? ||G(s)||? ? 1 ? d(s) is stable Feedback control method （zhao等） A feedback control signal term is added in OV model 22( ) ( )( ( ) )iiid x t d x ta A x td t d t??? ? ????? ()iut?1( ) ( ( ) ( ) ) , i s t h e f e e d b a c k g a i n .i i iu t k v t v t k???Theorem 1. A feedback signal ui(t) is added to the OV traffic system. If the following conditions are satisfied, and where ? is oneorder derivative of OV function at steady state, then traffic jams will never occur in the controlled system . ak ??2ak ???Simulations Observation ? spatiotemporal pattern of traffic flow ? distance headway , velocity Initial conditions ? 100 vehicles, a single road, length 200m ? open boundary condition ? parameters, a=, xc=2, v0= ? ?xi(0)=xc, vi(0)=v0 Case 1 Noise 1 ? dimensionless ? random ? maximum amplitude, 103 Case 1: Simulations results 1 Without control signal Fig. 2(a) Spatiotemporal pattern of the traffic flow With control signal Fig. 3(a) Spatiotemporal pattern of the traffic flow Case 1: Simulations results 2 Without control signal Fig. 2(bd) headway distance and velocity at t=100s and t=500s with control signal Fig. 3(bd) headway distance and velocity at t=100s and t=500s Noise 2 ? random noise 1 ? step external disturbance on the leader ??????????o t h e r w i s eifvtifvtifvtv,/,/)(0001 13513021151102Case 2 Case 2: Simulations results 1 Without control signal Fig. 4(a) Spatiotemporal pattern of the traffic flow Without control signal Fig. 4(bd) headway distance and velocity at t=100s and t=500s Case2: Simulations results 2 with control signal Fig. 5(bd) headway distance and velocity at t=100s and t=500s With control signal Fig. 5(a) Spatiotemporal pattern of the traffic flow 在減速帶的應(yīng)用 時(shí)空?qǐng)D Li等的方法 ? KEPING LI and ZIYOU GAO CONTROLLING THE STATES OF TRAFFIC FLOW AT THE INTERSECTIO
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