Neural approximations for feedback optimal control of freeway systems

The problem of clearing congestion situations in freeway traffic is addressed for both an N-stage and an infinite-stage control horizon (in the latter case, a receding-horizon control mechanism is used). Traffic is controlled by regulating the vehicle access to the freeway and by limiting the vehicle speed by means of variable message signs. To describe the traffic behavior, a "classical" macroscopic model, first proposed by Payne (1971), is adapted. Even though the problem is stated within a deterministic context, an optimal control law in feedback form is sought to react to unpredictable events. The resulting functional optimization problem is reduced to a nonlinear programming problem by constraining the control law to take on a fixed structure in which free parameters have to be optimized. For such a structure, a multilayer feedforward neural mapping is chosen. Simulation results show the effectiveness of the proposed method in two different case studies. For the simulation of the second case study, real traffic data are used, which allows one to very well represent critical traffic conditions on freeways.

[1]  L. A. Pipes.  An Operational Analysis of Traffic Dynamics , 1953 .

[2]  M J Lighthill,et al.  On kinematic waves II. A theory of traffic flow on long crowded roads , 1955, Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences.

[3]  R. B. Potts,et al.  Car-Following Theory of Steady-State Traffic Flow , 1959 .

[4]  Robert E. Larson,et al.  State increment dynamic programming , 1968 .

[5]  M. Athans,et al.  The design of suboptimal linear time-varying systems , 1968 .

[6]  Robert H Whitson,et al.  MULTILEVEL APPROACH TO THE DESIGN OF A FREEWAY CONTROL SYSTEM , 1969 .

[7]  Harold J Payne,et al.  MODELS OF FREEWAY TRAFFIC AND CONTROL. , 1971 .

[8]  Leif Isaksen,et al.  Design of a Traffic-Responsive Control System for a Los Angeles Freeway , 1973, IEEE Trans. Syst. Man Cybern..

[9]  L. Isaksen,et al.  Freeway traffic surveillance and control , 1973 .

[10]  G. Siouris,et al.  Optimum systems control , 1979, Proceedings of the IEEE.

[11]  N. B. Goldstein,et al.  A decentralized control strategy for freeway regulation , 1982 .

[12]  Markos Papageorgiou,et al.  Optimal decomposition methods applied to motorway traffic control , 1982 .

[13]  Markos Papageorgiou,et al.  Applications of Automatic Control Concepts to Traffic Flow Modeling and Control , 1983 .

[14]  S A Smulders,et al.  Modelling and filtering of freeway traffic flow , 1987 .

[15]  E. Gilbert,et al.  Optimal infinite-horizon feedback laws for a general class of constrained discrete-time systems: Stability and moving-horizon approximations , 1988 .

[16]  D. Mayne,et al.  Receding horizon control of nonlinear systems , 1990 .

[17]  Markos Papageorgiou,et al.  Modelling and real-time control of traffic flow on the southern part of Boulevard Peripherique in Paris: Part I: Modelling , 1990 .

[18]  Stef Smulders,et al.  Control of freeway traffic flow by variable speed signs , 1990 .

[19]  Derrick H. Nguyen,et al.  Neural networks for self-learning control systems , 1990 .

[20]  J. J. Klijnhout.  Freeway Control: An Overview , 1991 .

[21]  Ping Yi,et al.  DEVELOPMENT OF AN IMPROVED HIGH-ORDER CONTINUUM TRAFFIC FLOW MODEL , 1992 .

[22]  R. Zoppoli,et al.  Learning Techniques and Neural Networks for the Solution of N-Stage Nonlinear Nonquadratic Optimal Control Problems , 1992 .

[23]  Andrew R. Barron,et al.  Universal approximation bounds for superpositions of a sigmoidal function , 1993, IEEE Trans. Inf. Theory.

[24]  Ying Li,et al.  Numerical Solution of Continuous-State Dynamic Programs Using Linear and Spline Interpolation , 1993, Oper. Res..

[25]  D. Mayne,et al.  Robust receding horizon control of constrained nonlinear systems , 1993, IEEE Trans. Autom. Control..

[26]  Thomas Parisini,et al.  Neural networks for feedback feedforward nonlinear control systems , 1994, IEEE Trans. Neural Networks.

[27]  Semyon M. Meerkov,et al.  Feedback control of highway congestion by a fair on-ramp metering , 1994, Proceedings of 1994 33rd IEEE Conference on Decision and Control.

[28]  Yorgos J. Stephanedes,et al.  COMPARATIVE EVALUATION OF ADAPTIVE AND NEURAL-NETWORK EXIT DEMAND PREDICTION FOR FREEWAY CONTROL , 1994 .

[29]  Markos Papageorgiou,et al.  Motorway network control via nonlinear optimization , 1995 .

[30]  Markos Papageorgiou,et al.  Route diversion control in motorway networks via nonlinear optimization , 1995, IEEE Trans. Control. Syst. Technol..

[31]  Thomas Parisini,et al.  A receding-horizon regulator for nonlinear systems and a neural approximation , 1995, Autom..

[32]  Harold J. Kushner,et al.  Stochastic Approximation Algorithms and Applications , 1997, Applications of Mathematics.

[33]  Antonella Ferrara,et al.  Optimal control of freeways via speed signalling and ramp metering , 1997 .

[34]  A. Ferrara,et al.  Modelling freeway systems: a new traffic fundamental diagram , 1997 .

[35]  Petros A. Ioannou,et al.  Traffic Density Control for Automated Highway Systems , 1997, Autom..

[36]  Thomas Parisini,et al.  Neural approximations for infinite-horizon optimal control of nonlinear stochastic systems , 1998, IEEE Trans. Neural Networks.

[37]  Markos Papageorgiou,et al.  SOME REMARKS ON MACROSCOPIC TRAFFIC FLOW MODELLING , 1998 .

[38]  Thomas Parisini,et al.  Nonlinear stabilization by receding-horizon neural regulators , 1998 .