Stochastic predictive freeway ramp metering from Signal Temporal Logic specifications

We propose a ramp metering strategy capable of treating exogenous arrivals as random variables since freeway network arrivals are stochastic by nature. In order to express desired temporal properties of the network, we adopt Signal Temporal Logic (STL) as our specification language and present a general framework for synthesizing controllers for piecewise affine systems subject to stochastic uncertainties. We synthesize controllers that satisfy these stochastic STL specifications through sample average approximation techniques. We further showcase our approach for a freeway ramp metering example, we use sampling techniques to obtain ramp flows that minimize the expectation of the total travel time.

[1]  Borrelli Francesco,et al.  Stable hybrid Model Predictive Control for ramp metering , 2016 .

[2]  Tito Homem-de-Mello,et al.  Monte Carlo sampling-based methods for stochastic optimization , 2014 .

[3]  Murat Arcak,et al.  Freeway traffic control from linear temporal logic specifications , 2014, 2014 ACM/IEEE International Conference on Cyber-Physical Systems (ICCPS).

[4]  John Lygeros,et al.  Performance Bounds for the Scenario Approach and an Extension to a Class of Non-Convex Programs , 2013, IEEE Transactions on Automatic Control.

[5]  Alberto L. Sangiovanni-Vincentelli,et al.  Model predictive control with signal temporal logic specifications , 2014, 53rd IEEE Conference on Decision and Control.

[6]  Roberto Horowitz,et al.  Fusing Loop and GPS Probe Measurements to Estimate Freeway Density , 2015, IEEE Transactions on Intelligent Transportation Systems.

[7]  C. E. Clark.  The Greatest of a Finite Set of Random Variables , 1961 .

[8]  Roberto Horowitz,et al.  Optimal freeway ramp metering using the asymmetric cell transmission model , 2006 .

[9]  Oded Maler,et al.  Robust Satisfaction of Temporal Logic over Real-Valued Signals , 2010, FORMATS.

[10]  Sanjit A. Seshia,et al.  Reactive synthesis from signal temporal logic specifications , 2015, HSCC.

[11]  Calin Belta,et al.  Control with Probabilistic Signal Temporal Logic , 2015, ArXiv.

[12]  A. Hegyi,et al.  Optimal coordination of ramp metering and variable speed control-an MPC approach , 2002, Proceedings of the 2002 American Control Conference (IEEE Cat. No.CH37301).

[13]  Roberto Horowitz,et al.  Probabilistic controller synthesis for freeway traffic networks , 2016, 2016 American Control Conference (ACC).

[14]  Markos Papageorgiou,et al.  Freeway ramp metering: an overview , 2002, IEEE Trans. Intell. Transp. Syst..

[15]  Ufuk Topcu,et al.  Receding horizon control for temporal logic specifications , 2010, HSCC '10.

[16]  Ashish Kapoor,et al.  Safe Control under Uncertainty with Probabilistic Signal Temporal Logic , 2016, Robotics: Science and Systems.

[17]  Dejan Nickovic,et al.  Monitoring Temporal Properties of Continuous Signals , 2004, FORMATS/FTRTFT.

[18]  D. Sylvester,et al.  A New Statistical Max Operation for Propagating Skewness in Statistical Timing Analysis , 2006, 2006 IEEE/ACM International Conference on Computer Aided Design.

[19]  Markos Papageorgiou,et al.  ALINEA: A LOCAL FEEDBACK CONTROL LAW FOR ON-RAMP METERING , 1990 .

[20]  Sanjit A. Seshia,et al.  Compositional controller synthesis for vehicular traffic networks , 2015, 2015 54th IEEE Conference on Decision and Control (CDC).

[21]  S. Shankar Sastry,et al.  A learning based approach to control synthesis of Markov decision processes for linear temporal logic specifications , 2014, 53rd IEEE Conference on Decision and Control.

[22]  Roberto Horowitz,et al.  Probabilistic Freeway Ramp Metering , 2016 .

[23]  Calin Belta,et al.  Traffic Network Control From Temporal Logic Specifications , 2014, IEEE Transactions on Control of Network Systems.

[24]  Calin Belta,et al.  Controlling a network of signalized intersections from temporal logical specifications , 2015, 2015 American Control Conference (ACC).