Formal Synthesis of Distributed Optimal Traffic Control Policies

We propose a formal methods approach to control traffic signals optimally from specifications described by metric temporal logic (MTL). Since real-time optimization is computationally infeasible beyond small-scale networks, we use a divide and conquer approach. We decompose the network into smaller subnetworks and synthesize assume-guarantee contracts for their interconnections. We show how to exploit mathematical properties of traffic dynamics to find time varying contracts by solving a constraint satisfaction problem. A model predictive control (MPC) approach is used to find local controls for each subnetwork to minimize induced delays, while assume-guarantee contracts and appropriately designed terminal constraints ensure the satisfaction of the specification all over the network. We present a case study on an urban traffic network.

[1]  Calin Belta,et al.  Formal Synthesis of Control Strategies for Positive Monotone Systems , 2017, IEEE Transactions on Automatic Control.

[2]  Petter Nilsson,et al.  Synthesis of separable controlled invariant sets for modular local control design , 2015, 2016 American Control Conference (ACC).

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

[4]  Calin Belta,et al.  Temporal Logic Control of Discrete-Time Piecewise Affine Systems , 2012, IEEE Transactions on Automatic Control.

[5]  Ron Koymans,et al.  Specifying real-time properties with metric temporal logic , 1990, Real-Time Systems.

[6]  Jorge Cortés,et al.  Finite-time convergent gradient flows with applications to network consensus , 2006, Autom..

[7]  Alex A. Kurzhanskiy,et al.  Mixed monotonicity of partial first-in-first-out traffic flow models , 2016, 2016 IEEE 55th Conference on Decision and Control (CDC).

[8]  Wang,et al.  Review of road traffic control strategies , 2003, Proceedings of the IEEE.

[9]  Pitu B. Mirchandani,et al.  A REAL-TIME TRAFFIC SIGNAL CONTROL SYSTEM: ARCHITECTURE, ALGORITHMS, AND ANALYSIS , 2001 .

[10]  Jorge Cort.  Finite-time convergent gradient o ws with applications to network consensus ? , 2006 .

[11]  Nathan H. Gartner,et al.  OPAC: A DEMAND-RESPONSIVE STRATEGY FOR TRAFFIC SIGNAL CONTROL , 1983 .

[12]  Thomas A. Henzinger,et al.  You Assume, We Guarantee: Methodology and Case Studies , 1998, CAV.

[13]  Calin Belta,et al.  Robust temporal logic model predictive control , 2015, 2015 53rd Annual Allerton Conference on Communication, Control, and Computing (Allerton).

[14]  Brian A. Davey,et al.  An Introduction to Lattices and Order , 1989 .

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

[16]  C. Martin.  2015 , 2015, Les 25 ans de l’OMC: Une rétrospective en photos.

[17]  Sanjit A. Seshia,et al.  Directed Specifications and Assumption Mining for Monotone Dynamical Systems , 2016, HSCC.

[18]  KoymansRon.  Specifying real-time properties with metric temporal logic , 1990 .

[19]  Calin Belta,et al.  Safety control of monotone systems with bounded uncertainties , 2016, 2016 IEEE 55th Conference on Decision and Control (CDC).

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

[21]  R D Bretherton,et al.  SCOOT-a Traffic Responsive Method of Coordinating Signals , 1981 .

[22]  Georgios E. Fainekos,et al.  On-Line Monitoring for Temporal Logic Robustness , 2014, RV.

[23]  E. Kerrigan.  Robust Constraint Satisfaction: Invariant Sets and Predictive Control , 2000 .

[24]  Murat Arcak,et al.  Efficient finite abstraction of mixed monotone systems , 2015, HSCC.

[25]  Emilio Frazzoli,et al.  Capacity-Aware Backpressure Traffic Signal Control , 2013, IEEE Transactions on Control of Network Systems.

[26]  Florence March,et al.  2016 , 2016, Affair of the Heart.

[27]  Ufuk Topcu,et al.  Compositional Synthesis with Parametric Reactive Controllers , 2016, HSCC.

[28]  Majid Zamani,et al.  Compositional construction of approximate abstractions , 2015, HSCC.

[29]  Bart De Schutter,et al.  Equivalence of hybrid dynamical models , 2001, Autom..

[30]  Christel Baier,et al.  Principles of model checking , 2008 .

[31]  Paulo Tabuada,et al.  Linear Time Logic Control of Discrete-Time Linear Systems , 2006, IEEE Transactions on Automatic Control.

[32]  Jitendra Malik,et al.  Normalized cuts and image segmentation , 1997, Proceedings of IEEE Computer Society Conference on Computer Vision and Pattern Recognition.

[33]  Bart De Schutter,et al.  Model predictive control for optimal coordination of ramp metering and variable speed limits , 2005 .

[34]  G. Como,et al.  Convexity and Robustness of Dynamic Network Traffic Assignment for Control of Freeway Networks , 2016 .