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Adaptive model predictive control for traffic signal timing with unknown demand and parameters

Zhexian Li, Ketan Savla

TL;DR

The paper tackles traffic signal timing under unknown demand and network parameters by integrating set-membership based parameter learning with model predictive control. It introduces an adaptive MPC framework that uses varying terminal sets to identify saturation flows and turn ratios in finite time, followed by a one-step MPC that optimizes queue-length-related costs using learned parameters without needing demand data. Theoretical guarantees include recursive feasibility, finite termination with exact parameter identification, and input-to-state practical stability for the closed-loop system. Numerical simulations on a $4\times4$ grid show improved transient queue performance over max-pressure and proportional-fair policies, demonstrating practical impact for adaptive, distributed traffic control. The work suggests promising directions for responsive, information-efficient traffic management with robust stability properties.

Abstract

This paper designs traffic signal control policies for a network of signalized intersections without knowing the demand and parameters. Within a model predictive control (MPC) framework, control policies consist of an algorithm that estimates parameters and a one-step MPC that computes control inputs using estimated parameters. The algorithm switches between different terminal sets of the MPC to explore different regions of the state space, where different parameters are identifiable. The one-step MPC minimizes a cost that approximates the sum of squares of all the queue lengths within a constant and does not require demand information. We show that the algorithm can estimate parameters exactly in finite time, and the one-step MPC renders maximum throughput in terms of input-to-state practical stability. Simulations indicate better transient performance regarding queue lengths under our proposed policies than existing ones.

Adaptive model predictive control for traffic signal timing with unknown demand and parameters

TL;DR

The paper tackles traffic signal timing under unknown demand and network parameters by integrating set-membership based parameter learning with model predictive control. It introduces an adaptive MPC framework that uses varying terminal sets to identify saturation flows and turn ratios in finite time, followed by a one-step MPC that optimizes queue-length-related costs using learned parameters without needing demand data. Theoretical guarantees include recursive feasibility, finite termination with exact parameter identification, and input-to-state practical stability for the closed-loop system. Numerical simulations on a grid show improved transient queue performance over max-pressure and proportional-fair policies, demonstrating practical impact for adaptive, distributed traffic control. The work suggests promising directions for responsive, information-efficient traffic management with robust stability properties.

Abstract

This paper designs traffic signal control policies for a network of signalized intersections without knowing the demand and parameters. Within a model predictive control (MPC) framework, control policies consist of an algorithm that estimates parameters and a one-step MPC that computes control inputs using estimated parameters. The algorithm switches between different terminal sets of the MPC to explore different regions of the state space, where different parameters are identifiable. The one-step MPC minimizes a cost that approximates the sum of squares of all the queue lengths within a constant and does not require demand information. We show that the algorithm can estimate parameters exactly in finite time, and the one-step MPC renders maximum throughput in terms of input-to-state practical stability. Simulations indicate better transient performance regarding queue lengths under our proposed policies than existing ones.

Paper Structure

This paper contains 12 sections, 4 theorems, 22 equations, 4 figures, 1 algorithm.

Table of Contents

  1. Introduction
  2. Problem Formulation
  3. Adaptive MPC
  4. Numerical simulations
  5. Conclusions
  6. Algorithm
  7. Max-pressure control
  8. Input-to-state practical stability
  9. Proof of Theorem 1
  10. Recursive feasibility
  11. Finite termination
  12. Proof of Theorem 2

Key Result

Theorem 1

Let Assumptions assumption:signal and assumption:bounds hold. Suppose $\ell(\bar{x},u)=0$ if $(\bar{x},\underaccent{\bar{}}{x})\in\mathcal{X}_f$ and $\ell(\bar{x},u) = l^T\bar{x}$ otherwise with cost coefficient $l\in\mathbb{R}^{n_x}_{>0}$. Then, Algorithm alg:adpative-mpc terminates in finite time

Figures (4)

  • Figure 1: A $4\times4$ grid network
  • Figure 2: Illustration of a four-phase architecture at an intersection
  • Figure 3: Evolution of queue lengths at link 20 under the adaptive MPC
  • Figure 4: Comparison of $\|x\|_2^2$ under different control policies

Theorems & Definitions (13)

  • Example 1
  • Remark 1
  • Remark 2
  • Theorem 1
  • Remark 3
  • Remark 4
  • Remark 5
  • Theorem 2
  • Remark 6
  • Lemma 1
  • ...and 3 more