skip to main content
US FlagAn official website of the United States government
dot gov icon
Official websites use .gov
A .gov website belongs to an official government organization in the United States.
https lock icon
Secure .gov websites use HTTPS
A lock ( lock ) or https:// means you've safely connected to the .gov website. Share sensitive information only on official, secure websites.


Title: Model Predictive Control for Urban Traffic Signals with Stability Guarantees
Traditional traffic signal control focuses more on the optimization aspects whereas the stability and robustness of the closed-loop system are less studied. This paper aims to establish the stability properties of traffic signal control systems through the analysis of a practical model predictive control (MPC) scheme, which models the traffic network with the conservation of vehicles based on a store-and-forward model and attempts to balance the traffic densities. More precisely, this scheme guarantees the exponential stability of the closed-loop system under state and input constraints when the inflow is feasible and traffic demand can be fully accessed. Practical exponential stability is achieved in case of small uncertain traffic demand by a modification of the previous scheme. Simulation results of a small-scale traffic network validate the theoretical analysis.  more » « less
Award ID(s):
2210320
PAR ID:
10513224
Author(s) / Creator(s):
; ; ;
Publisher / Repository:
Society for Industrial and Applied Mathematics
Date Published:
Journal Name:
2023 Proceedings of the Conference on Control and its Applications (CT)
Page Range / eLocation ID:
64-71
Subject(s) / Keyword(s):
Model Predictive Control Stability traffic signal control
Format(s):
Medium: X
Location:
Society for Industrial and Applied Mathematics
Sponsoring Org:
National Science Foundation
More Like this
  1. null (Ed.)
    In wireless power transfer (WPT) applications, the multi-level switched capacitor topology achieves significant advantages in terms of efficiency, system loading, THD, and output regulation. The topology requires dual-loop control in order to harness these benefits. First, a small signal discrete time model for the 7-level rectifier WPT system is developed. Then, a control loop is designed that enables the rectifier to regulate DC load voltage by varying its modulation scheme. Next, the WPT carrier frequency is sensed and a phase-locked loop is used in combination with the small signal power stage model to design a closed-loop controller that synchronizes frequency and regulates control phase through adjustments of the switching period. Finally, cross-coupling interactions between the two control loops are modeled, and stable dual-loop operation is shown. 
    more » « less
  2. Functional electrical stimulation (FES) induced cycling provides a means of therapeutic exercise and functional restoration for people affected by neuromuscular disorders. A challenge in closed-loop FES control of coordinated motion is the presence of a potentially destabilizing input delay between the application of the electrical stimulation and the resulting muscle contraction. Moreover, switching amongst multiple actuators (e.g., between FES control of various muscle groups and a controlled electric motor) presents additional challenges for overall system stability. In this paper, a closed-loop controller is developed to yield exponential cadence tracking, despite an unknown input delay, switching between FES and motor only control, uncertain nonlinear dynamics, and additive disturbances. Lyapunov-Krasovskii functionals are used in a Lyapunov-based stability analysis to ensure exponential convergence for all time. 
    more » « less
  3. A periodic model predictive control (MPC) scheme is proposed for tracking halo orbits. The problem is formulated and solved in the elliptic restricted three-body problem (ER3BP) setting. The reference trajectory to be tracked is designed by using eccentricity continuation techniques. The MPC design exploits the periodicity of the tracking model and guarantees exponential stability of the linearized closed-loop system, through a suitable choice of the terminal set and weight matrices. A sum-of-norms cost function is adopted to promote fuel saving. The proposed control scheme is validated on two simulated missions in the Earth–Moon system, which, respectively, involve station keeping on a halo orbit near the L1 Lagrange point and rendezvous to a halo orbit near the L2 Lagrange point. Results illustrate the advantage of designing the reference trajectory and the periodic control directly in the ER3BP setting versus approximate solutions based on the circular restricted three-body problem (CR3BP). 
    more » « less
  4. As more non-synchronous renewable energy sources (RES) participate in power systems, the system's inertia decreases and becomes time dependent, challenging the ability of existing control schemes to maintain frequency stability. System operators, research laboratories, and academic institutes have expressed the importance to adapt to this new power system paradigm. As one of the potential solutions, virtual inertia has become an active research area. However, power dynamics have been modeled as time-invariant, by not modeling the variability in the system's inertia. To address this, we propose a new modeling framework for power system dynamics to simulate a time-varying evolution of rotational inertia coefficients in a network. We model power dynamics as a hybrid system with discrete modes representing different rotational inertia regimes of the network. We test the performance of two classical controllers from the literature in this new hybrid modeling framework: optimal closed-loop Model Predictive Control (MPC) and virtual inertia placement. Results show that the optimal closed-loop MPC controller (Linear MPC) performs the best in terms of cost; it is 82 percent less expensive than virtual inertia placement. It is also more efficient in terms of energy injected/absorbed to control frequency. To address the lower performance of virtual inertia placement, we then propose a new Dynamic Inertia Placement scheme and we find that it is more efficient in terms of cost (74 percent cheaper) and energy usage, compared to classical inertia placement schemes from the literature. 
    more » « less
  5. This paper is focused on the output tracking control problem of a wave equation with both matched and unmatched boundary uncertainties. An adaptive boundary feedback control scheme is proposed by utilizing radial basis function neural networks (RBF NNs) to deal with the effect of system uncertainties. Specifically, two RBF NN models are first developed to approximate the matched and unmatched system uncertain dynamics respectively. Based on this, an adaptive NN control scheme is derived, which consists of: (i) an adaptive boundary feedback controller embedded by the NN model approximating the matched uncertainty, for rendering stable and accurate tracking control; and (ii) a reference model embedded by the NN model approximating the unmatched uncertainty, for generating a prescribed reference trajectory. Rigorous analysis is performed using the Lyapunov theory and the C0-semigroup theory to prove that our proposed control scheme can guarantee closed-loop stability and wellposedness. Simulation study has been conducted to demonstrate effectiveness of the proposed approach. 
    more » « less