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Network-wide signal control optimization is of practical importance to shorten and stabilize travel time, improve productivity, enhance energy consumption efficiency, mitigate congestion, and re­duce vehicle emissions. In this study, a deep learning-empowered distributed control strategy is developed to adaptively optimize network-wide traffic signal control coordination. To simplify the problem formulation and enhance its applicability, the entire traffic system is decomposed into multiple areas, and multilayer perceptron concepts are used to formulate traffic control system operations in each area. The distributed deep learning, velocity-based model predictive control (MPC) strategy is designed to optimize traffic signal coordination. Furthermore, a gain-scheduling control model is developed to linearize each learned nonlinear system around its most recent oper­ating status, and then a distributed MPG controller is applied to the linearized systems. Simulation results demonstrate that the proposed control strategy can effectively reduce travel time by 15.1% compared with fixed-time control plans and by 8.0% compared with a decentralized control plan. This study is the first research effort to integrate the deep learning framework and multiagent MPG to optimize traffic control coordination. Moreover, a sufficient condition is theoretically formu­lated for the bounded-input, bounded-output stability of the closed-loop, large-scale traffic system based on the nonlinear small-gain theorem. 

Feedback optimization aims at regulating the output of a dynamical system to a value that minimizes a cost function. This problem is beyond the reach of the traditional output regulation theory, because the desired value is generally unknown and the reference signal evolves according to a gradient flow using the system’s real-time output. This paper complements the output regulation theory with the nonlinear small-gain theory to address this challenge. Specifically, the authors assume that the cost function is strongly convex and the nonlinear dynamical system is in lower triangular form and is subject to parametric uncertainties and a class of external disturbances. An internal model is used to compensate for the effects of the disturbances while the cyclic small-gain theorem is invoked to address the coupling between the reference signal, the compensators, and the physical system. The proposed solution can guarantee the boundedness of the closed-loop signals and regulate the output of the system towards the desired minimizer in a global sense. Two numerical examples illustrate the effectiveness of the proposed method. 

This paper studies the distributed feedback optimization problem for linear multi-agent systems without precise knowledge of local costs and agent dynamics. The proposed solution is based on a hierarchical approach that uses upper-level coordinators to adjust reference signals toward the global optimum and lower-level controllers to regulate agents’ outputs toward the reference signals. In the absence of precise information on local gradients and agent dynamics, an extremum-seeking mechanism is used to enforce a gradient descent optimization strategy, and an adaptive dynamic programming approach is taken to synthesize an internal-model-based optimal tracking controller. The whole procedure relies only on measurements of local costs and input-state data along agents’ trajectories. Moreover, under appropriate conditions, the closed-loop signals are bounded and the output of the agents exponentially converges to a small neighborhood of the desired extremum. A numerical example is conducted to validate the efficacy of the proposed method.