In a mixed traffic with connected automated vehicles (CAVs) and human-driven vehicles (HDVs), data-driven predictive control of CAVs promises system-wide traffic performance improvements. Yet, most existing approaches focus on a centralized setup, which is computationally unscalable while failing to protect data privacy. The robustness against unknown disturbances has not been well addressed either, causing safety concerns. In this paper, we propose a decentralized robustDeeP-LCC(Data-EnablEd Predictive Leading Cruise Control) approach for CAVs to smooth mixed traffic. In particular, each CAV computes its control input based on locally available data from its involved subsystem. Meanwhile, the interaction between neighboring subsystems is modeled as a bounded disturbance, for which appropriate estimation methods are proposed. Then, we formulate a robust optimization problem and present its tractable computational solutions. Compared with the centralized formulation, our method greatly reduces computation complexity with better safety performance, while naturally preserving data privacy. Extensive traffic simulations validate its wave-dampening ability, safety performance, and computational benefits.

We address the problem of verifying neural networks against geometric transformations of the input image, including rotation, scaling, shearing, and translation. The proposed method computes provably sound piecewise linear constraints for the pixel values by using sampling and linear approximations in combination with branch-and-bound Lipschitz optimisation. The method obtains provably tighter over-approximations of the perturbation region than the present state-of-the-art. We report results from experiments on a comprehensive set of verification benchmarks on MNIST and CIFAR10. We show that our proposed implementation resolves up to 32% more verification cases than present approaches.

Lipschitz constant estimation plays an important role in understanding generalization, robustness, and fairness in deep learning. Unlike naive bounds based on the network weight norm product, semidefinite programs (SDPs) have shown great promise in providing less conservative Lipschitz bounds with polynomial-time complexity guarantees. However, due to the memory consumption and running speed, standard SDP algorithms cannot scale to modern neural network architectures. In this paper, we transform the SDPs for Lipschitz constant estimation into an eigenvalue optimization problem, which aligns with the modern large-scale optimization paradigms based on first-order methods. This is amenable to autodiff frameworks such as PyTorch and TensorFlow, requiring significantly less memory than standard SDP algorithms. The transformation also allows us to leverage various existing numerical techniques for eigenvalue optimization, opening the way for further memory improvement and computational speedup. The essential technique of our eigenvalue-problem transformation is to introduce redundant quadratic constraints and then utilize both Lagrangian and Shor's SDP relaxations under a certain trace constraint. Notably, our numerical study successfully scales the SDP-based Lipschitz constant estimation to address large neural networks on ImageNet. Our numerical examples on CIFAR10 and ImageNet demonstrate that our technique is more scalable than existing approaches. Our code is available at https://github.com/z1w/LipDiff.

Augmented Lagrangian Methods (ALMs) are widely employed in solving constrained optimizations, and some efficient solvers are developed based on this framework. Under the quadratic growth assumption, it is known that the dual iterates and the Karush–Kuhn–Tucker (KKT) residuals of ALMs applied to conic programs converge linearly. In contrast, the convergence rate of the primal iterates has remained elusive. In this paper, we resolve this challenge by establishing new $\textit{quadratic growth}$ and $\textit{error bound}$ properties for primal and dual conic programs under the standard strict complementarity condition. Our main results reveal that both primal and dual iterates of the ALMs converge linearly contingent solely upon the assumption of strict complementarity and a bounded solution set. This finding provides a positive answer to an open question regarding the asymptotically linear convergence of the primal iterates of ALMs applied to conic optimization.

In this article, we present the first experimental results of data-driven predictive control for connected and autonomous vehicles (CAVs) in dissipating traffic waves. In particular, we consider a recent strategy of Data-EnablEd Predictive Leading Cruise Control (DeeP-LCC), which bypasses the need of identifying the driving behaviors of surrounding vehicles and directly relies on measurable traffic data to achieve safe and optimal CAV control in mixed traffic. We present the implementation details ofDeeP-LCC, including data collection, equilibrium estimation, and control execution. Based on a miniature experiment platform, we reproduce the phenomenon of stop-and-go waves in two typical traffic scenarios: 1) open straight-road scenario under external disturbances and 2) closed ring-road scenario with no bottlenecks. Our experiments clearly demonstrate thatDeeP-LCCenables one or a few CAVs to dissipate the traffic waves in both traffic scenarios. These experimental findings validate the great potential ofDeeP-LCCin smoothing practical traffic flow in the presence of noisy data, uncertain low-level vehicle dynamics, and communication and computation delays. The code and videos of our experimental results are available athttps://github.com/soc-ucsd/DeeP-LCC.

Data-driven predictive control of connected and automated vehicles (CAVs) has received increasing attention as it can achieve safe and optimal control without relying on explicit dynamical models. However, employing the data-driven strategy involves the collection and sharing of privacy-sensitive vehicle information, which is vulnerable to privacy leakage and might further lead to malicious activities. In this paper, we develop a privacy-preserving data-enabled predictive control scheme for CAVs in a mixed traffic environment, where human-driven vehicles (HDVs) and CAVs coexist. We tackle external eavesdroppers and honest-but-curious central unit eavesdroppers who wiretap the communication channel of the mixed traffic system and intend to infer the CAVs’ state and input information. An affine masking-based privacy protection method is designed to conceal the true state and input signals, and an extended form of the data-enabled predictive leading cruise control under different data matrix structures is derived to achieve privacy-preserving optimal control for CAVs. Numerical simulations demonstrate that the proposed scheme can protect the privacy of CAVs against attackers without affecting control performance or incurring heavy computations.

We propose an enhanced semidefinite program (SDP) relaxation to enable the tight and efficient verification of neural networks (NNs). The tightness improvement is achieved by introducing a nonlinear constraint to existing SDP relaxations previously proposed for NN verification. The efficiency of the proposal stems from the iterative nature of the proposed algorithm in that it solves the resulting non-convex SDP by recursively solving auxiliary convex layer-based SDP problems. We show formally that the solution generated by our algorithm is tighter than state-of-the-art SDP-based solutions for the problem. We also show that the solution sequence converges to the optimal solution of the non-convex enhanced SDP relaxation. The experimental results on standard benchmarks in the area show that our algorithm achieves the state-of-the-art performance whilst maintaining an acceptable computational cost.

We present a novel semidefinite programming (SDP) relaxation that enables tight and efficient verification of neural networks. The tightness is achieved by combining SDP relaxations with valid linear cuts, constructed by using the reformulation-linearisation technique (RLT). The computational efficiency results from a layerwise SDP formulation and an iterative algorithm for incrementally adding RLT-generated linear cuts to the verification formulation. The layer RLT-SDP relaxation here presented is shown to produce the tightest SDP relaxation for ReLU neural networks available in the literature. We report experimental results based on MNIST neural networks showing that the method outperforms the state-of-the-art methods while maintaining acceptable computational overheads. For networks of approximately 10k nodes (1k, respectively), the proposed method achieved an improvement in the ratio of certified robustness cases from 0% to 82% (from 35% to 70%, respectively).

Cooperative formation and control of autonomous vehicles (AVs) promise increased efficiency and safety on public roads. In single-lane mixed traffic consisting of AVs and human-driven vehicles (HDVs), the prevailing platooning of multiple AVs is not the only choice for cooperative formation. In this paper, we investigate how different formations of AVs impact traffic performance from a set-function optimization perspective. We first reveal a stability invariance property and a diminishing improvement property of noncooperative formation when AVs adopt an independently designed Adaptive Cruise Control (ACC) strategy. Then, we focus on the case of cooperative formation where AVs utilize a centralized optimal controller. We further investigate the corresponding optimal formation of multiple AVs using set-function optimization. Two predominant optimal formations,i.e., uniform distribution and platoon formation, emerge from extensive numerical experiments. Interestingly, platooning might have the least potential to improve traffic performance when HDVs have poor string stability behavior. These results suggest more opportunities for cooperative formation of AVs, beyond platooning, in practical mixed traffic flow.

Connected and autonomous vehicles (CAVs) have great potential to improve road transportation systems. Most existing strategies for CAVs’ longitudinal control focus on downstream traffic conditions, but neglect the impact of CAVs’ behaviors on upstream traffic flow. In this paper, we introduce a notion of Leading Cruise Control (LCC), in which the CAV maintains car-following operations adapting to the states of its preceding vehicles, and also aims to lead the motion of its following vehicles. Specifically, by controlling the CAV, LCC aims to attenuate downstream traffic perturbations and smooth upstream traffic flow actively. We first present the dynamical modeling of LCC, with a focus on three fundamental scenarios: car-following, free-driving, and Connected Cruise Control. Then, the analysis of controllability, observability, and head-to-tail string stability reveals the feasibility and potential of LCC in improving mixed traffic flow performance. Extensive numerical studies validate that the capability of CAVs in dissipating traffic perturbations is further strengthened when incorporating the information of the vehicles behind into the CAVs’ control.

We introduce an efficient and tight layer-based semidefinite relaxation for verifying local robustness of neural networks. The improved tightness is the result of the combination between semidefinite relaxations and linear cuts. We obtain a computationally efficient method by decomposing the semidefinite formulation into layerwise constraints. By leveraging on chordal graph decompositions, we show that the formulation here presented is provably tighter than current approaches. Experiments on a set of benchmark networks show that the approach here proposed enables the verification of more instances compared to other relaxation methods. The results also demonstrate that the SDP relaxation here proposed is one order of magnitude faster than previous SDP methods.

Connected and automated vehicles (CAVs) have a great potential to improve traffic efficiency in mixed traffic systems, which has been demonstrated by multiple numerical simulations and field experiments. However, some fundamental properties of mixed traffic flow, including controllability and stabilizability, have not been well understood. This paper analyzes the controllability of mixed traffic systems and designs a system-level optimal control strategy. Using the Popov-Belevitch-Hautus (PBH) criterion, we prove for the first time that a ring-road mixed traffic system with one CAV and multiple heterogeneous human-driven vehicles is not completely controllable, but is stabilizable under a very mild condition. Then, we formulate the design of a system-level control strategy for the CAV as a structured optimal control problem, where the CAV’s communication ability is explicitly considered. Finally, we derive an upper bound for reachable traffic velocity via controlling the CAV. Extensive numerical experiments verify the effectiveness of our analytical results and the proposed control strategy. Our results validate the possibility of utilizing CAVs as mobile actuators to smooth traffic flow actively.

The emergence of autonomous vehicles (AVs) is expected to revolutionize road transportation in the near future. Although large-scale numerical simulations and small-scale experiments have shown promising results, a comprehensive theoretical understanding to smooth traffic flow via AVs is lacking. In this article, from a control-theoretic perspective, we establish analytical results on the controllability, stabilizability, and reachability of a mixed traffic system consisting of human-driven vehicles and AVs in a ring road. We show that the mixed traffic system is not completely controllable, but is stabilizable, indicating that AVs can not only suppress unstable traffic waves but also guide the traffic flow to a higher speed. Accordingly, we establish the maximum traffic speed achievable via controlling AVs. Numerical results show that the traffic speed can be increased by over 6% when there are only 5% AVs. We also design an optimal control strategy for AVs to actively dampen undesirable perturbations. These theoretical findings validate the high potential of AVs to smooth traffic flow.

Connected and automated vehicles (CAVs) have a great potential to actively influence traffic systems. This has been demonstrated by large-scale numerical simulations and small-scale real experiments, whereas a comprehensive theoretical analysis is still lacking. In this paper, we focus on mixed traffic systems with one single CAV and heterogeneous human-driven vehicles, and present rigorous controllability analysis and optimal controller synthesis. Using the PBH controllability criterion, we reveal controllability properties of a linearized mixed traffic system in a ring road. It is proved that the mixed traffic flow can be stabilized by one single CAV under a very mild condition. We formulate the problem of designing CAV control strategies under a pre-specified communication topology as structured optimal controller synthesis. This formulation considers a system-level performance index that allows the CAV to actively dampen undesired perturbations in traffic flow. Numerical experiments verify the effectiveness of our results.

This paper considers the robustness analysis and distributed 'I-1∞(H-infinity) controller synthesis for a platoon of connected vehicles with undirected topologies. We first formulate a unified model to describe the collective behavior of homogeneous platoons with external disturbances using graph theory. By exploiting the spectral decomposition of a symmetric matrix, the collective dynamics of a platoon is equivalently decomposed into a set of subsystems sharing the same size with one single vehicle. Then, we provide an explicit scaling trend of robustness measure γ-gain, and introduce a scalable multistep procedure to synthesize a distributed 'I-1∞controller for large-scale platoons. It is shown that communication topology, especially the leader's information, exerts great influence on both robustness performance and controller synthesis. Furthermore, an intuitive optimization problem is formulated to optimize an undirected topology for a platoon system, and the upper and lower bounds of the objective are explicitly analyzed, which hints us that coordination of multiple mini-platoons is one reasonable architecture to control large-scale platoons. Numerical simulations are conducted to illustrate our findings.

In addition to decentralized controllers, the information flow among vehicles can significantly affect the dynamics of a platoon. This paper studies the influence of information flow topology on the internal stability and scalability of homogeneous vehicular platoons moving in a rigid formation. A linearized vehicle longitudinal dynamic model is derived using the exact feedback linearization technique, which accommodates the inertial delay of powertrain dynamics. Directed graphs are adopted to describe different types of allowable information flow interconnecting vehicles, including both radar-based sensors and vehicle-to-vehicle (V2V) communications. Under linear feedback controllers, a unified internal stability theorem is proved by using the algebraic graph theory and Routh-Hurwitz stability criterion. The theorem explicitly establishes the stabilizing thresholds of linear controller gains for platoons, under a large class of different information flow topologies. Using matrix eigenvalue analysis, the scalability is investigated for platoons under two typical information flow topologies, i.e., 1) the stability margin of platoon decays to zero as 0(1/N2) for bidirectional topology; and 2) the stability margin is always bounded and independent of the platoon size for bidirectional-leader topology. Numerical simulations are used to illustrate the results.

The platooning of autonomous ground vehicles has potential to largely benefit the road traffic, including enhancing highway safety, improving traffic utility and reducing fuel consumption. The main goal of platoon control is to ensure all the vehicles in the same group to move at consensual speed while maintaining desired spaces between adjacent vehicles. This paper presents an overview of vehicular platoon control techniques from networked control perspective, which naturally decomposes a platoon into four interrelated components, i.e., 1) node dynamics (ND), 2) information flow topology (IFT), 3) distributed controller (DC) and, 4) geometry formation (GF). Under the four-component framework, existing literature are categorized and analyzed according to their technical features. Three main performance metrics, i.e. string stability, stability margin and coherence behavior, are also discussed.