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Computational complexity has been a major challenge in game-theoretic model predictive control (GT-MPC), as real-time solutions to a game (e.g., Nash equilibria (NEs)) have to be computed at each sampling instant of an MPC. This challenge…
Accurate prediction of travel time is an essential feature to support Intelligent Transportation Systems (ITS). The non-linearity of traffic states, however, makes this prediction a challenging task. Here we propose to use dynamic linear…
Service platforms must determine rules for matching heterogeneous demand (customers) and supply (workers) that arrive randomly over time and may be lost if forced to wait too long for a match. Our objective is to maximize the cumulative…
We consider traffic flow dynamics for a network of signalized intersections, where the outflow from every link is constrained to be equal to a given capacity function if the queue length is positive, and equal to the minimum of cumulative…
This paper presents a systematic approach for analyzing the departure-time choice equilibrium (DTCE) problem of a single bottleneck with heterogeneous commuters. The approach is based on the fact that the DTCE is equivalently represented as…
Travel Time Estimation (TTE) is indispensable in intelligent transportation system (ITS). It is significant to achieve the fine-grained Trajectory-based Travel Time Estimation (TTTE) for multi-city scenarios, namely to accurately estimate…
Understanding neural dynamics is a central topic in machine learning, non-linear physics and neuroscience. However, the dynamics is non-linear, stochastic and particularly non-gradient, i.e., the driving force can not be written as gradient…
Vehicle trajectory planning is a key component for an autonomous driving system. A practical system not only requires the component to compute a feasible trajectory, but also a comfortable one given certain comfort metrics. Nevertheless,…
This article presents new immersed finite element (IFE) methods for solving the popular second order elliptic interface problems on structured Cartesian meshes even if the involved interfaces have nontrivial geometries. These IFE methods…
Computing shortest paths is one of the most researched topics in algorithm engineering. Currently available algorithms compute shortest paths in mere fractions of a second on continental sized road networks. In the presence of…
Variational inequalities (VIs) encompass many fundamental problems in diverse areas ranging from engineering to economics and machine learning. However, their considerable expressivity comes at the cost of computational intractability. In…
We study a continuous-time, infinite-horizon dynamic bipartite matching problem. Suppliers arrive according to a Poisson process; while waiting, they may abandon the queue at a uniform rate. Customers on the other hand must be matched upon…
In many mobile robotics scenarios, such as drone racing, the goal is to generate a trajectory that passes through multiple waypoints in minimal time. This problem is referred to as time-optimal planning. State-of-the-art approaches either…
Congestion pricing has emerged as an effective tool for mitigating traffic congestion, yet implementing welfare or revenue-optimal dynamic tolls is often impractical. Most real-world congestion pricing deployments, including New York City's…
The stochastic interpolant framework offers a powerful approach for constructing generative models based on ordinary differential equations (ODEs) or stochastic differential equations (SDEs) to transform arbitrary data distributions.…
The development of extremum seeking (ES) has progressed, over the past hundred years, from static maps, to finite-dimensional dynamic systems, to networks of static and dynamic agents. Extensions from ODE dynamics to maps and agents that…
Modeling the interaction between traffic agents is a key issue in designing safe and non-conservative maneuvers in autonomous driving. This problem can be challenging when multi-modality and behavioral uncertainties are engaged. Existing…
Using finite difference method, time evolution of a typical metal molecule metal system is studied by introducing a new method to solve general related Volterra integro differential equation (IDE). Discretization in time domain is applied…
In this paper, we investigate the seeking of Nash equilibrium (NE) in a non-cooperative quadratic game where all agents exchange their delayed strategy information with their neighbors. To extend best-response algorithms to the delayed…
In recent years, numerous vision and learning tasks have been (re)formulated as nonconvex and nonsmooth programmings(NNPs). Although some algorithms have been proposed for particular problems, designing fast and flexible optimization…