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In this paper, we introduce methods from convex optimization to solve the multimarginal transport type problems arise in the context of density functional theory. Convex relaxations are used to provide outer approximation to the set of…
In this paper, we present an optimal control framework to address motion coordination of connected automated vehicles (CAVs) in the presence of human-driven vehicles (HDVs) in merging scenarios. Our framework combines an unconstrained…
Connected and automated vehicles (CAVs) provide the most intriguing opportunity to improve energy efficiency, traffic flow, and safety. In earlier work, we addressed the constrained optimal coordination problem of CAVs at different traffic…
Here we derive a nonsmooth maximum principle for optimal control problems with both state and mixed constraints. Crucial to our development is a convexity assumption on the "velocity set". The approach consists of applying known…
We present a set-oriented graph-based computational framework for continuous-time optimal transport over nonlinear dynamical systems. We recover provably optimal control laws for steering a given initial distribution in phase space to a…
We look into modeling fuel cell hybrid trains for the purpose of optimizing their operation using convex optimization. Models and constraints necessary to form a physically feasible yet convex problem are reviewed. This effort is described…
We study global optimization of non-convex functions through optimal control theory. Our main result establishes that (quasi-)optimal trajectories of a discounted control problem converge globally and practically asymptotically to the set…
We consider the problem of determining a sequence of payments among a set of entities that clear (if possible) the liabilities among them. We formulate this as an optimal control problem, which is convex when the objective function is, and…
We address the problem to control a population of noncooperative heterogeneous agents, each with convex cost function depending on the average population state, and all sharing a convex constraint, towards an aggregative equilibrium. We…
In this paper, we study a class of finite-time control problems for discrete-time positive linear systems with time-varying state parameters. Although several interesting control problems appearing in population biology, economics, and…
We consider a stochastic control problem where the set of controls is not necessarily convex and the system is governed by a nonlinear backward stochastic differential equation. We establish necessary as well as sufficient conditions of…
In this paper, we present an equivalent convex optimization formulation for discrete-time stochastic linear systems subject to linear chance constraints, alongside a tight convex relaxation for quadratic chance constraints. By lifting the…
In this paper, we study the well-posedness and approximate controllability of a class of network systems having delays and controls at the boundary conditions. The particularity of this work is that the network system is defined on infinite…
Modeling heterogeneous and multi-lane traffic flow is essential for understanding and controlling complex transportation systems. In this work, we consider three vehicle populations: two classes of human-driven vehicles (cars and trucks)…
An optimal control problem on finite-dimensional positive cones is stated. Under a critical assumption on the cone, the corresponding Bellman equation is satisfied by a linear function, which can be computed by convex optimization. A…
The optimal power flow (OPF) problem seeks to control power generation/demand to optimize certain objectives such as minimizing the generation cost or power loss in the network. It is becoming increasingly important for distribution…
In this paper, we develop an optimal control framework for dynamical systems when only an approximate model of the underlying plant is available. We consider a setting in which the control strategy is synthesized using a model-based optimal…
Congestion in transport networks is a topic of theoretical interest and practical importance. In this paper we study the flow of vehicles in urban street networks. In particular, we use a cellular automata model to simulate the motion of…
Connected and automated vehicles (CAVs) are expected to reshape traffic flow dynamics and present new challenges and opportunities for traffic flow modeling. While numerous studies have proposed optimal modeling and control strategies for…
In this paper, we present a novel control scheme for feedback optimization. That is, we propose a discrete-time controller that can steer the steady state of a physical plant to the solution of a constrained optimization problem without…