Related papers: High-Speed Driving of a Two-Level System

We study the dynamics of a two-level quantum system under the influence of sinusoidal driving in the intermediate frequency regime. Analyzing the Floquet quasienergy spectrum, we find combinations of the field parameters for which…

Optimal control is a central problem in quantum thermodynamics. When minimizing dissipated work and work fluctuations defined via the two-point measurement scheme in open quantum systems, existing approaches largely focus on the rapid- and…

A central goal of thermodynamics is to identify optimal processes during which the least amount of energy is dissipated into the environment. Generally, even for simple systems, such as the parametric harmonic oscillator, optimal control…

We discuss recent results obtained for the Hamiltonian Mean Field model. The model describes a system of N fully-coupled particles in one dimension and shows a second-order phase transition from a clustered phase to a homogeneous one when…

We consider a single particle tunnelling in a tight-binding model with nearest-neighbour couplings, in the presence of a periodic high-frequency force. An effective Hamiltonian for the particle is derived using an averaging method…

Transitions between two lanes often have a significant impact on various forms of road traffic. To address this problem, we have developed a two-lane asymmetric simple exclusion process model and two hypothetical traffic control strategies,…

Collisional Brownian engines have recently gained attention as alternatives to conventional nanoscale engines. However, a comprehensive optimization of their performance, which could serve as a benchmark for future engine designs, is still…

We propose an efficient strategy to find optimal control functions for state-to-state quantum control problems. Our procedure first chooses an input state trajectory, that can realize the desired transformation by adiabatic variation of the…

This paper addresses the closed-loop control of an actuator with both a continuous input variable (motor torque) and a discrete input variable (mode selection). In many applications, robots have to bear large loads while moving slowly and…

This paper presents a provably optimal, real-time capable energy management policy for race cars that provides simple human-driver-implementable control cues. Specifically, we first formulate the energy-constrained minimum-lap-time control…

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 solve the problem of optimal stopping of a Brownian motion subject to the constraint that the stopping time's distribution is a given measure consisting of finitely-many atoms. In particular, we show that this problem can be converted to…

We study an optimal transportation approach for recovering parameters in dynamical systems with a single smoothly varying attractor. We assume that the data is not sufficient for estimating time derivatives of state variables but enough to…

We consider an optimal control problem in which the state is governed by an unilateral obstacle problem (with obstacle from below) and restricted by a pointwise state constraint (from above). In the presence of control constraints, we…

We consider transport exponents associated with the dynamics of a wavepacket in a discrete one-dimensional quantum system and develop a general method for proving upper bounds for these exponents in terms of the norms of transfer matrices…

One of the fundamental tasks of autonomous driving is safe trajectory planning, the task of deciding where the vehicle needs to drive, while avoiding obstacles, obeying safety rules, and respecting the fundamental limits of road. Real-world…

We address the problem of optimal transport with a quadratic cost functional and a constraint on the flux through a constriction along the path. The constriction, conceptually represented by a toll station, limits the flow rate across. We…

Initially a car is placed with probability p at each site of the two-dimensional integer lattice. Each car is equally likely to be East-facing or North-facing, and different sites receive independent assignments. At odd time steps, each…

In this article, we present a long-duration autonomy approach for the control of connected and automated vehicles (CAVs) operating in a transportation network. In particular, we focus on the performance of CAVs at traffic bottlenecks,…

In this paper, we provide a decentralized theoretical framework for coordination of connected and automated vehicles (CAVs) at different traffic scenarios. The framework includes: (1) an upper-level optimization that yields for each CAV its…