Related papers: Solution to the quantum Zermelo navigation problem
Optimal transport has gained significant attention in recent years due to its effectiveness in deep learning and computer vision. Its descendant metric, the Wasserstein distance, has been particularly successful in measuring distribution…
The quantum-walk-based spatial search problem aims to find a marked vertex using a quantum walk on a graph with marked vertices. We describe a framework for determining the computational complexity of spatial search by continuous-time…
Geometric effects make evolution time vary for different evolution curves that connect the same two quantum states. Thus, it is important to be able to control along which path a quantum state evolve to achieve maximal speed in quantum…
We present an optimal hybrid control approach to the problem of stochastic route planning for sailing boats, especially in short course fleet races, in which minimum average time is an effective performance index. We show that the hybrid…
An efficient and accurate computational approach is proposed for optimal attitude control of a rigid body. The problem is formulated directly as a discrete time optimization problem using a Lie group variational integrator. Discrete…
A coordinate-free proof of the Maximum Principle is provided in the specific case of an optimal control problem with fixed time. Our treatment heavily relies on a special notion of variation of curves that consist of a concatenation of…
The dynamics of classical and quantum systems which are driven by a high frequency ($\omega$) field is investigated. For classical systems the motion is separated into a slow part and a fast part. The motion for the slow part is computed…
We propose Quantum Riemannian Hamiltonian Descent (QRHD), a quantum algorithm for continuous optimization on Riemannian manifolds that extends Quantum Hamiltonian Descent (QHD) by incorporating geometric structure of the parameter space via…
We investigate a quantum mechanical system on a noncommutative space for which the structure constant is explicitly time-dependent. Any autonomous Hamiltonian on such a space acquires a time-dependent form in terms of the conventional…
We take J. S. Bell's commendation of ``frame-dependent'' perspectives to the limit here, and consider motion on a ``map'' of landmarks and clocks fixed with respect to a single arbitrary inertial-reference frame. The metric equation…
This work considers the optimal covariance steering problem for systems subject to both additive noise and uncertain parameters which may enter multiplicatively with the state and the control. The unknown parameters are modeled as a…
We study a time minimization problem on the group of motions of a plane with admissible control in a half-disk. The considered control system describes a model of a car that can move forward on a plane and turn in place. Optimal…
We introduce an alternative approach for the analysis and numerical approximation of the optimal feedback control mapping. It consists in looking at a typical optimal control problem in such a way that feasible controls are mappings…
The optimal disturbance rejection control problem is considered for consensus tracking systems affected by external persistent disturbances and noise. Optimal estimated values of system states are obtained by recursive filtering for the…
Identifying the real and imaginary parts of wave functions with coordinates and momenta, quantum evolution may be mapped onto a classical Hamiltonian system. In addition to the symplectic form, quantum mechanics also has a positive-definite…
This paper considers the problem of fast and safe autonomous navigation in partially known environments. Our main contribution is a control policy design based on ellipsoidal trajectory bounds obtained from a quadratic state-dependent…
Optical techniques have been employed to coherently control the quantum transport through nanojunctions. Conventional works on optical control of quantum transport usually applied a tailored electrical pulses to perform specific tasks. In…
In this paper, problems of optimal control are considered where in the objective function, in addition to the control cost there is a tracking term that measures the distance to a desired stationary state. The tracking term is given by some…
We study the navigation problem for a robot moving amidst static and dynamic obstacles and rely on a hierarchical approach to solve it. First, the reference trajectory is planned by the safe interval path planning algorithm that is capable…
The Helmholtz equation is notoriously difficult to solve with standard numerical methods, increasingly so, in fact, at higher frequencies. Controllability methods instead transform the problem back to the time-domain, where they seek the…