Related papers: Shortest-path recovery from signature with an opti…
This paper studies the inverse optimal control problem for continuous-time linear quadratic regulators over finite-time horizon, aiming to reconstruct the control, state, and terminal cost matrices in the objective function from observed…
We investigate the optimization of quantum control from a differential geometric perspective. In our approach, optimal control minimizes the cost associated with evolving a quantum state, with the cost quantified by the length of the…
The aim of this article is to develop an explicit procedure that enables one to reconstruct any $C^1$ path (at natural parametrization) from its signature. We also explicitly quantify the distance between the reconstructed path and the…
We develop two methods to reconstruct a path of bounded variation from its signature. The first method gives a simple and explicit expression of any axis path in terms of its signature, but it does not apply directlty to more general ones.…
We revisit the optimal control problem with maximum cost with the objective to provide different equivalent reformulations suitable to numerical methods. We propose two reformulations in terms of extended Mayer problems with constraint, and…
In this paper we consider the problem of the optimal control of an ensemble of affine-control systems. After proving the well-posedness of the minimization problem under examination, we establish a $\Gamma$-convergence result that allows us…
Shortcut to isothermality is a driving strategy to steer the system to its equilibrium states within finite time, and enables evaluating the impact of a control promptly. Finding optimal scheme to minimize the energy cost is of critical…
In many problems in optimal control, one seeks to minimise an objective function subject to constraints on the velocity of the system. Imposing these constraints directly -- the ``hard-constrained'' approach -- is often analytically and…
We consider the motion planning of an object in a Riemannian manifold where the object is steered from an initial point to a final point utilizing optimal control. Considering Pontryagin Minimization Principle we compute the Optimal…
We propose a new approach to circumvent the sign problem in which the integration path is optimized to control the sign problem. We give a trial function specifying the integration path in the complex plane and tune it to optimize the cost…
We study a signature-driven numerical scheme to solve multi-dimensional linear-quadratic (LQ) stochastic control problems. Using that linear signature functionals are dense in the natural class of admissible controls, we show that our…
We present a method for optimal control with respect to a linear cost function for positive linear systems with coupled input constraints. We show that the optimal cost function and resulting sparse state feedback for these systems can be…
Moment optimization techniques have been recently proposed to solve globally various classes of optimal control problems. As those methods return truncated moment sequences of occupation measures, this paper explores a numeric method for…
We present an embedding of stochastic optimal control problems, of the so called path integral form, into reproducing kernel Hilbert spaces. Using consistent, sample based estimates of the embedding leads to a model free, non-parametric…
This paper proposes to parameterize open loop controls in stochastic optimal control problems via suitable classes of functionals depending on the driver's path signature, a concept adopted from rough path integration theory. We rigorously…
In this paper, we focus on a method based on optimal control to address the optimization problem. The objective is to find the optimal solution that minimizes the objective function. We transform the optimization problem into optimal…
A complete analytical solution to the optimal reversal of a macrospin with easy-axis anisotropy is presented. Optimal control path minimizing the energy cost of the reversal is identified and used to derive time-dependent direction and…
This work presents an efficient method to solve a class of continuous-time, continuous-space stochastic optimal control problems of robot motion in a cluttered environment. The method builds upon a path integral representation of the…
We present a method for obtaining approximate solutions to the problem of optimal execution, based on a signature method. The framework is general, only requiring that the price process is a geometric rough path and the price impact…
In this paper, we describe a constrained Lagrangian and Hamiltonian formalism for the optimal control of nonholonomic mechanical systems. In particular, we aim to minimize a cost functional, given initial and final conditions where the…