Related papers: Optimal control of gradient flows via the Weighted…
We consider generalized gradient systems in Banach spaces whose evolutions are generated by the interplay between an energy functional and a dissipation potential. We focus on the case in which the dual dissipation potential is given by a…
Wave energy converters (WECs) represent an innovative technology for power generation from renewable sources (marine energy). Although there has been a great deal of research into such devices in recent decades, the power output of a single…
A gradient ascent method for optimal quantum control synthesis is presented that employs a gradient derived with respect to the coefficients of a functional basis expansion of the control. Restricting the space of allowable controls to…
Nonlinear control-affine systems with time-varying vector fields are considered in the paper. We propose a unified control design scheme with oscillating inputs for solving the trajectory tracking and stabilization problems. This…
In this work, we consider an optimal control problem subject to a nonlinear PDE constraint and apply it to the regularized $p$-Laplace equation. To this end, a reduced unconstrained optimization problem in terms of the control variable is…
In this work we study the convergence of gradient methods for nonconvex optimization problems -- specifically the effect of the problem formulation to the convergence behavior of the solution of a gradient flow. We show through a simple…
This paper focuses on finding approximate solutions to stochastic optimal control problems with control domains being not necessarily convex, where the state trajectory is subject to controlled stochastic differential equations. The…
We consider the numerical approximation of compressible flow in a pipe network. Appropriate coupling conditions are formulated that allow us to derive a variational characterization of solutions and to prove global balance laws for the…
In this paper we study the mixed virtual element approximation to an elliptic optimal control problem with boundary observations. The objective functional of this type of optimal control problem contains the outward normal derivatives of…
We investigated a cost-constrained static ergodic control problem of the variance of measure-valued affine processes and its application in streamflow management. The controlled system is a jump-driven mixed moving average process that…
We derive a limit on energy savings in controlled channel flow. For flow in a channel driven by pressure, shear, or any combination of the two, and controlled via wall transpiration or spanwise wall motion, the uncontrolled laminar state…
Devising optimal interventions for constraining stochastic systems is a challenging endeavour that has to confront the interplay between randomness and nonlinearity. Existing methods for identifying the necessary dynamical adjustments…
We consider mixed-integer optimal control problems with combinatorial constraints that couple over time such as minimum dwell times. We analyze a lifting and decomposition approach into a mixed-integer optimal control problem without…
This paper considers a class of distributed resource allocation problems where each agent privately holds a smooth, potentially non-convex local objective, subject to a globally coupled equality constraint. Built upon the existing method,…
It was shown in \cite{bloch2000optimal} that an optimal control formulation for incompressible ideal fluid flow yields Euler's equations. In this paper, we consider a variational obstacle-avoidance formulation for incompressible ideal flows…
The paper proposes a general framework to analyze control problems for conservation law models on a network. Namely we consider a general class of junction distribution controls and inflow controls and we establish the compactness in $L^1$…
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…
Existing analyses of optimization in deep learning are either continuous, focusing on (variants of) gradient flow, or discrete, directly treating (variants of) gradient descent. Gradient flow is amenable to theoretical analysis, but is…
A variational time discretization of anisotropic Willmore flow combined with a spatial discretization via piecewise affine finite elements is presented. Here, both the energy and the metric underlying the gradient flow are anisotropic,…
We propose a novel continuous-time algorithm for inequality-constrained convex optimization inspired by proportional-integral control. Unlike the popular primal-dual gradient dynamics, our method includes a proportional term to control the…