Related papers: Optimal Control from a Fluid Dynamics Perspective
We give a short overview of advantages and drawbacks of the classical formulation of minimum cost network flow problems and solution techniques, to motivate a reformulation of classical static minimum cost network flow problems as optimal…
This paper presents a mathematical formulation to perform temporal parallelisation of continuous-time optimal control problems, which can be solved via the Hamilton--Jacobi--Bellman (HJB) equation. We divide the time interval of the control…
In this paper we study optimal control problems for nonholonomic systems defined on Lie algebroids by using quasi-velocities. We consider both kinematic, i.e. systems whose cost functional depends only on position and velocities, and…
This work reformulates language generation as a stochastic optimal control problem, providing a unified theoretical perspective to analyze autoregressive and diffusion models and explain their limitations (Efficiency-Fidelity Paradox,…
In Stochastic Optimal Control (SOC) one minimizes the average cost-to-go, that consists of the cost-of-control (amount of efforts), cost-of-space (where one wants the system to be) and the target cost (where one wants the system to arrive),…
We study a generalized version of Zermelo's navigation problem where the set of admissible velocities is a general compact convex set, replacing the classical Euclidean ball. After establishing existence results under the natural assumption…
We consider an optimal control problem for a two-dimensional Navier-Stokes-Cahn-Hilliard system arising in the modeling of fluid-membrane interaction. The fluid dynamics is governed by the incompressible Navier-Stokes equations, which are…
In this paper we consider an energy storage optimization problem in finite time in a model with partial information that allows for a changing economic environment. The state process consists of the storage level controlled by the storage…
In this paper, we consider a time-optimal control problem with uncertainties. Dynamics of controlled object is expressed by crisp linear system of differential equations with fuzzy initial and final states. We introduce a notion of fuzzy…
Optimal control of diffusion processes is intimately connected to the problem of solving certain Hamilton-Jacobi-Bellman equations. Building on recent machine learning inspired approaches towards high-dimensional PDEs, we investigate the…
The preparation of highly entangled many-body systems is one of the central challenges of both basic and applied science. The complexity of interparticle interaction and environment coupling increases rapidly with the number of…
We consider the approximation of some optimal control problems for the Navier-Stokes equation via a Dynamic Programming approach. These control problems arise in many industrial applications and are very challenging from the numerical point…
We consider a pathwise stochastic optimal control problem and study the associated (not necessarily adapted) Hamilton-Jacobi-Bellman stochastic partial differential equation. We show that the value process is the unique solution of this…
In this paper we develop a Hamiltonian approach to sufficient conditions in optimal control problems. We extend the known conditions for $C^2$ maximised Hamiltonians into two directions: on the one hand we explain the role of a super…
The quantum navigation problem of finding the time-optimal control Hamiltonian that transports a given initial state to a target state through quantum wind, that is, under the influence of external fields or potentials, is analysed. By…
We develop a discrete analogue of Hamilton-Jacobi theory in the framework of discrete Hamiltonian mechanics. The resulting discrete Hamilton-Jacobi equation is discrete only in time. We describe a discrete analogue of Jacobi's solution and…
We consider piecewise-deterministic optimal control problems in which the environment randomly switches among several deterministic modes, and the goal is to optimize the expected cost up to the termination while taking the likelihood of…
Robotic locomotion often relies on sequenced gaits to efficiently convert control input into desired motion. Despite extensive studies on gait optimization, achieving smooth and efficient gait transitions remains challenging. In this paper,…
This paper presents sufficient conditions for optimal control of systems with dynamics given by a linear operator, in order to obtain an explicit solution to the Bellman equation that can be calculated in a distributed fashion. Further, the…
In this paper, we first investigate necessary optimality conditions for problems governed by systems describing the flow of an incompressible second grade fluid. Next, we study the asymptotic behavior of the optimal solution when the…