相关论文: Direct Integral Pseudospectral and Integral Spectr…
In order to solve continuous-time optimal control problems, direct methods transcribe the infinite-dimensional problem to a nonlinear program (NLP) using numerical integration methods. In cases where the integration error can be manipulated…
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…
We propose a primal--dual technique that applies to infinite dimensional equality constrained problems, in particular those arising from optimal control. As an application of our general framework, we solve a control-constrained double…
This paper introduces a framework for solving time-autonomous nonlinear infinite horizon optimal control problems, under the assumption that all minimizers satisfy Pontryagin's necessary optimality conditions. In detail, we use methods from…
We revisit the linear programming approach to deterministic, continuous time, infinite horizon discounted optimal control problems. In the first part, we relax the original problem to an infinite-dimensional linear program over a measure…
An infinite-dimensional bilinear optimal control problem with infinite-time horizon is considered. The associated value function can be expanded in a Taylor series around the equilibrium, the Taylor series involving multilinear forms which…
The solution of a constrained linear-quadratic regulator problem is determined by the set of its optimal active sets. We propose an algorithm that constructs this set of active sets for a desired horizon N from that for horizon N-1. While…
We introduce tensor numerical techniques for solving optimal control problems constrained by elliptic operators in $\mathbb{R}^d$, $d=2,3$, with variable coefficients, which can be represented in a low rank separable form. We construct a…
In this paper, we propose a Transformer-based framework for approximating solutions to infinite-dimensional optimization problems: calculus of variations problems and optimal control problems. Our approach leverages offline training on data…
The paper aims at the development of an apparatus for analysis and construction of near optimal solutions of singularly perturbed (SP) optimal controls problems (that is, problems of optimal control of SP systems) considered on the infinite…
Pseudospectral methods represent an efficient approach for solving optimal control problems. While Legendre-Gauss-Lobatto (LGL) collocation points have traditionally been considered inferior to Legendre-Gauss (LG) and Legendre-Gauss-Radau…
In this paper we study numerically solving optimal control problems with bang-bang control functions. We present a formal Lagrangian approach for solving the optimal control problem, and address difficulties encountered when numerically…
This paper offers a unified perspective on different approaches to the solution of optimal control problems through the lens of constrained sequential quadratic programming. In particular, it allows us to find the relationships between…
Direct policy gradient methods for reinforcement learning and continuous control problems are a popular approach for a variety of reasons: 1) they are easy to implement without explicit knowledge of the underlying model 2) they are an…
We propose and analyze a numerical algorithm for solving a class of optimal control problems for learning-informed semilinear partial differential equations. The latter is a class of PDEs with constituents that are in principle unknown and…
We examine the problem of two-point boundary optimal control of nonlinear systems over finite-horizon time periods with unknown model dynamics by employing reinforcement learning. We use techniques from singular perturbation theory to…
In this paper, we present a unified computational method based on pseudospectral approximations for the design of optimal pulse sequences in open quantum systems. The proposed method transforms the problem of optimal pulse design, which is…
Semi-lagrangian schemes for discretization of the dynamic programming principle are based on a time discretization projected on a state-space grid. The use of a structured grid makes this approach not feasible for high-dimensional problems…
This work presents an algorithmic scheme for solving the infinite-time constrained linear quadratic regulation problem. We employ an accelerated version of a popular proximal gradient scheme, commonly known as the Forward-Backward Splitting…
Path Integral Control methods were developed for stochastic optimal control covering a wide class of finite horizon formulations with control affine nonlinear dynamics. Characteristic for this class is that the HJB equation is linear and…