Related papers: Minimal-time nonlinear control via semi-infinite p…
We obtain weighted uniform estimates for the gradient of the solutions to a class of linear parabolic Cauchy problems with unbounded coefficients. Such estimates are then used to prove existence and uniqueness of the mild solution to a…
We present an algorithm for approximating semidefinite programs with running time that is sublinear in the number of entries in the semidefinite instance. We also present lower bounds that show our algorithm to have a nearly optimal running…
We address the problem of combined stochastic and impulse control for a market maker operating in a limit order book. The problem is formulated as a Hamilton-Jacobi-Bellman quasi-variational inequality (HJBQVI). We propose an implicit…
This paper addresses the problem of robust control of a linear discrete-time system subject to bounded disturbances and to measurement and control budget constraints. Using Q-parameterization and a polytope containment method, we prove that…
This paper is concerned with a stochastic linear-quadratic optimal control problem in a finite time horizon, where the coefficients of the control system are allowed to be random, and the weighting matrices in the cost functional are…
We deal with finite dimensional linear and nonlinear control systems. If the system is linear and autonomous and satisfies the classical normality assumption, we improve the well known result on the strict convexity of the reachable set…
The aim of this work is to deal with a discontinuous Hamilton-Jacobi equation in the whole euclidian N-dimensional space, associated to a possibly unbounded optimal control problem. Here, the discontinuities are located on a hyperplane and…
An abstract framework guaranteeing the local continuous differentiability of the value function associated with optimal stabilization problems subject to abstract semilinear parabolic equations subject to a norm constraint on the controls…
This paper proposes an operator-theoretic framework that recasts the minimal value function of a nonlinear optimal control problem as an abstract bilinear form on a suitable function space. The resulting bilinear form is shown to satisfy an…
The design of an automated vehicle controller can be generally formulated into an optimal control problem. This paper proposes a continuous-time finite-horizon approximate dynamicprogramming (ADP) method, which can synthesis off-line…
We consider the problem of finite-horizon optimal control design under uncertainty for imperfectly observed discrete-time systems with convex costs and constraints. It is known that this problem can be cast as an infinite-dimensional convex…
This work presents and analyzes space-time finite element methods on fully unstructured simplicial space-time meshes for the numerical solution of parabolic optimal control problems. Using Babu\v{s}ka's theorem, we show well-posedness of…
We mathematically analyze and numerically study an actor-critic machine learning algorithm for solving high-dimensional Hamilton-Jacobi-Bellman (HJB) partial differential equations from stochastic control theory. The architecture of the…
In the present work we employ, for the first time, backward stochastic differential equations (BSDEs) to study the optimal control of semi-Markov processes on finite horizon, with general state and action spaces. More precisely, we prove…
This paper presents a new and straightforward procedure for solving bilinear quadratic optimal control problem. In this method, first the original optimal control problem is transformed into a nonlinear twopoint boundary value problem…
This paper deals with a family of stochastic control problems in Hilbert spaces which arises in typical applications (such as boundary control and control of delay equations with delay in the control) and for which is difficult to apply the…
In this paper, we propose a novel method for addressing Optimal Control Problems (OCPs) with input-affine dynamics and cost functions. This approach adopts a Model Predictive Control (MPC) strategy, wherein a controller is synthesized to…
The aim of this work is to develop a deep learning method for solving high-dimensional stochastic control problems based on the Hamilton--Jacobi--Bellman (HJB) equation and physics-informed learning. Our approach is to parameterize the…
We consider the class of nonlinear optimal control problems (OCP) with polynomial data, i.e., the differential equation, state and control con- straints and cost are all described by polynomials, and more generally for OCPs with smooth…
This paper presents a novel operator-theoretic approach for optimal control of nonlinear stochastic systems within reproducing kernel Hilbert spaces. Our learning framework leverages data samples of system dynamics and stage cost functions,…