Related papers: Hopf-type representation formulas and efficient al…
We present a partial-differential-equation-based optimal path-planning framework for curvature constrained motion, with application to vehicles in 2- and 3-spatial-dimensions. This formulation relies on optimal control theory, dynamic…
Solving high dimensional optimal control problems and corresponding Hamilton-Jacobi PDEs are important but challenging problems in control engineering. In this paper, we propose two abstract neural network architectures which are…
In this article, two methods for solving mean-field type optimal control problems are proposed and investigated. The two methods are iterative methods: at each iteration, a Hamilton-Jacobi-Bellman equation is solved, for a terminal…
We introduce a numerical technique for controlling the location and stability properties of Hopf bifurcations in dynamical systems. The algorithm consists of solving an optimization problem constrained by an extended system of nonlinear…
We survey the main numerical techniques for finite-dimensional nonlinear optimal control. The chapter is written as a guide to practitioners who wish to get rapidly acquainted with the main numerical methods used to efficiently solve an…
We investigate feedback control for infinite horizon optimal control problems for partial differential equations. The method is based on the coupling between Hamilton-Jacobi-Bellman (HJB) equations and model reduction techniques. It is…
Optimal control problems are crucial in various domains, including path planning, robotics, and humanoid control, demonstrating their broad applicability. The connection between optimal control and Hamilton-Jacobi (HJ) partial differential…
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 study an inverse problem of the stochastic optimal control of general diffusions with performance index having the quadratic penalty term of the control process. Under mild conditions on the system dynamics, the cost functions, and the…
We propose a local regularization of elliptic optimal control problems which involves the nonconvex $L^q$ fractional penalizations in the cost function. The proposed \emph{Huber type} regularization allows us to formulate the PDE…
We prove a representation formula of Hopf-Lax type for the solution of a Hamilton-Jacobi equation involving Caputo time-fractional derivative. Equations of these type are associated with optimal control problems where the controlled…
We present a neural network approach for approximating the value function of high-dimensional stochastic control problems. Our training process simultaneously updates our value function estimate and identifies the part of the state space…
A Deterministic affine quadratic optimal control problem is considered. Due to the nature of the problem, optimal controls exist under some very mild conditions. Further, it is shown that under some assumptions, the value function is…
Presented is a method to compute certain classes of Hamilton-Jacobi equations that result from optimal control and trajectory generation problems with time delays. Many robotic control and trajectory problems have limited information of the…
Maximum entropy reinforcement learning (RL) methods have been successfully applied to a range of challenging sequential decision-making and control tasks. However, most of existing techniques are designed for discrete-time systems. As a…
This is the first in a series of papers in which we study an efficient approximation scheme for solving the Hamilton-Jacobi-Bellman equation for multi-dimensional problems in stochastic control theory. The method is a combination of a WKB…
This paper considers optimal control of dynamical systems which are represented by nonlinear stochastic differential equations. It is well-known that the optimal control policy for this problem can be obtained as a function of a value…
This paper presents a systematic approach for computing local solutions to motion planning problems in non-convex environments using numerical optimal control techniques. It extends the range of use of state-of-the-art numerical optimal…
This paper presents the design and analysis of a Hybrid High-Order (HHO) approximation for a distributed optimal control problem governed by the Poisson equation. We propose three distinct schemes to address unconstrained control problems…
We examine the minimization of a quadratic cost functional composed of the output and the final state of abstract infinite-dimensional evolution equations in view of existence of solutions and optimality conditions. While the initial value…