Related papers: An Inverse Optimality Method to Solve a Class of O…
Most inverse optimization models impute unspecified parameters of an objective function to make an observed solution optimal for a given optimization problem with a fixed feasible set. We propose two approaches to impute unspecified…
In this paper, we investigate optimal control problems for Allen-Cahn equations with singular nonlinearities and a dynamic boundary condition involving singular nonlinearities and the Laplace-Beltrami operator. The approach covers both the…
This paper introduces a notion of viscosity solutions for second order elliptic Hamilton-Jacobi-Bellman (HJB) equations with infinite delay associated with infinite-horizon optimal control problems for stochastic differential equations with…
This paper concerns a first-order algorithmic technique for a class of optimal control problems defined on switched-mode hybrid systems. The salient feature of the algorithm is that it avoids the computation of Fr\'echet or G\^ateaux…
This paper introduces a novel methodology that leverages the Hamilton-Jacobi solution to enhance non-linear model predictive control (MPC) in scenarios affected by navigational uncertainty. Using Hamilton-Jacobi-Theoretic approach, a…
We propose a fine analysis of second order optimality conditions for the optimal control of semi-linear parabolic equations with respect to the initial condition. More precisely, we investigate the following problem: maximise with respect…
We prove a sufficient optimality condition for non-linear optimal control problems with delays in both state and control variables. Our result requires the verification of a Hamilton-Jacobi partial differential equation and is obtained…
The optimal \(H_{\infty}\) control problem over an infinite time horizon, which incorporates a performance function with a discount factor \(e^{-\alpha t}\) (\(\alpha > 0\)), is important in various fields. Solving this optimal…
We give a new perspective on the existence of viscosity solutions for a stationary and a time-dependent first-order Hamilton-Jacobi equation. Following recent comparison principles, we work in a framework in which we consider a subsolution…
In this note, we demonstrate that a locally semiconvex viscosity supersolution to a possibly degenerate fully nonlinear elliptic Hamilton-Jacobi-Bellman (HJB) equation is differentiable along the directions spanned by the range of the…
The paper deals with an optimal control problem in a dynamical system described by a linear differential equation with the Caputo fractional derivative. The goal of control is to minimize a Bolza-type cost functional, which consists of two…
In this paper, we first establish the dynamic programming principle for stochastic optimal control problems defined on compact Riemannian manifolds without boundary. Subsequently, we derive the associated Hamilton-Jacobi-Bellman (HJB)…
A learning technique for finite horizon optimal control problems and its approximation based on polynomials is analyzed. It allows to circumvent, in part, the curse dimensionality which is involved when the feedback law is constructed by…
Controlling systems of ordinary differential equations (ODEs) is ubiquitous in science and engineering. For finding an optimal feedback controller, the value function and associated fundamental equations such as the Bellman equation and the…
Inverse optimization refers to the inference of unknown parameters of an optimization problem based on knowledge of its optimal solutions. This paper considers inverse optimization in the setting where measurements of the optimal solutions…
In this work, we address the challenge of approximating unknown system dynamics and costs by representing them as a bilinear system using Koopman-based Inverse Optimal Control (IOC). Using optimal trajectories, we construct a bilinear…
In this paper we introduce a new procedure to solve nonlinear optimal control problems with delays which exploits indirect methods combined with numerical homotopy procedures. It is known that solving this kind of problems via indirect…
Optimal feedback control with implicit Hamiltonians poses a fundamental challenge for learning-based value function methods due to the absence of closed-form optimal control laws. Recent work~\cite{gelphman2025end} introduced an implicit…
This paper addresses the problem of robust and optimal control for the class of nonlinear quadratic systems subject to norm-bounded parametric uncertainties and disturbances, and in presence of some amplitude constraints on the control…
We present a simple and easy to implement method for the numerical solution of a rather general class of Hamilton-Jacobi-Bellman (HJB) equations. In many cases, the considered problems have only a viscosity solution, to which, fortunately,…