Related papers: Conjugate times and regularity of the minimum time…
We consider a semi-Lagrangian scheme for solving the minimum time problem, with a given target, and the associated eikonal type equation. We first use a discrete time deterministic optimal control problem interpretation of the time…
This article develops variational integrators for a class of underactuated mechanical systems using the theory of discrete mechanics. Further, a discrete optimal control problem is formulated for the considered class of systems and…
This paper presents the equivalence between minimal time and minimal norm control problems for internally controlled heat equations. The target is an arbitrarily fixed bounded, closed and convex set with a nonempty interior in the state…
The minimum-time control problem consists in finding a control policy that will drive a given dynamic system from a given initial state to a given target state (or a set of states) as quickly as possible. This is a well-known challenging…
This paper is devoted to the analysis of a finite horizon discrete-time stochastic optimal control problem, in presence of constraints. We study the regularity of the value function which comes from the dynamic programming algorithm. We…
This paper is devoted to the study of the Hausdorff dimension of the singular set of the minimum time function $T$ under controllability conditions which do not imply the Lipschitz continuity of $T$. We consider first the case of normal…
The approximation of integral type functionals is studied for discrete observations of a continuous It\^o semimartingale. Based on novel approximations in the Fourier domain, central limit theorems are proved for $L^2$-Sobolev functions…
We study existence of random elements with partially specified distributions. The technique relies on the existence of a positive extension for linear functionals accompanied by additional conditions that ensure the regularity of the…
We study the finite-time behaviour of the popular temporal difference (TD) learning algorithm when combined with tail-averaging. We derive finite time bounds on the parameter error of the tail-averaged TD iterate under a step-size choice…
Optimal Dirichlet boundary control for a fractional/normal evolution with a final observation is considered. The unique existence of the solution and the first-order optimality condition of the optimal control problem are derived. The…
This article concerns second-order time discretization of subdiffusion equations with time-dependent diffusion coefficients. High-order differentiability and regularity estimates are established for subdiffusion equations with…
The hybrid optimal control problem with reach time to a target set is addressed and the continuity and uniqueness of the associated value function is proved. Hybrid systems involves interaction of different types of dynamics: continuous and…
In this paper we relax the current regularity theory for the eikonal equation by using the recent theory of { set-valued} iterated Lie brackets. We give sufficient conditions for small time local attainability of general, symmetric,…
This paper presents a class of event-triggering rules for dynamical control systems with guaranteed positive minimum inter-event time (MIET). We first propose an event-based function design with guaranteed control performance under a…
This paper establishes a strict mathematical relationship between an arbitrary continuous function on a compact set and its global minima, like the well-known first order optimality condition for convex and differentiable functions. By…
In this paper, first of all, we introduce the basic concepts of generating function in combinatorics and some combinatorial identities. In order to facilitate the understanding of m-order time optimal control synthesis function of discrete…
We prove a general existence result in stochastic optimal control in discrete time where controls take values in conditional metric spaces, and depend on the current state and the information of past decisions through the evolution of a…
In this paper we introduce the concept of modulus of regularity as a tool to analyze the speed of convergence, including the finite termination, for classes of Fej\'er monotone sequences which appear in fixed point theory, monotone operator…
This paper is devoted to the distributed continuous-time optimization problem with time-varying objective functions and time-varying nonlinear inequality constraints. Different from most studied distributed optimization problems with…
Metric regularity is among the central concepts of nonlinear and variational analysis, constrained optimization, and their numerous applications. However, metric regularity can be elusive for some important ill-posed classes of problems…