相关论文: Regularity of the Hamiltonian along Optimal Trajec…

We study the time optimal control problem with a general target $\mathcal S$ for a class of differential inclusions that satisfy mild smoothness and controllability assumptions. In particular, we do not require Petrov's condition at the…

This paper studies the regularity of the minimum time function, $T(\cdot)$, for a control system with a general closed target, taking the state equation in the form of a differential inclusion. Our first result is a sensitivity relation…

The recent approach based on Hamiltonian systems and the implicit parametri\-za\-tion theorem, provides a general fixed domain approximation method in shape optimization problems, using optimal control theory. In previous works, we have…

We consider the Lagrange problem of optimal control with unrestricted controls and address the question: under what conditions we can assure optimal controls are bounded? This question is related to the one of Lipschitzian regularity of…

We consider the control problem with \textit{exit time}. Unlike the Bolza and Mayer problems, in this problem the terminal time of the trajectories is not fixed, but it is the first time at which they reach a given closed subset -…

Motivated by optimal control problems and differential games for functional differential equations of retarded type, the paper deals with a Cauchy problem for a path-dependent Hamilton--Jacobi equation with a right-end boundary condition.…

This paper continues the investigations from [7] and is concerned with the derivation of first-order conditions for a control constrained optimization problem governed by a non-smooth elliptic PDE. The control enters the state equation not…

A class of optimal control problems of hybrid nature governed by semilinear parabolic equations is considered. These problems involve the optimization of switching times at which the dynamics, the integral cost, and the bounds on the…

We consider a Cauchy problem for a (first-order) path-dependent Hamilton--Jacobi equation with coinvariant derivatives and a right-end boundary condition. Such problems arise naturally in the study of properties of the value functional in…

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…

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…

This paper investigates the central role played by the Hamiltonian in continuous-time nonlinear optimal control problems. We show that the strict convexity of the Hamiltonian in the control variable is a sufficient condition for the…

Consider control systems described by a differential equation with a control term or, more generally, by a differential inclusion with velocity set $F(t,x)$. Certain properties of state trajectories can be derived when, in addition to other…

In continuous-time optimal control, evaluating the Hamiltonian requires solving a constrained optimization problem using the system's dynamics model. Hamilton-Jacobi reachability analysis for safety verification has demonstrated practical…

Inductive bias refers to restrictions on the hypothesis class that enable a learning method to generalize effectively from limited data. A canonical example in control is linearity, which underpins low sample-complexity guarantees for…

In this paper we investigate necessary conditions of optimality for infinite-horizon optimal control problems with overtaking optimality as an optimality criterion. For the case of local Lipschitz continuity of the payoff function, we…

Considering deterministic classical lattice systems with continuous variables, we show that, if the initial conditions are sampled according to a probability distribution in which the dynamical variables are statistically independent, the…

We introduce a notion of bounded variation solution for a new class of nonlinear control systems with ordinary and impulsive controls, in which the drift function depends not only on the state, but also on its past history, through a finite…

This article studies the solutions of time-dependent differential inclusions which is motivated by their utility in the modeling of certain physical systems. The differential inclusion is described by a time-dependent set-valued mapping…

A variant of the optimal control problem is considered which is nonstandard in that the performance index contains "stochastic" integrals, that is, integrals against very irregular functions. The motivation for considering such performance…