Related papers: Optimal Stopping under Nonlinear Expectation
Optimal stopping is the problem of determining when to stop a stochastic system in order to maximize reward, which is of practical importance in domains such as finance, operations management and healthcare. Existing methods for…
The famous proof of the Pontryagin maximum principle for control problems on a finite horizon bases on the needle variation technique, as well as the separability concept of cones created by disturbances of the trajectories. In this…
We discretize a risk-neutral optimal control problem governed by a linear elliptic partial differential equation with random inputs using a Monte Carlo sample-based approximation and a finite element discretization, yielding finite…
We propose a semi-discrete numerical scheme and establish well-posedness of a class of parabolic systems. Such systems naturally arise while studying the optimal control of grain boundary motions. The latter is typically described using a…
We present an approach for accelerating nonlinear model predictive control. If the current optimal input signal is saturated, also the optimal signals in subsequent time steps often are. We propose to use the open-loop optimal input signals…
In this paper we prove existence and uniqueness of viscosity solutions of elliptic systems associated to fully nonlinear operators for minimization problems that involve interconnected obstacles. This system appears, among other, in the…
This paper is concerned with the design of optimal control for finite-dimensional control-affine nonlinear dynamical systems. We introduce an optimal control problem that specifically optimizes nonlinear observability in addition to…
We introduce a model of infinite horizon linear dynamic optimization with linear constraints and obtain results concerning feasibility of trajectories and optimal solutions necessarily satisfying conditions that resemble the Euler condition…
The paper describes a receding horizon control design framework for continuous-time stochastic nonlinear systems subject to probabilistic state constraints. The intention is to derive solutions that are implementable in real-time on…
The paper aims at the development of an apparatus for analysis and construction of near optimal solutions of singularly perturbed (SP) optimal controls problems (that is, problems of optimal control of SP systems) considered on the infinite…
This paper concerns optimal control problems for a class of sweeping processes governed by discontinuous unbounded differential inclusions that are described via normal cone mappings to controlled moving sets. Largely motivated by…
The objective of this work is to study continuous-time Markov decision processes on a general Borel state space with both impulsive and continuous controls for the infinite-time horizon discounted cost. The continuous-time controlled…
This paper is concerned with optimal switching over multiple modes in continuous time and on a finite horizon. The performance index includes a running reward, terminal reward and switching costs that can belong to a large class of…
We study an optimal control problem on infinite time horizon with semimartingale strategies, random coefficients and regime switching. The value function and the optimal strategy can be characterized in terms of three systems of backward…
We consider the neural ODE and optimal control perspective of supervised learning, with $\ell^1$-control penalties, where rather than only minimizing a final cost (the \emph{empirical risk}) for the state, we integrate this cost over the…
We study the problem of bounding path-dependent expectations (within any finite time horizon $d$) over the class of discrete-time martingales whose marginal distributions lie within a prescribed tolerance of a given collection of benchmark…
We show that empirical risk minimization procedures and regularized empirical risk minimization procedures satisfy nonexact oracle inequalities in an unbounded framework, under the assumption that the class has a subexponential envelope…
This work provides a novel convergence analysis for stochastic optimization in terms of stopping times, addressing the practical reality that algorithms are often terminated adaptively based on observed progress. Unlike prior approaches,…
In this paper we develop novel results on self triggering control of nonlinear systems, subject to perturbations and actuation delays. First, considering an unperturbed nonlinear system with bounded actuation delays, we provide conditions…
The main objective of this paper and the accompanying one \cite{ETZ2} is to provide a notion of viscosity solutions for fully nonlinear parabolic path-dependent PDEs. Our definition extends our previous work \cite{EKTZ}, focused on the…