相关论文: Guaranteed error control bounds for the stabilised…

This paper presents a new formulation for model-free robust optimal regulation of continuous-time nonlinear systems. The proposed reinforcement learning based approach, referred to as incremental adaptive dynamic programming (IADP),…

We show how a posteriori goal oriented error estimation can be used to efficiently solve the subproblems occurring in a Model Predictive Control (MPC) algorithm. In MPC, only an initial part of a computed solution is implemented as a…

Evolutionary Algorithms (EAs) are being routinely applied for a variety of optimization tasks, and real-parameter optimization in the presence of constraints is one such important area. During constrained optimization EAs often create…

In this paper, we introduce a novel pseudospectral method for the numerical solution of optimal control problems governed by a parabolic distributed parameter system. The infinite-dimensional optimal control problem is reduced into a…

In this paper, we compute finite sample bounds for data-driven approximations of the solution to stochastic reachability problems. Our approach uses a nonparametric technique known as kernel distribution embeddings, and provides…

Coherent lower previsions are general probabilistic models allowing incompletely specified probability distributions. However, for complete description of a coherent lower prevision -- even on finite underlying sample spaces -- an infinite…

Safety-critical navigation applications require that estimation errors be reliably quantified and bounded. This can be challenging for linear dynamic systems if the process noise or measurement errors have uncertain time correlation. In…

We present a space-time finite element method for the heat equation that computes quasi-optimal approximations with respect to natural norms while incorporating local mesh refinements in space-time. The discretized problem is solved with a…

In this work, we study the optimal discretization error of stochastic integrals, in the context of the hedging error in a multidimensional It\^{o} model when the discrete rebalancing dates are stopping times. We investigate the convergence,…

We study problem-dependent rates, i.e., generalization errors that scale near-optimally with the variance, the effective loss, or the gradient norms evaluated at the "best hypothesis." We introduce a principled framework dubbed "uniform…

This work presents and analyzes space-time finite element methods on fully unstructured simplicial space-time meshes for the numerical solution of parabolic optimal control problems. Using Babu\v{s}ka's theorem, we show well-posedness of…

This paper deals with a general form of variational problems in Banach spaces which encompasses variational inequalities as well as minimization problems. We prove a characterization of local error bounds for the distance to the…

Stochastic variance reduced methods have shown strong performance in solving finite-sum problems. However, these methods usually require the users to manually tune the step-size, which is time-consuming or even infeasible for some…

We consider the problem of adaptive control of a class of feedback linearizable plants with matched parametric uncertainties whose states are accessible, subject to state constraints, which often arise due to safety considerations. In this…

The effectiveness of non-parametric, kernel-based methods for function estimation comes at the price of high computational complexity, which hinders their applicability in adaptive, model-based control. Motivated by approximation techniques…

We present a fully explicit dynamic formulation for geometrically exact shear-deformable beams. The starting point of this work is an existing isogeometric collocation (IGA-C) formulation which is explicit in the strict sense of the time…

The support recovery problem consists of determining a sparse subset of a set of variables that is relevant in generating a set of observations, and arises in a diverse range of settings such as compressive sensing, and subset selection in…

We consider an optimal control problem constrained by a parabolic partial differential equation (PDE) with Robin boundary conditions. We use a well-posed space-time variational formulation in Lebesgue--Bochner spaces with minimal…

The paper addresses parametric inequality systems described by polynomial functions in finite dimensions, where state-dependent infinite parameter sets are given by finitely many polynomial inequalities and equalities. Such systems can be…

We study uniqueness of solutions to degenerate parabolic problems, posed in bounded domains, where no boundary conditions are imposed. Under suitable assumptions on the operator, uniqueness is obtained for solutions that satisfy an…