Related papers: Further extensions on the successive approximation…
In recent years, much effort in designing numerical methods for the simulation and optimization of mechanical systems has been put into schemes which are structure preserving. One particular class are variational integrators which are…
This paper presents a comprehensive review of techniques proposed in the literature for solving bilevel optimization problems encountered in various real-life applications. Bilevel optimization is an appropriate choice for hierarchical…
Optimal designs are usually model-dependent and likely to be sub-optimal if the postulated model is not correctly specified. In practice, it is common that a researcher has a list of candidate models at hand and a design has to be found…
We consider a continuous time stochastic optimal control problem under both equality and inequality constraints on the expectation of some functionals of the controlled process. Under a qualification condition, we show that the problem is…
Model-based reinforcement learning is an appealing framework for creating agents that learn, plan, and act in sequential environments. Model-based algorithms typically involve learning a transition model that takes a state and an action and…
We study high-dimensional stochastic optimal control problems in which many agents cooperate to minimize a convex cost functional. We consider both the full-information problem, in which each agent observes the states of all other agents,…
In this chapter, we are concerned with inverse optimal control problems, i.e., optimization models which are used to identify parameters in optimal control problems from given measurements. Here, we focus on linear-quadratic optimal control…
A framework is introduced for sequentially solving convex stochastic minimization problems, where the objective functions change slowly, in the sense that the distance between successive minimizers is bounded. The minimization problems are…
The paper considers the problem of a leader that seeks to optimally influence the opinions of agents in a directed network through connecting with a limited number of the agents ("direct followers"), possibly in the presence of a fixed…
Pseudo-arclength continuation is a well-established method for generating a numerical curve approximating the solution of an underdetermined system of nonlinear equations. It is an inherently sequential predictor-corrector method in which…
We examine the problem of two-point boundary optimal control of nonlinear systems over finite-horizon time periods with unknown model dynamics by employing reinforcement learning. We use techniques from singular perturbation theory to…
The Method of Successive Approximations (MSA) is a fixed-point iterative method used to solve stochastic optimal control problems. It is an indirect method based on the conditions derived from the Stochastic Maximum Principle (SMP), an…
Reinforcement learning based adaptive/approximate dynamic programming (ADP) is a powerful technique to determine an approximate optimal controller for a dynamical system. These methods bypass the need to analytically solve the nonlinear…
In this contribution we apply an adaptive model hierarchy, consisting of a full-order model, a reduced basis reduced order model, and a machine learning surrogate, to parametrized linear-quadratic optimal control problems. The involved…
We consider recent work of Haber and Ruthotto 2017 and Chang et al. 2018, where deep learning neural networks have been interpreted as discretisations of an optimal control problem subject to an ordinary differential equation constraint. We…
The purpose of this work is the design and analysis of a reliable and efficient a posteriori error estimator for the so-called pointwise tracking optimal control problem. This linear-quadratic optimal control problem entails the…
This paper proposes a new family of algorithms for training neural networks (NNs). These are based on recent developments in the field of non-convex optimization, going under the general name of successive convex approximation (SCA)…
We consider a class of nonconvex nonsmooth optimization problems whose objective is the sum of a smooth function and a finite number of nonnegative proper closed possibly nonsmooth functions (whose proximal mappings are easy to compute),…
In this note, we develop the first-order theory of optimal control problems with box constraints on the control. We emphasize the precise modification of Pontryagin's maximum principle when the admissible control set is compact, the…
The article is devoted to the problem of applying the maximum principle for finding optimal control parameters in simulation tasks of interest for a variety of engineering and industrial systems and processes. Especially important is the…