Related papers: Indirect methods in optimal control on Banach spac…
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…
Optimality conditions in the form of a variational inequality are proved for a class of constrained optimal control problems of stochastic differential equations. The cost function and the inequality constraints are functions of the…
This work introduces a sequential convex programming framework for non-linear, finite-dimensional stochastic optimal control, where uncertainties are modeled by a multidimensional Wiener process. We prove that any accumulation point of the…
We study the problem of estimating the fixed point of a contractive operator defined on a separable Banach space. Focusing on a stochastic query model that provides noisy evaluations of the operator, we analyze a variance-reduced stochastic…
We consider a stochastic control problem where the set of controls is not necessarily convex and the system is governed by a nonlinear backward stochastic differential equation. We establish necessary as well as sufficient conditions of…
In this paper we consider a parabolic optimal control problem with a Dirac type control with moving point source in two space dimensions. We discretize the problem with piecewise constant functions in time and continuous piecewise linear…
Optimal control under uncertainty is a prevailing challenge for many reasons. One of the critical difficulties lies in producing tractable solutions for the underlying stochastic optimization problem. We show how advanced approximate…
An adaptive direct collocation method is developed for solving optimal control problems constrained by parabolic partial differential equations. The partial differential equation is first reformulated in a variational setting, where the…
We introduce and analyze a fast iterative method based on sequential Bregman projections for nonlinear inverse problems in Banach spaces. The key idea, in contrast to the standard Landweber method, is to use multiple search directions per…
This article concerns the problem of computing solutions to state-constrained optimal control problems whose trajectory is affected by a flow field. This general mathematical framework is particularly pertinent to the requirements…
We consider stochastic optimal control of linear dynamical systems with additive non-Gaussian disturbance. We propose a novel, sampling-free approach, based on Fourier transformations and convex optimization, to cast the stochastic optimal…
Optimal control problems are usually addressed with the help of the famous Pontryagin Maximum Principle (PMP) which gives a generalization of the classical Euler-Lagrange and Weierstrass necessary optimality conditions of the calculus of…
In this paper, we study the optimal control of a discrete-time stochastic differential equation (SDE) of mean-field type, where the coefficients can depend on both a function of the law and the state of the process. We establish a new…
This paper deals with the infinite-horizon optimal control problem for Boolean control networks (BCNs) with a discounted-cost criterion. This problem has been investigated in existing studies with algorithms characterized by high…
This paper studies the continuous-time dynamics generated by control-theoretic Lagrangian methods for equality-constrained optimization. In particular, we consider dynamics induced by proportional-integral and feedback linearization…
We present a novel direct transcription method to solve optimization problems subject to nonlinear differential and inequality constraints. We prove convergence of our numerical method under reasonably mild assumptions: boundedness and…
The entropy regularization is inspired by information entropy from machine learning and the ideas of exploration and exploitation in reinforcement learning, which appears in the control problem to design an approximating algorithm for the…
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…
Direct optimal control theory for quantum dynamical problems presents itself as an interesting alternative to the traditional indirect optimal control. The method relies on the first discretize and then optimize paradigm, where a…
We survey some representative results on fuzzy fractional differential equations, controllability, approximate controllability, optimal control, and optimal feedback control for several different kinds of fractional evolution equations.…