Related papers: The optimal control and its multiple applications
Optimal Control Theory is a powerful mathematical tool, which has known a rapid development since the 1950s, mainly for engineering applications. More recently, it has become a widely used method to improve process performance in quantum…
This paper is a survey on some recent aspects and developments in stochastic control. We discuss the two main historical approaches, Bellman's optimality principle and Pontryagin's maximum principle, and their modern exposition with…
The aim of this notes is to give a concise introduction to control theory for systems governed by stochastic partial differential equations. We shall mainly focus on controllability and optimal control problems for these systems. For the…
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…
In this paper we combine two main topics in mechanics and optimal control theory: contact Hamiltonian systems and Pontryagin Maximum Principle. As an important result, among others, we develop a contact Pontryagin Maximum Principle that…
Mathematical theory of the quantum systems control is based on some ideas of the optimal control theory. These ideas are developed here as applied to these systems. The results obtained meet the deficiencies in the basis and algorithms of…
We present a new geometric unfolding of a prototype problem of optimal control theory, the Mayer problem. This approach is crucially based on the Stokes Theorem and yields to a necessary and sufficient condition that characterizes the…
For an optimal control problem, the concept of a strong local infimum is introduce, for which necessary conditions consisting of some family of "maximum principles" are formulated. If a function delivers a strong local minimum in this…
In this study, we consider an optimal control problem driven by a stochastic differential equation with state constraints. Here, the state constraints mean the constraints about the path of state. In order to show the maximum principe for…
We provide an improvment of the maximum principle of Pon-tryagin of the optimal control problems, for a system governed by an ordinary differential equation, in presence of final constraints, in the setting of the piece-wise differentiable…
We consider optimal control problems, where the control appears in the main part of the operator. We derive the Pontryagin maximum principle as a necessary optimality condition. The proof uses the concept of topological derivatives. In…
Motivated by the applications, a class of optimal control problems is investigated, where the goal is to influence the behavior of a given population through another controlled one interacting with the first. Diffusive terms accounting for…
Quantum optimal control is a set of methods for designing time-varying electromagnetic fields to perform operations in quantum technologies. This tutorial paper introduces the basic elements of this theory based on the Pontryagin maximum…
We discuss a mathematical framework for analysis of optimal control problems on infinite-dimensional manifolds. Such problems arise in study of optimization for partial differential equations with some symmetry. It is shown that some…
Since the second half of the 20th century, Pontryagin's Maximum Principle has been widely discussed and used as a method to solve optimal control problems in medicine, robotics, finance, engineering, astronomy. Here, we focus on the proof…
This paper is dedicated to the elementary proof of Pontryagin's maximum principle for problems with free right end point. The proof for the standard problem is taken from the monography of Ioffe and Tichomirov. We assume piecewise…
The Pontryagin's Maximum Principle allows, in most cases, the design of optimal controls of affine nonlinear control systems by considering the sign of a smooth function. There are cases, although, where this function vanishes on a whole…
This paper presents an optimal control problem to analyze the efficacy of counter-terrorism tactics. We present an algorithm that efficiently combines the Minimum Principle of Pontryagin, the shooting method and the cyclic descent of…
We study in optimal control the important relation between invariance of the problem under a family of transformations, and the existence of preserved quantities along the Pontryagin extremals. Several extensions of Noether theorem are…
Using the Pontryagin maximum principle, the generic structure of optimal policies is deduced for typical quantum control tasks involving coherent lasers, magnetic fields and reservoir engineering. In addition, the periodic optimization is…