Search results for "Optimal control"
showing 10 items of 209 documents
Indirect Methods for Optimal Control Problems
2003
This chapter is dedicated to the numerical approximation of Optimal Control Problems. The algorithms are based on the necessary conditions for optimality which allow us to use a descent method for the minimization of the cost functional.
Introduction to the Pontryagin Maximum Principle for Quantum Optimal Control
2021
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 technologies by means of highly efficient control of quantum dynamics. This tutorial aims at providing an introduction to key concepts of optimal control theory which is accessible to physicists and engineers working in quantum control or in related fields. The different mathematical results are introduced intuitively, before being rigorously stated. This tutorial describes modern aspects of optimal control theory, with a particular focus on the Pontryagin …
External constraints on optimal control strategies in molecular orientation and photofragmentation: Role of zero-area fields
2013
We propose a new formulation of optimal and local control algorithms which enforces the constraint of time-integrated zero-area on the control field. The fulfillment of this requirement, crucial in many physical applications, is mathematically implemented by the introduction of a Lagrange multiplier aiming at penalizing the pulse area. This method allows to design a control field with an area as small as possible, while bringing the dynamical system close to the target state. We test the efficiency of this approach on two control purposes in molecular dynamics, namely, orientation and photodissociation.
Time optimization and state-dependent constraints in the quantum optimal control of molecular orientation
2014
We apply two recent generalizations of monotonically convergent optimization algorithms to the control of molecular orientation by laser fields. We show how to minimize the control duration by a step-wise optimization and maximize the field-free molecular orientation using state-dependent constraints. We discuss the physical relevance of the different results.
Optimal Impulse Control When Control Actions Have Random Consequences
1997
We consider a generalised impulse control model for controlling a process governed by a stochastic differential equation. The controller can only choose a parameter of the probability distribution of the consequence of his control action which is therefore random. We state optimality results relating the value function to quasi-variational inequalities and a formal optimal stopping problem. We also remark that the value function is a viscosity solution of the quasi-variational inequalities which could lead to developments and convergence proofs of numerical schemes. Further, we give some explicit examples and an application in financial mathematics, the optimal control of the exchange rate…
Sub-Finsler Geodesics on the Cartan Group
2018
This paper is a continuation of the work by the same authors on the Cartan group equipped with the sub-Finsler $\ell_\infty$ norm. We start by giving a detailed presentation of the structure of bang-bang extremal trajectories. Then we prove upper bounds on the number of switchings on bang-bang minimizers. We prove that any normal extremal is either bang-bang, or singular, or mixed. Consequently, we study mixed extremals. In particular, we prove that every two points can be connected by a piecewise smooth minimizer, and we give a uniform bound on the number of such pieces.
Mixed integer optimal compensation: Decompositions and mean-field approximations
2012
Mixed integer optimal compensation deals with optimizing integer- and real-valued control variables to compensate disturbances in dynamic systems. The mixed integer nature of controls might be a cause of intractability for instances of larger dimensions. To tackle this issue, we propose a decomposition method which turns the original n-dimensional problem into n independent scalar problems of lot sizing form. Each scalar problem is then reformulated as a shortest path one and solved through linear programming over a receding horizon. This last reformulation step mirrors a standard procedure in mixed integer programming. We apply the decomposition method to a mean-field coupled multi-agent s…
About the role of hamiltonian singularities in controlled systems : applications in quantum mechanics and nonlinear optics
2012
This thesis has two goals: the first one is to improve the control techniques in quantum mechanics, and more specifically in NMR, by using the tools of geometric optimal control. The second one is the study of the influence of Hamiltonian singularities in controlled systems. The chapter about optimal control study three classical problems of NMR : the inversion problem, the influence of the radiation damping term, and the steady state technique. Then, we apply the geometric optimal control to the problem of the population transfert in a three levels quantum system to recover the STIRAP scheme.The two next chapters study Hamiltonian singularities. We show that they allow to control the polar…
An adaptive prudent-daring evolutionary algorithm for noise handling in on-line PMSM drive design
2007
This paper studies the problem of the optimal control design of permanent magnet synchronous motor (PMSM) drives taking into account the noise due to sensors and measurement devices. The problem is analyzed by means of an experimental approach which considers noisy data returned by the real plant (on-line). In other words, each fitness evaluation does not come from a computer but from a real laboratory experiment. In order to perform the optimization notwithstanding presence of the noise, this paper proposes an Adaptive Prudent- Daring Evolutionary Algorithm (APDEA). The APDEA is an evolutionary algorithm with a dynamic parameter setting. Furthermore, the APDEA employs a dynamic penalty ter…
Numerical methods for nonlinear inverse problems
1996
AbstractInverse problems of distributed parameter systems with applications to optimal control and identification are considered. Numerical methods and their numerical analysis for solving this kind of inverse problems are presented, main emphasis being on the estimates of the rate of convergence for various schemes. Finally, based on the given error estimates, a two-grid method and related algorithms are introduced, which can be used to solve nonlinear inverse problems effectively.