Search results for " optimal control"

Functional A Posteriori Error Estimates for Time-Periodic Parabolic Optimal Control Problems

2015

This article is devoted to the a posteriori error analysis of multiharmonic finite element approximations to distributed optimal control problems with time-periodic state equations of parabolic type. We derive a posteriori estimates of the functional type, which are easily computable and provide guaranteed upper bounds for the state and co-state errors as well as for the cost functional. These theoretical results are confirmed by several numerical tests that show high efficiency of the a posteriori error bounds. peerReviewed

Error Estimates for a Class of Elliptic Optimal Control Problems

2016

In this article, functional type a posteriori error estimates are presented for a certain class of optimal control problems with elliptic partial differential equation constraints. It is assumed that in the cost functional the state is measured in terms of the energy norm generated by the state equation. The functional a posteriori error estimates developed by Repin in the late 1990s are applied to estimate the cost function value from both sides without requiring the exact solution of the state equation. Moreover, a lower bound for the minimal cost functional value is derived. A meaningful error quantity coinciding with the gap between the cost functional values of an arbitrary admissible …

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.

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…

Guaranteed lower bounds for cost functionals of time-periodic parabolic optimization problems

2019

In this paper, a new technique is shown for deriving computable, guaranteed lower bounds of functional type (minorants) for two different cost functionals subject to a parabolic time-periodic boundary value problem. Together with previous results on upper bounds (majorants) for one of the cost functionals, both minorants and majorants lead to two-sided estimates of functional type for the optimal control problem. Both upper and lower bounds are derived for the second new cost functional subject to the same parabolic PDE-constraints, but where the target is a desired gradient. The time-periodic optimal control problems are discretized by the multiharmonic finite element method leading to lar…

Optimal Impulse Control Problems and Linear Programming

2009

Optimal impulse control problems are, in general, difficult to solve. A current research goal is to isolate those problems that lead to tractable solutions. In this paper, we identify a special class of optimal impulse control problems which are easy to solve. Easy to solve means that solution algorithms are polynomial in time and therefore suitable to the on-line implementation in real-time problems. We do this by using a paradigm borrowed from the Operations Research field. As main result, we present a solution algorithm that converges to the exact solution in polynomial time. Our approach consists in approximating the optimal impulse control problem via a binary linear programming proble…

Sub-Optimal Control Law for Active Magnetic Bearings Suspension

2012

This paper deals with the comparison of three types of sub-optimal control law for the stable levitation of a turbojet shaft, sustained by two radial active magnetic bearings (AMBs). Shaft is considered rigid for the procedure simplification. The utilized approach leads to development of different sub-optimal control laws to use in speed-varying simulations in the angular speed of the shaft. The first control matrix is obtained by explicit relationships of the parameters of the control law vs. speed, obtained using a curve-fitting procedure neglecting the speed-varying elements out of the main diagonal of each single block constituting the entire control matrix. The second control law is ob…

Application to an italian distribution system of a multiobjective optimal Volt/VAR control strategy: improvements and management problems

2007

In this paper, the experiences and results deriving from the application of a multiobjective optimal management strategy to a distribution network supplying an area in province of Palermo, Italy, are presented. The adopted strategy allows, through the interventions on the Under Load Tap Changers (ULTC) of the primary substations and on tie-switches, to reduce power losses and improve the voltage profiles. To solve the optimization problem, an evolutionary approach has been adopted; it employs fuzzy logic for an adequate and simultaneous fulfilment of the different objectives. The application section presents a deep technical and economical analysis of the results attained, applying the opti…

Robust Mean Field Games

2015

Recently there has been renewed interest in large-scale games in several research disciplines, with diverse application domains as in the smart grid, cloud computing, financial markets, biochemical reaction networks, transportation science, and molecular biology. Prior works have provided rich mathematical foundations and equilibrium concepts but relatively little in terms of robustness in the presence of uncertainties. In this paper, we study mean field games with uncertainty in both states and payoffs. We consider a population of players with individual states driven by a standard Brownian motion and a disturbance term. The contribution is threefold: First, we establish a mean field syste…

Sustainability and tourist flow networks: a mean field bi-level optimization approach

The widespread acknowledgement of tourism as a strategic pillar for economic growth and development has boosted competitiveness among tourist destinations. This concept has been greatly emphasized during the current COVID-19 pandemic crisis. Nevertheless, the massive presence of tourists imposes the challenge of adopting sustainable tourism practices to balance economic prosperity opportunities with potential threats to the environment and local communities. There are many definitions for sustainability, but the most effective one is ``the capacity to endure'' [Emel et al, 1997]: from an economic perspective this leads to find an equilibrium between short and long-term objectives so that to…