Search results for "Optimal control"
showing 10 items of 209 documents
Optimal Starting Conditions for the Rendezvous Maneuver, Part 2: Mathematical Programming Approach
2008
In a companion paper (Part 1, J. Optim. Theory Appl. 137(3), [2008]), we determined the optimal starting conditions for the rendezvous maneuver using an optimal control approach. In this paper, we study the same problem with a mathematical programming approach.
Necessary Optimality Conditions in Multiobjective Dynamic Optimization
2004
We consider a nonsmooth multiobjective optimal control problem related to a general preference. Both differential inclusion and endpoint constraints are involved. Necessary conditions and Hamiltonian necessary conditions expressed in terms of the limiting Frechet subdifferential are developed. Examples of useful preferences are given.
On necessary optimality conditions for optimal control problems governed by elliptic systems
2005
The article considers an optimal control problem for the linear elliptic system div for the case where the coefficient matrix A plays the role of control and belongs to a nonconvex set and the cost functional is a quadratic form with respect to . By transforming the original problem to a more suitable one and by using ideas from the homogenization theory a necessary optimality condition is derived.
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 …
Shape optimization of elasto-plastic bodies under plane strains: Sensitivity analysis and numerical implementation
1992
Optimal shape design problems for an elastic body made from physically nonlinear material are presented. Sensitivity analysis is done by differentiating the discrete equations of equilibrium. Numerical examples are included.
Voltage Regulation and Power Losses Minimization in Automated Distribution Networks by an Evolutionary Multiobjective Approach
2004
In this paper, the problem of voltage regulation and power losses minimization for automated distribution systems is dealt with. The classical formulation of the problem of optimal control of shunt capacitor banks and Under Load Tap Changers located at HV/MV substations has been coupled with the optimal control of tie-switches and capacitor banks on the feeders of a large radially operated meshed distribution system with the aim of attaining minimum power losses and the flattening of the voltage profile. The considered formulation requires the optimization of two different objectives; therefore the use of adequate multiobjective heuristic optimization methods is needed. The heuristic strate…
Wavelet-Based Optimal Control of a Wind Turbine System: A Computational Approach
2011
This paper deals with a computational optimization approach to the problem of state-feedback control design for a wind turbine system. The first step of the study is to develop a reduced order model for the system by considering the most important physical phenomena of aerodynamics and structural dynamics. Moreover, the behavior of the system can be influenced by the coupled dynamics between the tower motions and the blade pitch and turbine speed which can cause instabilities in the control loops in the worst case. By using a suitable wavelet funcation, called Haar functions, a recursive computational procedure is established for finding the system dynamics approximately by solving only alg…
Geometric optimal control of the contrast problem in Magnetic Resonance Imaging
2012
Abstract The control of the dynamics of spin systems by magnetic fields has opened intriguing possibilities in quantum computing and in Nuclear Magnetic Resonance spectroscopy. In this framework, optimal control theory has been used to design control fields able to realize a given task while minimizing a prescribed cost such as the energy of the field or the duration of the process. However, some of the powerful tools of optimal control had not been used yet for NMR applications in medical imagery. Here, we show that the geometric control theory approach can be advantageously combined with NMR methods to crucially optimize the imaging contrast. This approach is applied to a benchmark proble…
Two-Sided Guaranteed Estimates of the Cost Functional for Optimal Control Problems with Elliptic State Equations
2014
In the paper, we discuss error estimation methods for optimal control problems with distributed control functions entering the right-hand side of the corresponding elliptic state equations. Our analysis is based on a posteriori error estimates of the functional type, which were derived in the last decade for many boundary value problems. They provide guaranteed two-sided bounds of approximation errors for any conforming approximation. If they are applied to approximate solutions of state equations, then we obtain new variational formulations of optimal control problems and guaranteed bounds of the cost functional. Moreover, for problems with linear state equations this procedure leads to gu…