24 research outputs found
Asymptotic Preserving time-discretization of optimal control problems for the Goldstein-Taylor model
We consider the development of implicit-explicit time integration schemes for
optimal control problems governed by the Goldstein-Taylor model. In the
diffusive scaling this model is a hyperbolic approximation to the heat
equation. We investigate the relation of time integration schemes and the
formal Chapman-Enskog type limiting procedure. For the class of stiffly
accurate implicit-explicit Runge-Kutta methods (IMEX) the discrete optimality
system also provides a stable numerical method for optimal control problems
governed by the heat equation. Numerical examples illustrate the expected
behavior
Interferometric Observatories in Earth Orbit
Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/76217/1/AIAA-1728-623.pd
Spline parameterization based nonlinear trajectory optimization along 4D waypoints
Flight trajectory optimization has become an important factor not only to reduce the operational costs (e.g.,, fuel and time related costs) of the airliners but also to reduce the environmental impact (e.g.,, emissions, contrails and noise etc.) caused by the airliners. So far, these factors have been dealt with in the context of 2D and 3D trajectory optimization, which are no longer efficient. Presently, the 4D trajectory optimization is required in order to cope with the current air traffic management (ATM). This study deals with a cubic spline approximation method for solving 4D trajectory optimization problem (TOP). The state vector, its time derivative and control vector are parameterized using cubic spline interpolation (CSI). Consequently, the objective function and constraints are expressed as functions of the value of state and control at the temporal nodes, this representation transforms the TOP into nonlinear programming problem (NLP). The proposed method is successfully applied to the generation of a minimum length optimal trajectories along 4D waypoints, where the method generated smooth 4D optimal trajectories with very accurate results.info:eu-repo/semantics/publishedVersio
Consistent Approximations to Impulsive Optimal Control Problems
We analyse the theory of consistent approximations given by Polak and we use
it in an impulsive optimal control problem. We reparametrize the original
system and build consistent approximations for this new reparametrized problem.
So, we prove that if a sequence of solution of the consistent approximations is
converging, it will converge to a solution of the reparametrized problem, and,
finally, we show that from a solution of the reparametrized problem we can find
a solution of the original one
Age-structured optimal control in population economics
This paper brings both intertemporal and age-dependent features to a theory of population policy at the macro-level. A Lotkatype renewal model of population dynamics is combined with a Solow/Ramsey economy. By using a new maximum principle for distributed parameter control we derive meaningful qualitative results for the optimal migration path and the optimal saving rate.
Implicit-Explicit Runge-Kutta schemes for numerical discretization of optimal control problems
Implicit-explicit (IMEX) Runge-Kutta methods play a major rule in the
numerical treatment of differential systems governed by stiff and non-stiff
terms. This paper discusses order conditions and symplecticity properties of a
class of IMEX Runge-Kutta methods in the context of optimal control problems.
The analysis of the schemes is based on the continuous optimality system. Using
suitable transformations of the adjoint equation, order conditions up to order
three are proven as well as the relation between adjoint schemes obtained
through different transformations is investigated. Conditions for the IMEX
Runge-Kutta methods to be symplectic are also derived. A numerical example
illustrating the theoretical properties is presented