The dual weighted residuals approach to optimal control of ordinary differential equations

نویسندگان

  • Karin Kraft
  • Stig Larsson
چکیده

The aim of this work is to make a first investigation of how adaptive finite element methods can be used to solve optimal control problems. Our approach is based on an adaptive algorithm with error control based on a posteriori error estimates. The work was initiated from and motivated by a need to solve optimal control problems in vehicle dynamics. The methodology of dual weighted residuals was developed in [1] in the context of finite element methods for partial differential equations. In this paper, we adapt the methodology to optimal control problems of the form: Find states x and controls u

برای دانلود رایگان متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Numerical inversion of Laplace transform via wavelet in ordinary differential equations

This paper presents a rational Haar wavelet operational method for solving the inverse Laplace transform problem and improves inherent errors from irrational Haar wavelet. The approach is thus straightforward, rather simple and suitable for computer programming. We define that $P$ is the operational matrix for integration of the orthogonal Haar wavelet. Simultaneously, simplify the formulaes of...

متن کامل

T-lymphocyteCell InjectionCancer Immunotherapy‎: an Optimal Control Approach

We consider amathematical model in the form of a system of ordinary differential equations (ODE) foroptimally administrating cancer treatments. The ODE systemdynamics characterized by locating equilibrium points and stability propertiesare determined by linearization and usingappropriate Lyapunovfunctions. By applying optimal control theory, we seek to minimize the cost function associated with...

متن کامل

An application of differential transform method for solving nonlinear optimal control problems

In this paper, we present a capable algorithm for solving a class of nonlinear optimal control problems (OCP's). The approach rest mainly on the differential transform method (DTM) which is one of the approximate methods. The DTM is a powerful and efficient technique for finding solutions of nonlinear equations without the need of a linearization process. Utilizing this approach, the optimal co...

متن کامل

APPLICATION NEURAL NETWORK TO SOLVE ORDINARY DIFFERENTIAL EQUATIONS

In this paper, we introduce a hybrid approach based on neural network and optimization teqnique to solve ordinary differential equation. In proposed model we use heyperbolic secont transformation function in hiden layer of neural network part and bfgs teqnique in optimization part. In comparison with existing similar neural networks proposed model provides solutions with high accuracy. Numerica...

متن کامل

Adaptive Finite Element Methods for Partial Differential Equations

The numerical simulation of complex physical processes requires the use of economical discrete models. This lecture presents a general paradigm of deriving a posteriori error estimates for the Galerkin finite element approximation of nonlinear problems. Employing duality techniques as used in optimal control theory the error in the target quantities is estimated in terms of weighted ‘primal’ an...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

عنوان ژورنال:

دوره   شماره 

صفحات  -

تاریخ انتشار 2010