Computation of exact gradients in distributed dynamic systems*
作者:
Yuri Evtushenko,
期刊:
Optimization Methods and Software
(Taylor Available online 1998)
卷期:
Volume 9,
issue 1-3
页码: 45-75
ISSN:1055-6788
年代: 1998
DOI:10.1080/10556789808805686
出版商: Gordon and Breach Science Publishers
关键词: Fast Automatic Differentiation;Optimal Control Problem;Differentiation of Elementary Functions;Rounding Error Estimation;Parabolic System;Hyperbolic System;Adjoint Equation;Sensitivity Analysis
数据来源: Taylor
摘要:
A new and unified methodology for computing first order derivatives of functions obtained in complex multistep processes is developed on the basis of general expressions for differentiating a composite function. From these results, we derive the formulas for fap automatic differentiation of elementary functions, for gradients arising in optimal control problems, nonlinear programming and gradients arising in discretizations of processes governed by partial differential equations. In the proposed approach we start with a chosqn discretization scheme for the state equation and derive the exact gradient expression. Thus a unique discretization scheme is automatically generated for the adjoint equation For optimal control problems, the proposed computational formulas correspond to the integration of the adjoint system of equations that appears in Pontryagin's maximum principle. This technique appears to be very efficient, universal, and applicable to a wide variety of distributed controlled dynamic systems and to sensitivity analysis
点击下载:
PDF (789KB)
返 回