Adjoint Sensitivity Analysis for Differential-Algebraic Equations: The Adjoint DAE System and Its Numerical Solution
نویسندگان
چکیده
An adjoint sensitivity method is presented for parameter-dependent differentialalgebraic equation systems (DAEs). The adjoint system is derived, along with conditions for its consistent initialization, for DAEs of index up to two (Hessenberg). For stable linear DAEs, stability of the adjoint system (for semi-explicit DAEs) or of an augmented adjoint system (for fully implicit DAEs) is shown. In addition, it is shown for these systems that numerical stability is maintained for the adjoint system or for the augmented adjoint system.
منابع مشابه
On the adjoint formulation of design sensitivity analysis of multibody dynamics cs
Numerical methods for design sensitivity analysis of multibody dynamics are presented. An analysis of the index-3 adjoint differential-algebraic equations is conducted and stability of the integration of the adjoint differential-algebraic equations in the backward direction is proven. Stabilized index-1 formulations are presented and convergence of backward differentiation formulas is shown for...
متن کاملSensitivity Analysis for Differential Algebraic Equations
In this paper we propose a new method based on adjoint systems for parametric sensitivity analysis of DAE’s. This method is employed in a series of experiments, and the results are compared with the estimation of sensitivity by a finite differences method, widely used because of the simplicity of its implementation. In addition, we propose a method extension based on the use of estimation funct...
متن کاملMinimax state estimation for linear stationary differential-algebraic equations ?
This paper presents a generalization of the minimax state estimation approach for singular linear Differential-Algebraic Equations (DAE) with uncertain but bounded input and observation’s noise. We apply generalized Kalman Duality principle to DAE in order to represent the minimax estimate as a solution of a dual control problem for adjoint DAE. The latter is then solved converting the adjoint ...
متن کاملThe discrete adjoint method for parameter identification in multibody system dynamics
The adjoint method is an elegant approach for the computation of the gradient of a cost function to identify a set of parameters. An additional set of differential equations has to be solved to compute the adjoint variables, which are further used for the gradient computation. However, the accuracy of the numerical solution of the adjoint differential equation has a great impact on the gradient...
متن کاملEfficient Computation of Sensitivities for Ordinary Differential Equation Boundary Value Problems
For models described by ordinary differential equation boundary value problems (ODE BVPs), we derive adjoint equations for sensitivity analysis, giving explicit forms for the boundary conditions of the adjoint boundary value problem. The solutions of the adjoint equations are used to efficiently compute gradients of both integral-form and pointwise constraints. Existence and stability results a...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
- SIAM J. Scientific Computing
دوره 24 شماره
صفحات -
تاریخ انتشار 2003