Formal adjoints of linear DAE operators and their role in optimal control
نویسندگان
چکیده
For regular strangeness-free linear differential-algebraic equations (DAEs) the definition of an adjoint DAE is straightforward. This definition can be formally extended to general linear DAEs. In this paper, we analyze the properties of the formal adjoints and their implications in solving linear-quadratic optimal control problems with DAE constraints.
منابع مشابه
Ela Formal Adjoints of Linear Dae Operators and Their Role in Optimal Control∗
where (omitting obvious arguments in the functions) E∈C(I,R), A∈C(I,R), and f ∈ C(I,R). In order to introduce the concept of an adjoint (linear) DAE associated with (1.1), we must formulate (1.1) as an operator equation in appropriate Banach spaces as part of appropriate dual systems; see, e.g., [6]. To obtain a suitable Banach space formulation, we replace (1.1) by a so-called strangeness-free...
متن کاملNeumann-Neumann Domain Decomposition Preconditioners for Linear-Quadratic Elliptic Optimal Control Problems
We present a class of domain decomposition (DD) preconditioners for the solution of elliptic linear-quadratic optimal control problems. Our DD preconditioners are extensions of Neumann–Neumann DD preconditioners, which have been successfully applied to the solution of single PDEs. The DD preconditioners are based on a decomposition of the optimality conditions for the elliptic linear-quadratic ...
متن کاملAn Introduction to Adjoints and Output Error Estimation in Computational Fluid Dynamics
In recent years, the use of adjoint vectors in Computational Fluid Dynamics (CFD) has seen a dramatic rise. Their utility in numerous applications, including design optimization, data assimilation, and mesh adaptation has sparked the interest of both researchers and practitioners alike. In many of these fields, the concept of an adjoint is explained differently, with various notations and motiv...
متن کاملThe critical period of weed control in corn in Birjand region, Iran
The critical period for weed control (CPWC) is the period in the crop growth cycle during which weeds must be controlled to prevent unacceptable yield losses. Field studies were conducted in 2005 and 2006 in the University of Birjand at the south east of Iran to determine CPWC of corn using a randomized complete block design with 14 treatments and three replications. The treatments consisted of...
متن کاملLinear Algebra and the Basic Mathematical Tools for Finite-Dimensional Entanglement Theory
2 Linear Operators 6 2.1 Outer Products, Adjoints, and Eigenvalues . . . . . . . . . . . . . . . . . . . . . . . . 6 2.2 Important Types of Operators . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 2.2.1 Projections . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 2.2.2 Normal Operators . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ...
متن کامل