Optimal Control with Pointwise Constraints on the Gradient of the State
نویسندگان
چکیده
We analyze a finite element approximation of an elliptic optimal control problem with pointwise bounds on the gradient of the state variable. We derive convergence rates if the control space is discretized implicitly by the state equation. In contrast to prior work we obtain these results directly from classical results for the W 1,∞-error of the finite element projection, without using adjoint information. If the control space is discretized directly, we first prove a regularity result for the optimal control to control the approximation error, based on which we then obtain analogous convergence rates.
منابع مشابه
Preconditioned Conjugate Gradient Method for Optimal Control Problems with Control and State Constraints
Optimality systems and their linearizations arising in optimal control of partial differential equations with pointwise control and (regularized) state constraints are considered. The preconditioned conjugate gradient (pcg) method in a non-standard inner product is employed for their efficient solution. Preconditioned condition numbers are estimated for problems with pointwise control constrain...
متن کاملA priori error estimates for optimal control problems with pointwise constraints on the gradient of the state
We analyze a finite element approximation of an elliptic optimal control problem with pointwise bounds on the gradient of the state variable. We derive convergence rates if the control space is discretized implicitly by the state equation. In contrast to prior work we obtain these results directly from classical results for the W 1,∞-error of the finite element projection, without using adjoint...
متن کاملOptimal Control of Elliptic Equations with Pointwise Constraints on the Gradient of the State in Nonsmooth Polygonal Domains
This article is concerned with optimal control problems subject to a second order elliptic PDE and additional pointwise constraints on the gradient of the state. In particular, existence of solutions on nonsmooth polygonal or polyhedral domains is analyzed. In this situation the solution operator for the partial differential equation does not provide enough regularity to state the pointwise con...
متن کاملElliptic control problems with gradient constraints - variational discrete versus piecewise constant controls
We consider an elliptic optimal control problem with pointwise bounds on the gradient of the state. To guarantee the required regularity of the state we include the Lr-norm in our cost functional with r > d, (d = 2, 3). We investigate variational discretization of the control problem [6] as well as piecewise constant approximations of the control. In both cases we use standard piecewise linear ...
متن کاملClassical and Relaxed Optimization Methods for Optimal Control Problems
We consider an optimal control problem for systems governed by nonlinear ordinary differential equations, with control and state constraints, including pointwise state constraints. The problem is formulated in the classical and in the relaxed form. Various necessary/sufficient conditions for optimality are first given for both problems. For the numerical solution of these problems, we then prop...
متن کامل