Numerical Analysis of Optimality-System POD for Constrained Optimal Control
نویسندگان
چکیده
In this work linear-quadratic optimal control problems for parabolic equations with control and state constraints are considered. Utilizing a Lavrentiev regularization we obtain a linear-quadratic optimal control problem with mixed controlstate constraints. For the numerical solution a Galerkin discretization is applied utilizing proper orthogonal decomposition (POD). Based on a perturbation method it is determined by a-posteriori error analysis how far the suboptimal control, computed on the basis of the POD method, is from the (unknown) exact one. POD basis updates are computed by optimality-system POD. Numerical examples illustrate the theoretical results for control and state constrained optimal control problems.
منابع مشابه
The Exact Solution of Min-Time Optimal Control Problem in Constrained LTI Systems: A State Transition Matrix Approach
In this paper, the min-time optimal control problem is mainly investigated in the linear time invariant (LTI) continuous-time control system with a constrained input. A high order dynamical LTI system is firstly considered for this purpose. Then the Pontryagin principle and some necessary optimality conditions have been simultaneously used to solve the optimal control problem. These optimality ...
متن کاملOptimality system POD and a-posteriori error analysis for linear-quadratic problems
In this paper an abstract linear-quadratic optimal control problem governed by an evolution equation is considered. To solve this problem numerically a reduced-order approach based on proper orthogonal decomposition (POD) is applied. The error between the POD suboptimal control and the optimal control of the original problem is controlled by an a-posteriori error analysis. However, if the POD b...
متن کاملOptimality conditions and POD a-posteriori error estimates for a semilinear parabolic optimal control
In the present paper the authors consider an optimal control problem for a parametrized nonlinear parabolic differential equation, which is motivated by lithium-ion battery models. A standard finite element (FE) discretization leads to a large-scale nonlinear optimization problem so that its numerical solution is very costly. Therefore, a reduced-order modelling based on proper orthogonal decom...
متن کاملPOD a-posteriori error analysis for optimal control problems with mixed control-state constraints
In this work linear-quadratic optimal control problems for parabolic equations with mixed control-state constraints are considered. These problems arise when a Lavrentiev regularization is utilized for state constrained linearquadratic optimal control problems. For the numerical solution a Galerkin discretization is applied utilizing proper orthogonal decomposition (POD). Based on a perturbatio...
متن کاملMultigrid Solution of a Lavrentiev-Regularized State-Constrained Parabolic Control Problem
A mesh-independent, robust, and accurate multigrid scheme to solve a linear state-constrained parabolic optimal control problem is presented. We first consider a Lavrentiev regularization of the state-constrained optimization problem. Then, a multigrid scheme is designed for the numerical solution of the regularized optimality system. Central to this scheme is the construction of an iterative p...
متن کامل