Optimal sparse boundary control for a semilinear parabolic equation with mixed control-state constraints

Abstract: A problem of sparse optimal boundary control for a semilinear parabolic partial di?erential equation is considered, where pointwise bounds on the control and mixed pointwise control-state constraints are given. A standard quadratic objective functional is to be minimized that includes a Tikhonov regularization term and the L1-norm of the control accounting for the sparsity. Applying a recent linearization theorem, we derive ?rst-order necessary optimality conditions in terms of a variational inequality under linearized mixed control state constraints. Based on this preliminary result, a Lagrange multiplier rule with bounded and measurable multipliers is derived and sparsity results on the optimal control are demonstrated.

 Autoría: Casas E., Tröltzsch F.,

 Fuente: Control and Cybernetics, 2019, 48(1), 89-124

Editorial: Systems Research Institute of the Polish Academy of Sciences

 Año de publicación: 2019

Nº de páginas: 36

Tipo de publicación: Artículo de Revista

ISSN: 0324-8569