Error estimates for the approximation of multibang control problems
Provides theoretical guarantees for solving a class of optimal control problems with discrete-valued controls, but the contribution is incremental.
The paper derives error estimates for the Moreau-Yosida approximation and discretization of multibang control problems, supported by numerical results.
This work is concerned with optimal control problems where the objective functional consists of a tracking-type functional and an additional "multibang" regularization functional that promotes optimal control taking values from a given discrete set pointwise almost everywhere. Under a regularity condition on the set where these discrete values are attained, error estimates for the Moreau--Yosida approximation (which allows its solution by a semismooth Newton method) and the discretization of the problem are derived. Numerical results support the theoretical findings.