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We revisit a class of integer optimal control problems for which atrust-region method has been proposed and analyzed in arXiv:2106.13453v3[math.OC]. While the algorithm proposed in arXiv:2106.13453v3 [math.OC]successfully solves the class of optimization problems under consideration, itsconvergence analysis requires restrictive regularity assumptions. There aremany examples of integer optimal control problems involving partialdifferential equations where these regularity assumptions are not satisfied. Inthis article we provide a way to bypass the restrictive regularity assumptionsby introducing an additional partial regularization of the control inputs bymeans of mollification and proving a $\Gamma$-convergence-type result when thesupport parameter of the mollification is driven to zero. We highlight theapplicability of this theory in the case of fluid flows through deformableporous media equations that arise in biomechanics. We show that the regularityassumptions are violated in the case of poro-visco-elastic systems, and thusone needs to use the regularization of the control input introduced in thisarticle. Associated numerical results show that while the homotopy can help tofind better objective values and points of lower instationarity, the practicalperformance of the algorithm without the input regularization may be on parwith the homotopy.

Input Regularization for Integer Optimal Control in BV with Applications to Control of Poroelastic and Poroviscoelastic Systems