The combinatorial integral approximation (CIA) decomposition suggests to solve mixed-integer optimal control problems (MIOCPs) by solving one continuous nonlinear control problem and one mixed-integer linear program (MILP). Unrealistic frequent switching can be avoided by adding a constraint on the total variation to the MILP. Within this work, we present a fast heuristic way to solve this CIA problem and investigate in which situations optimality of the provided solution is guaranteed. Our proof reveals a link from the CIA problem to scheduling theory. In the second part of this article, we show tight bounds on the integrality gap between a relaxed continuous control trajectory and an integer feasible one. Finally, we present numerical experiments to highlight the advantages of the proposed algorithm in terms of run time and solution quality.

## Citation

Sager, Sebastian and Zeile, Clemens, "On Mixed-Integer Optimal Control with Constrained Total Variation of the Integer Control", MathOpt Group, Faculty of Mathematics, Otto-von-Guericke-University Magdeburg, Germany.

## Article

View On Mixed-Integer Optimal Control with Constrained Total Variation of the Integer Control