An Efficient Mixed‐Integer Formulation and an Iterative Method for Optimal Control of Switched Systems Under Dwell Time Constraints

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This paper presents an efficient mixed‐integer nonlinear programming (MINLP) formulation for systems with discrete control inputs under minimum dwell time (MDT) constraints. By viewing such systems as switched systems, the problem is decomposed into a sequence optimization (SO) and a switching time optimization (STO)—the former providing the sequence of the switched system, and the latter calculating the optimal switching times. By limiting the feasible set of SO to subsequences of a master sequence, this formulation requires a small number of binary variables, independent of the number of time discretization nodes. This enables the proposed formulation to provide solutions efficiently, even for a large number of time discretization nodes. To provide even faster solutions, an iterative algorithm is introduced to heuristically solve STO and SO. The proposed approaches are then showcased on four different switched systems, and the results demonstrate the efficiency of the MINLP formulation and the iterative algorithm.