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

TL;DR

This paper introduces a novel, efficient mixed-integer nonlinear programming formulation and an iterative heuristic algorithm for optimal control of switched systems with dwell time constraints, enabling faster solutions even with many discretization points.

Contribution

It proposes a new decomposition-based MINLP formulation with limited binary variables and an iterative method for faster solution of switched system control problems.

Findings

The formulation reduces binary variables, improving efficiency.

The iterative algorithm accelerates solution times.

Results show effectiveness on multiple switched systems.

Abstract

This paper presents an efficient Mixed-Integer Nonlinear Programming (MINLP) formulation for systems with discrete control inputs under dwell time constraints. By viewing such systems as a switched system, 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 large numbers 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 results demonstrate the efficiency of the MINLP formulation and the iterative algorithm.