Multiphase Iterative Algorithm for Mixed-Integer Optimal Control

Mixed-integer optimal control problems (MIOCPs) frequently arise in the domain of optimal control problems (OCPs) when decisions including integer variables are involved. However, existing state-of-the-art approaches for solving MIOCPs are often plagued by drawbacks such as high computational costs, low precision, and compromised optimality. In this study, we propose a novel multiphase scheme coupled with an iterative second-order cone programming (SOCP) algorithm to efficiently and effectively address these challenges in MIOCPs. In the first phase, we relax the discrete decision constraints and account for the terminal state constraints and certain path constraints by introducing them as penalty terms in the objective function. After formulating the problem as a quadratically constrained quadratic programming (QCQP) problem, we propose the iterative SOCP algorithm to solve general QCQPs. In the second phase, we reintroduce the discrete decision constraints to generate the final solution. We substantiate the efficacy of our proposed multiphase scheme and iterative SOCP algorithm through successful application to two practical MIOCPs in planetary exploration missions.