Mixed-Integer Optimal Control: Computational Algorithms and Applications
Creators: name: Pei, Chaoying
Publisher: name: Purdue University Graduate School
Year: 2024
Subjects: classificationCode: 400107
subject: Satellite, space vehicle and missile design and testing

description: This thesis presents a comprehensive exploration of advanced optimization strategies for addressing mixed-integer optimal control problems (MIOCPs) in aerospace applications, emphasizing the enhancement of convergence robustness, computational efficiency, and accuracy. The research develops a broad spectrum of optimization methodologies, including multi-phase approaches, parallel computing, reinforcement learning (RL), and distributed algorithms, to tackle complex MIOCPs characterized by highly nonlinear dynamics, intricate constraints, and discrete control variables.Through discretization and reformulation, MIOCPs are transformed into general quadratically constrained quadratic programming (QCQP) problems, which are then equivalently converted into rank-one constrained semidefinite programs problems. To address these, iterative algorithms are developed specifically for solving such problems. Initially, two iterative search methods are introduced to achieve convergence: one is a hybrid alternating direction method of multipliers (ADMM) designed for large-scale QCQP problems, and the other is an iterative second-order cone programming (SOCP) algorithm developed to achieve global convergence. Moreover, to facilitate the convergence of these iterative algorithms and to enhance their solution quality, a multi-phase strategy is proposed. This strategy integrates with both the iterative ADMM and SOCP algorithms to optimize the solving of QCQP problems, improving both the convergence rate and the optimality of the solutions. To validate the effectiveness and improved computational performance of the proposed multi-phase iterative algorithms, the proposed algorithms were applied to several aerospace optimization problems, including six-degree-of-freedom (6-DoF) entry trajectory optimization, fuel-optimal powered descent, and multi-point precision landing challenges in a human-Mars mission. Theoretical analyses of convergence properties along with simulation results have been conducted, demonstrating the efficiency, robustness, and enhanced convergence rate of the optimization framework.However, the iteration based multi-phase algorithms primarily guarantee only local optima for QCQP problems. This research introduces a novel approach that integrates a distributed framework with stochastic search techniques to overcome this limitation. By leveraging multiple initial guesses for collaborative communication among computation nodes, this method not only accelerates convergence but also enhances the exploration of the solution space in QCQP problems. Additionally, this strategy extends to tackle general nonlinear programming (NLP) problems, effectively steering optimization toward more globally promising directions. Numerical simulations and theoretical proofs validate these improvements, marking significant advancements in solving complex optimization challenges.Following the use of multiple agents in QCQP problems, this research expand this advantage to address more general rank-constrained semidefinite programs (RCSPs). This research developed a method that decomposes matrices into smaller submatrices for parallel processing by multiple agents within a distributed framework. This approach significantly enhances computational efficiency and has been validated in applications such as image denoising, showcasing substantial improvements in both efficiency and effectiveness.Moreover, to address uncertainties in applications, a learning-based algorithm for QCQPs with dynamic parameters is developed. This method creates high-performing initial guesses to enhance iterative algorithms, specifically applied to the iterative rank minimization (IRM) algorithm. Empirical evaluations show that the RL-guided IRM algorithm outperforms the original, delivering faster convergence and improved optimality, effectively managing the challenges of dynamic parameters.In summary, this thesis introduces advanced optimization strategies that significantly enhance the resolution of MIOCPs and extends these methodologies to more general issues like NLP and RCSP. By integrating multi-phase approaches, parallel computing, distributed techniques, and learning methods, it improves computational efficiency, convergence, and solution quality. The effectiveness of these methods has been empirically validated and theoretically confirmed, representing substantial progress in the field of optimization.