Enhanced Numerical Methods for Constrained Nonlinear Model Predictive Control

该研究项目将为计算效率高的模型预测控制创造新的、严格接地的方法。模型预测控制是基于计算系统控制输入响应传感器的测量，通过使用实时数值优化。它已被证明在许多重要的应用中是无价的，包括在航空航天和汽车工业中。在存在建模误差和不可预测干扰的情况下，需要实时优化大型约束非线性动力学方程系统的响应，这是计算方面的挑战。在复杂的工程系统中应用模型预测控制存在很大的困难，特别是在机载计算能力有限的情况下。应对这些挑战的最有效方法是利用特定于问题的结构，而不是“一刀切”的策略。这个项目将产生各种计算效率高的解决方法，这些方法可以适当地针对特定的问题特征进行定制。所开发的理论和方法将应用于汽车发动机和飞机推进系统的控制问题，以解决严格的性能要求、日益增长的系统复杂性和众多限制。对航天器轨道控制的影响也将被追求，以实现扩展航天器自主性和弹性的模型预测控制解决方案。项目人员将以汽车和飞机发动机以及航天器任务为基础，扩大STEM向当地高中学生的推广工作，这些学生来自代表性不足的群体。本研究项目的目的是发展先进的方法，以减少求解非线性模型预测控制问题的计算成本，同时保持可接受的精度。本文将探讨这些方法的理论论证及其有效的算法实现。在适当的最优性必要条件下，将发展求解变分不等式/包含的非精确顺序二次规划型方法。其中一些方法将只在起点或某些选定的迭代中计算导数，而其他方法将使用不精确的牛顿迭代。成本函数、约束、闭环稳定性和性能之间的相互作用将在这类实现的背景下进行研究。此外，在分析非线性模型预测控制问题的Lipschitz稳定性和灵敏度的基础上，将开发新的计算和约束处理策略。离线和在线约束转换的理论合理方法也将作为基于灵敏度分析获得计算简化的另一种一般途径而发展。提供误差分析的同伦程序将用于实现模型预测控制解的高效计算。

This research project will create new, rigorously grounded, methods for computationally efficient model predictive control. Model predictive control is based on computing system control inputs in response to sensor measurements through the use of real-time numerical optimization. It has proved invaluable in many important applications, including in the aerospace and automotive industries. Computational challenges stem from the need to optimize in real-time the response of large systems of constrained nonlinear dynamic equations in the presence of modeling errors and unpredictable disturbances. There are major difficulties in applying model predictive control to complex engineering systems, particularly when on-board computing power is limited. The most effective ways to address these challenges exploit problem-specific structure, in contrast to a "one size fits all" strategy. This project will produce classes of computationally efficient solution methods that can be appropriately tailored to specific problem characteristics. The developed theory and methods will be applied to control problems for automotive engines and aircraft propulsion systems, to address stringent performance requirements, growing system complexity, and numerous constraints. The implications for spacecraft orbital control will also be pursued to enable model predictive control solutions which expand spacecraft autonomy and resiliency. Project personnel will build on illustrations from automobile and aircraft engines and spacecraft missions to amplify STEM outreach efforts to local high school students from underrepresented groups.The aim of this research project is to develop advanced methods for reducing the computational cost of solving nonlinear model predictive control problems, while maintaining acceptable accuracy. Both a theoretical justification of these methods and their efficient algorithmic implementation will be pursued. Inexact sequential quadratic programming-type methods for solving variational inequalities/inclusions associated with appropriate necessary conditions for optimality will be developed. Some of these methods will compute derivatives just at the starting point or at some selected iterations, while others will utilize inexact Newton iterations. The interplay between cost functions, constraints, closed-loop stability and performance will be studied in the context of these kind of implementations. In addition, novel computational and constraint handling strategies will be developed based on the analysis of Lipschitz stability and sensitivity of nonlinear model predictive control problems considered. Theoretically justified approaches to both offline and online constraint transformations will also be developed as another general pathway to obtain computational simplifications based on sensitivity analysis. Homotopy procedures supplied with error analysis will be applied to achieve efficient computation of model predictive control solutions.