Optimization-based control for constrained systems with fast dynamics

本研究提案的主要目标是推进基于优化的控制的知识和应用，用于具有快速动态的约束系统，例如在汽车，机器人和航空航天领域中普遍存在的系统。 虽然存在许多快速的计算方案和优化算法的无约束系统，经常遇到的困难时，将约束直接到问题的制定。 我的研究旨在开发控制算法，允许在具有快速动态的系统上一致和实际地实施约束优化方案。 这包括将广义状态、输出和控制约束纳入快速计算方案，以及使用和验证应用近似解和次优控制的技术，以允许实时计算限制。基于优化的模型预测控制（MPC）方法将被用作控制算法开发的起点。 将MPC应用于具有线性约束的线性系统，使用二次成本函数导致二次规划（QP）子问题。 我打算调查的应用程序的非可行的有效集方法的QP问题，以制定一个新的解决方案，以更快的计算MPC问题。 可能发生的沉重的计算负担也导致需要进一步研究近似解和实时次优控制。 在这一领域的约束优化和控制的研究将推进该领域的现实可能性，相应的技术可以转移到加拿大工业的积极回报。 此外，这一研究领域对行业的重要性使其成为HQP培训的重要基础领域。

The primary objective of this research proposal is to advance the knowledge and application of optimization-based control for constrained systems with fast dynamics, such as those prevalent in the automotive, robotics and aerospace fields.  Although many fast computational schemes and optimization algorithms exist for the unconstrained system, difficulties are often encountered when incorporating constraints directly into the problem formulation.  My research aims to develop control algorithms that allow for consistent and practical implementation of constrained optimization schemes on systems with fast dynamics.  This involves both the incorporation of generalized state, output and control constraints to fast computational schemes as well as the use and validation of techniques which apply approximate solutions and suboptimal control in order to allow for real-time computational limitations.Optimization-based model predictive control (MPC) methodology will be used as a starting point for the development of control algorithms.  Applying MPC to a linear system with linear constraints using a quadratic cost function leads to a quadratic programming (QP) sub-problem.  I intend to investigate the application of non-feasible active set methods to the QP problem in order to formulate a new solution to the faster computation of the MPC problem.  The heavy computational burden which can occur also leads to the need to further investigate approximate solutions and real-time suboptimal control.  Research in this area of constrained optimization and control would advance the field with the realistic possibility that consequential technologies could be transferred to Canadian industry with positive returns.  Furthermore, the importance of this area of research to industry makes it a fundamental area of importance for the training of HQP.