Finite-Horizon Optimal Control for Linear and Nonlinear Systems Relying on Constant Optimal Costate

• 成果类型: Article
• 署名作者: Tarantino, Lorenzo; Sassano, Mario; Galeani, Sergio; Astolfi, Alessandro
• 署名单位: Sapienza University Rome; Imperial College London
• 刊物名称: IEEE TRANSACTIONS ON AUTOMATIC CONTROL
• ISSN/ISSBN: 0018-9286
• DOI: 10.1109/TAC.2023.3328925
• 发表日期: 2024
• 页码: 2174-2188
• 关键词: Iterative learning control; Nonlinear systems; optimal control

摘要

A class of finite-horizon optimal control problems, the solution of which relies on a time-varying change of coordinates that incorporates the transition matrix of the system linearized along the current estimate of the optimal process, is studied. The transformed dynamics exhibit a constant optimal costate. Differently from existing methods that hinge upon similar tools, the proposed strategy does not require at each step the (numerical) solution of a two-point boundary value problem or of a time-varying Riccati equation, and only the solution of a linear initial value problem is needed. The method is firstly illustrated in the setting of linear dynamics and quadratic cost for which the construction permits the identification of a class of problems in which the solution to the underlying (quadratic) Differential Riccati Equation exhibit a separation between homogeneous and particular contributions.