Optimal Control for Nonlinear Systems Driven by a Known Exogenous Signal

• 成果类型: Article
• 署名作者: Sassano, Mario; Mylvaganam, Thulasi; Astolfi, Alessandro
• 署名单位: University of Rome Tor Vergata; Imperial College London; Imperial College London
• 刊物名称: IEEE TRANSACTIONS ON AUTOMATIC CONTROL
• ISSN/ISSBN: 0018-9286
• DOI: 10.1109/TAC.2021.3115427
• 发表日期: 2022
• 页码: 3678-3684
• 关键词: Optimal control; COSTS; mathematical models; Partial differential equations; differential games; Time-varying systems; Task analysis; Hamilton-Jacobi-Bellman (HJB) equation; Nonlinear systems; optimal control problems

摘要

We consider optimal control problems for continuous-time systems with time-dependent dynamics, in which the time-dependence arises from the presence of a known exogenous signal. The problem has been elegantly solved in the case of linear input-affine systems, for which it has been shown that the solution has a remarkable structure: It is given by the sum of two contributions; a state feedback, which coincides with the unperturbed optimal control law, and a purely feedforward term in charge of compensating the effect of the exogenous signal. The objective of this article is to extend the above result to nonlinear input-affine systems. It is shown that, while some of the relevant features of the linear case indeed rely heavily on linearity and are not preserved in the nonlinear setting, several structural claims can be proved also in the nonlinear case.