Finite-Dimensional Characterization of Optimal Control Laws Over an Infinite Horizon for Nonlinear Systems

• 成果类型: Article
• 署名作者: Sassano, Mario; Mylvaganam, Thulasi
• 署名单位: University of Rome Tor Vergata; Imperial College London
• 刊物名称: IEEE TRANSACTIONS ON AUTOMATIC CONTROL
• ISSN/ISSBN: 0018-9286
• DOI: 10.1109/TAC.2022.3230764
• 发表日期: 2023
• 页码: 5954-5965
• 关键词: Hamiltonian systems; Nonlinear systems; optimal control; stability of nonlinear (NL) systems

摘要

Infinite-horizon optimal control problems for nonlinear systems are considered. Due to the nonlinear and intrinsically infinite-dimensional nature of the task, solving such optimal control problems is challenging. In this article, an exact finite-dimensional characterization of the optimal solution over the entire horizon is proposed. This is obtained via the (static) minimization of a suitably defined function of (projected) trajectories of the underlying Hamiltonian dynamics on a hypersphere of fixed radius. The result is achieved in the spirit of the so-called shooting methods by introducing, via simultaneous forward/backward propagation, an intermediate shooting point much closer to the origin, regardless of the actual initial state. A modified strategy allows one to determine an arbitrarily accurate approximate solution by means of standard gradient-descent algorithms over compact domains. Finally, to further increase the robustness of the control law, a receding-horizon architecture is envisioned by designing a sequence of shrinking hyperspheres. These aspects are illustrated by means of a benchmark numerical simulation.