In this paper, the optimal control problem for dynamical systems represented by general high-order fully actuated (HOFA) models is formulated. The problem aims to minimise an objective in the quadratic form of the states and their derivatives of certain orders. The designed controller is a combination of the linearising nonlinear controller and an optimal quadratic controller for a converted linear system. In the infinite-time output regulation case, the solution is in essence a nonlinear state feedback dependent on a well-known Riccati algebraic equation. In the sub-fully actuated system case, the feasibility of the controller is investigated and guaranteed by properly characterising a ball restriction area of the system initial values. Application of the optimal control technique for sub-fully actuated systems to a spacecraft attitude control provides very smooth and steady responses and well demonstrates the effect and simplicity of the proposed approach.

在本文中，制定了以通用高阶全驱动（HOFA）模型为代表的动态系统的最优控制问题。该问题旨在最小化状态及其某些阶的导数的二次形式的目标。设计的控制器是线性化非线性控制器和转换线性系统的最优二次控制器的组合。在无限时间输出调节情况下，解决方案本质上是一个非线性状态反馈，依赖于众所周知的 Riccati 代数方程。在次全驱动系统情况下，通过适当表征系统初始值的球限制区域来研究和保证控制器的可行性。