High-order fully actuated system approaches: Part VIII. Optimal control with application in spacecraft attitude stabilisation

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.