Near Optimal Control Based on the Tensor-Product Technique

This brief investigates the near optimal control problem and targets at the rigid body attitude dynamic system that are characterized by its typical nonlinearity. In order to apply the linear matrix inequality-based optimization, a second-order linear-parameter-varying model is specifically derived from the attitude system by means of the tensor-product transformation. Furthermore, an adaptive attitude tracking control law is designed to achieve both the offline optimization and online control simplification. The final control law is provided in a combined form. As a result, the dynamic response of the system mainly depends on the near optimal virtual controller and the stability can be further guaranteed by the adaptive tracking controller. Numerical simulations are conducted to verify the effectiveness of the proposed algorithms.