Computationally Efficient SDRE Control Design for 3-DOF Helicopter Benchmark System

This article presents new analytical results that fundamentally ensure the applicability of the state-dependent Riccati equation (SDRE) scheme, for the three-degree-of-freedom helicopter control system that is of benchmark importance. The analysis removes any online time-consuming applicability check that is in terms of the pointwise solvability of SDRE, which leverages a series of equivalence transformations and dimension reductions. This largely improves the computational performance since the checking routine accounts for the dominant burden, which is endorsed by complexity analysis and practical validations. The analysis also categorizes the entire state space, where the newly discovered inapplicable subspace is efficiently resolved using an alternative SDRE design. As for the second/other computational load (pointwise SDRE-solving), we novelly introduce a state-of-the-art solver, provide a MATLAB-compatible implementation, and demonstrate performance advantages in computing time and accuracy. Notably, the simulations reveal more potential advantages as compared to the recent literature, including the control effort efficiency and robustness to model uncertainty. Moreover, the generality of the proposed theoretical results includes parameter robustness of this aerospace application and various control systems within the SDRE design framework and beyond.