Distributed approach for aerodynamic model identification of the ice aircraft using the alternating direction method of multipliers in combination with simplotope b-splines

High performance control allocation methods for the Innovative Control Effectors (ICE) aircraft require accurate onboard aerodynamic models, with preferably first order continuity. Simplotope B-Splines, an extension on Simplex B-Splines, have a high approximation power by using local cost functions. However, enforcing global continuity produces computationally expensive optimization problems. This paper presents a distributed approach, using the Alternating DirectionMethod of Multipliers (ADMM), to reduce the complexity of the B-Coefficients’ estimation. ADMM decouples the simplotopes, and introduces coupling coefficients to enforce global continuity, resulting in a parallel estimation algorithm whose complexity is depending solely on the partition size, being independent of refinement of the model tessellation. Results show that for a 3D model, the distributed algorithm converges steadily to the global solution with a good approximation after a couple hundred iterations. Validation results of the distributed approach were similar to those of the global optimal solution for various noise intensities, and the continuity constraints were satisfied with maximum mismatches below 10-4. The distributed approach has been used to construct a first order continuous aerodynamic model for the ICE aircraft, which has been implemented in Simulink, and proven to perform well compared to the original model