Nonlinear analysis for wing rock system with adaptive control

Adaptive control has the potential to improve the performance and reliability of aircraft. However, the inherent nonlinearity of adaptive control causes difficulty in stability and robustness verification which is critical before entry into service. In this paper, the region of attraction (ROA) estimation using sum of squares (SOS) technique is explored for adaptive control systems. The problem of wing rock suppression by a model reference adaptive control (MRAC) serves as a benchmark example to demonstrate the effectiveness of the method. Considering the potential disturbance presented in measurement signals, the operative range of aircraft must be included in the ROA of the control system. Therefore, the ROA is evaluated using SOS polynomial optimization under various combinations of design parameters in the adaptive law, including adaptation rate and sigma modification values. This gives insight into the interactions of design parameters on the adaptive control performance.