A Design, Analysis, and Verification framework for Adaptive Flight Control

Safety-critical aerospace systems require stringent stabilization or tracking performance that have to be guaranteed in the face of large system uncertainties and abrupt changes on system dynamics. Considering Model Reference Adaptive Control (MRAC) schemes, while aggressive adaptation rates can, theoretically, produce a fast convergence of the tracking error to zero, this is often achieved at the expense of high frequency chattering and peaking in the control signal that could be unacceptable for practical applications. Due to the inherent nonlinear nature of MRAC schemes it is not easy to rigorously predict the response of the uncertain adaptive systems especially during transients. This is testified by the lack of clear and easy verification procedures for existing adaptive control schemes that relate design parameters to time domain specifications. To face this problem, we propose a design and validation framework where stability and performance requirements for the adaptive system are all formulated in terms of Linear Matrix Inequalities. This brings the advantage that the adaptive controller design and verification can be analyzed and optimized through the solution of a convex optimization whose objective is to guarantee the evolution of the error components within an a-priori specified invariant set. This approach was applied to verify the performance of a recently introduced MRAC scheme featuring a feedback contribution in the reference model that is proportional to the current tracking error. This architecture is deemed particularly appropriate to face uncertainty in real applications. A detailed design example applied to a generic flexible structure aircraft transport model is presented to highlight the efficacy of the proposed verification architecture.