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Measures and LMIs for V&V of Adaptive Control
Author: Daniel Wagner
Verification and Validation remains a critical and costly process in the field of aerospace. The current state-of-the-art relies on linear analysis and Monte-Carlo to identify worst case behavior and the existence of unsafe trajectories in the model. These methods remain applicable only to aircraft models with linear feedback. In practice, aircraft dynamics are seldom linear. This is due to inherent aerodynamic nonlinearities and actuators with rate/deflection saturation that do not follow the first order model. In that sense, adaptive control remains promising since it can, by design, reject exogenous disturbances and alleviate shortcomings with modeling accuracy. However, the added complexity makes it impossible to numerically validate using traditional methods. New stateof- the-art tools are required. This thesis utilizes occupation measures and LMI relaxations (called the moment sums of squares or Lasserre hierarchy) on nonlinear aircraft models with nonlinear feedback and piecewise constraints. This framework can be used in conjunction with Lyapunov analysis to impose strict transient/terminal performance guarantees on the closed-loop. This thesis provides the flight controls community with a powerful set of tools that can build confidence in using nonlinear controllers to reduce fatalities and loss-of-control events.