Comparison of Robust and Probabilistic LMI-Based Design of Adaptive Flight Controllers with Uncertain Input Dynamics

Adaptive control-based schemes have been implemented to date in a variety of different applications. However, the ability to obtain a predictable transient closed-loop performance in adaptive systems is still a challenging problem from a verification and validation point of view. To face this problem we have recently introduced an analysis and design framework for adaptive control systems in the presence of bounded uncertainty and bounded adaptive control (the boundedness can be enforced, for instance, by a parameter projection mechanism) showing that the transitory performance of a MRAC system can be expressed, analyzed, and optimized via a convex optimization formulation based on Linear Matrix Inequality (LMI) requirements. A key feature of this framework is that it is possible to tune the adaptive control parameters rigorously so that the tracking error of the closed-loop system evolves within an a priori specified region of the error space whose size can be minimized by selecting a suitable cost function.