# Daniel Wagner: A linear matrix inequality-based approach for the computation of actuator bandwidth limits in adaptive control

Everyone is welcome at the seminar given by Daniel Wagner - a PhD student (supervised by Didier Henrion) who have just joined our department. The seminar will start at **2pm** at **K14 seminar room**. In his talk, Daniel will give us an overview of the results that he achieved in his master thesis (downloadable at http://scholarsmine.mst.edu/masters_theses/7572/) defended in 1016 at Missouri University of Science and Technology.

Abstract: Linear matrix inequalities and convex optimization techniques have become popular tools to solve nontrivial problems in the field of adaptive control. Specif- ically, the stability of adaptive control laws in the presence of actuator dynamics remains as an important open control problem. In this thesis, we present a linear matrix inequalities-based hedging approach and evaluate it for model reference adap- tive control of an uncertain dynamical system in the presence of actuator dynamics. The ideal reference dynamics are modified such that the hedging approach allows the correct adaptation without being hindered by the presence of actuator dynam- ics. The hedging approach is first generalized such that two cases are considered where the actuator output and control effectiveness are known and unknown. We then show the stability of the closed-loop dynamical system using Lyapunov based stability analysis tools and propose a linear matrix inequality-based framework for the computation of the minimum allowable actuator bandwidth limits such that the closed-loop dynamical system remains stable. The results of the linear matrix inequality-based heading approach are then generalized to multiactuator systems with a new linear matrix inequality condition. The minimum actuator bandwidth solutions for closed-loop system stability are the- oretically guaranteed to exist in a convex set with a partially convex constraint and then solved numerically using an algorithm in the case where there are multiple ac- tuators. Finally, the efficacy of the results contained in this thesis are demonstrated using several illustrative numerical examples.