2021/09/22 by Shahab, Mohamad T., Miller, Daniel E. · 1 citation
#FOS: Electrical engineering #FOS: Mathematics #Optimization and Control (math.OC) #Systems and Control (eess.SY) #electronic engineering #information engineering
paper · doi:10.48550/arxiv.2109.10611
It is typically proven in adaptive control that asymptotic stabilization and tracking holds, and that at best a bounded-noise bounded-state property is proven. Recently, it has been shown in both the pole-placement control and the d-step ahead control settings that if, as part of the adaptive controller, a parameter estimator based on the original projection algorithm is used and the parameter estimates are restricted to a convex set, then the closed-loop system experiences linear-like behavior: exponential stability, a bounded gain on the noise in every p-norm, and a convolution bound on the exogenous inputs; this can be leveraged to provide tolerance to unmodelled dynamics and plant parameter time-variation. In this paper, we extend the approach to the more general Model Reference Adaptive Control (MRAC) problem and demonstrate that we achieve the same desirable linear-like closed-loop properties.