Adaptive State-Feedback Controller

Abstract

In this chapter, we derive a swapping-based state-feedback controller for the $n + 1$-system (13.1) with constant coefficients, under assumptions (13.7), (13.9) and (13.11). The goal is to design a control law U(t) in (13.1d) so that system (13.1) is adaptively stabilized when the parameters

$$\begin{aligned} \varSigma = \begin{bmatrix} \sigma _1&\sigma _2&\dots&\sigma _n \\ \end{bmatrix}^T, \omega , \varpi , q, c \end{aligned}$$

are unknown. Note that $\sigma _i^T$, $i = 1, \ldots , n$ are the rows of the matrix $\varSigma$. The control law employs full state-feedback, and the practical interest of the controller is therefore limited, since distributed measurements are at best a coarse approximation in practice. This problem was originally solved in Anfinsen and Aamo (25th mediterranean conference on control and automation, Valletta, Malta, 2017).