Adaptive Output-Feedback: Uncertain In-Domain Parameters

Abstract

We once again consider system (7.4) with measurement restricted to the boundary anti-collocated with actuation, that is

$$u_t(x, t) + \lambda (x) u_x(x, t) = c_{1}(x) v(x, t)$$

$$v_t(x, t) - \mu (x) v_x(x, t) = c_{2}(x) u(x, t)$$

$$u(0, t) = q v(0, t)$$

$$v(1, t) = U(t)$$

$$u(x, 0) = u_0(x)$$

$$v(x, 0) = v_0(x)$$

$$y_0(t) = v(0, t)$$