Adaptive regulator design for a viscous Burgers' system by boundary control (Q2745705)

The system is NEWLINE\[NEWLINE{\partial w(t, x) \over \partial t} = \varepsilon {\partial^2 w(t, x) \over \partial x^2} - a w(t, x) {\partial w(t, x) \over \partial x} \quad (0 < x < 1),NEWLINE\]NEWLINE NEWLINE\[NEWLINE{\partial w(t, 0) \over \partial x} + b w(t, 0) = - u_1(t) - \theta^T v(t), \quad {\partial w(t, 1) \over \partial x} = u_2(t)NEWLINE\]NEWLINE where \(\varepsilon, a, b\) are constants \((\varepsilon > 0).\) The output is the 2-dimensional vector \(y(t) = (w(t, 0), w(t, 1))\) and \(v(t)\) is the (\(\ell\)-dimensional) disturbance function. The objective is to construct a feedback control input \((u_1(t), u_2(t))\) such that the closed-loop system will be asymptotically stable for any choice of the unknown parameters \(\varepsilon, a, b\) and the unknown vector \(\theta.\)