Adaptive robust control providing a guaranteed result under conditions of bounded disturbances (Q1914116)

Consider the discrete-time system \[ a(q,t) y_t = q^k b(q,t) u_t + v_t \] where \[ a(q,t) = 1 + \sum^m_1 a_i (t)q^i, \quad b(q,t) = \sum^m_0 b_i (t)q^i, \quad t \in \mathbb{Z} \] and the coefficients satisfy the following restrictions \[ a_i (t) = a_i + \delta a_i (t),\;\bigl |\delta a_i (t) \bigr |\leq \delta_i,\;i = 1, \dots, n \] \[ b_j (t) = b_j + \delta b_j (t),\;\bigr |\delta b_j (t) \bigr |\leq \delta_{n + 1 + j}, \;j = 1, \dots, m \] \[ \theta = \text{col} (a_1, \dots, a_n, b_0, \dots, b_m) \in \Theta \subset \mathbb{R}^{n + m + 1}; \;\sup_t |v_t |< + \infty. \] For such systems several adaptive identification and control problems are formulated. A simple example to show how the algorithm proposed works is given.