Input reconstruction in a dynamic system from measurements of a part of phase coordinates (Q2332626)

In this paper, the author deals with the nonlinear control system \[ \dot x(t) = Ax(t)+ B(y(t))+Cu(t)+f_1(t), \ t\in T=[0,\vartheta], \] \[ \dot y(t) = A_1x(t)+B_1(y(t))+f_2(t) \] \[ x(0)=x_0,\ y(0)=y_0, \] where \(x\in\mathbb{R}^n,\) \(y\in\mathbb{R}^r,\) and a disturbance \(u\in\mathbb{R}^q;\) \(f_1(\cdot)\in W_{\infty}^1(T;\mathbb{R}^n)\) and \(f_2(\cdot)\in W_{\infty}^1(T;\mathbb{R}^r)\) are given functions; \(A,\) \(A_1,\) \(C\) are constant matrices of suitable dimensions, \(B\) and \(B_1\) are Lipschitz. The problem under discussion is to construct an algorithm for approximate reconstruction of unknown disturbance \(u(\cdot)\) from inaccurate measurements of the states \(y(\cdot).\) To solve this problem, an algorithm based on the dynamic inversion method and the extremal shift is proposed.