Algorithms for inversion of controllable systems with structured nonlinearity (Q5942502)

The authors consider a dynamical system described by a system of differential equations of the form \[ \dot x = Ax + b(\xi + u + f(x)), \] \[ y = cx , \tag{1} \] where \(x=x(t)\) is an \(n\)-dimensional state vector, \(y=y(t)\) is the output of the dynamical system, \(u\) is a scalar control, \(\xi\) is a signal, \(A, b, c\) are known matrices and vectors of suitable dimensions, and \(f\) is the given function of \(n\) variables. The problem of estimation of the unknown scalar input function \(\xi(t)\) of the controllable stationary system (1) when the measured values of the output function \(y(t)\) are known is discussed. To solve the problem some inversion algorithms are proposed. The stability of the algorithms under some classes of parametric perturbations is proved.