A formula for iterated derivatives along trajectories of nonlinear systems
A study is made of the iterated time derivative of the output y(t) of a nonlinear control system of the form \(\dot x=f(x)+g(x)u\), \(y=h(x)\) is given. The expression of the k-th order time derivative of y(t) as a function of the time derivatives of u(t) involves calculations in noncommuting variables. This approach is very much in line with the so called Fliess-expansion for y(t) as a sum of noncommuting iterated integrals of u; see \textit{M. Fliess}, Bull. Soc. Math. Fr. 109, 3-40 (1981; Zbl 0476.93021).
scientific article; zbMATH DE number 4057390