Dynamic decoupling for right-invertible nonlinear systems
Affine nonlinear control systems \[ (*)\quad x=A(x)+B(x)u,\quad y=C(x) \] with m inputs and p outputs are considered. Furthermore, let \(K=Rt\) denote the differential field of rational functions of t with real coefficients and assume that all the components of A(x), B(x) and C(x) are elementary transcendental functions of their arguments. Denote by \(Ky_ 1,y_ 2\), \(...,y_ p\) the differential field generated by the components of the output and define as differential output rank of the system (*) the differential transcendence degree of \(Ky_ 1,y_ 2\), \(...,y_ p\) over K. A system (*) is said to be invertible iff its differential output rank is p. The main result is the following. Any system (*) which is right invertible in the above sense can always be locally decoupled via dynamical state feedback. An algorithm to compute the decoupling feedback is given.
scientific article; zbMATH DE number 4001965
scientific article