Output tracking for nonlinear singular systems

The application of inversion theory to nonlinear singular systems is an important problem. The output tracking for affine nonlinear singular systems, especially for non-minimum phase systems, using stable inverse method is discussed in this paper. This method not only get the stable output tracking asymptotically, but also eliminate the transient error, thus achieve the salient advantages of both classical inversion and output regulation. First the form of desired output trajectory is given and stable inverse problem for nonlinear singular systems is defined. Then algorithm is given and a sufficient invertibility condition is proposed. Under some appropriate assumptions, given systems can be written in a normal form by coordinate transformation. Next the equivalence of stable inversion to two-input boundary ordinary differential equation is established, then control law for asymptotic tracking is designed. Final a numerical example is used to demonstrate the value of stable inverse for output tracking control.