Adaptive regularization for a class of nonlinear affine differential-algebraic equation systems

In this paper, the regularization problem is investigated for nonlinear differential-algebraic equation (DAE) systems with unknown parameters, which appear linearly in both differential and algebraic equations. It is shown that the feasibility of the proposed algorithms guarantees the existence of a feedback controller so that the resulting closed-loop systems admit equivalent ordinary differential equation (ODE) systems with lower triangular forms. As an application case of DAE systems, a constrained manipulator with flexible joints is studied to illustrate the proposed methodology.