Distributed realization of differential-algebraic systems using decentralized sliding mode control

Differential-algebraic Equation (DAE) systems present numerous difficulties in distributed simulation and control systems. The main problem is that most existing methods require an explicit state space model without algebraic constraints. One approach to address this problem is to reformulate the DAE system into an equivalent nonlinear control problem, in which the algebraic constraints are replaced by appropriate sliding manifolds. However, previous approaches based on this method are centralized leading to a great deal of computation and communication in distributed environments associated with inversion of the associated input decoupling matrix. In this work, this problem is addressed through application of decentralized sliding mode control. Relationships are developed for stability and performance in the presence of the neglected coupling terms. Inversion of the decoupling matrix is performed on a node basis. This allows the systematic division of the system into nodes that are more efficient for distributed computation. The new approach is applied to simulation of deformable surfaces in a real-time distributed computing environment