A Decentralized Sliding Control Approach for Distributed Simulation of Differential-Algebraic Equation Systems

Differential-algebraic equation 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 differential-algebraic equation 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 inherently centralized, potentially leading to a great deal of computation and communication in distributed environments associated with inversion of the input decoupling matrix. In this paper, 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 can thus be performed on multiple computing nodes in a more systematic and efficient manner. The new approach is applied to distributed simulation of a deformable surface problem.