Discussion on: “A Decentralized Sliding Control Approach for Distributed Simulation of Differential-Algebraic Equation Systems”

Abstract

The article by Azizi et al. deals with an application of the decentralized control methodology to a class of dynamical processes governed by differential-algebraic equations (DAEs) with an arbitrary finite index. The proposed approach is developed in a constructive framework of the distributed simulation techniques and is motivated by the high complexity of the classical analytical and computational methods related to the differential-algebraic systems. The main mathematical idea of this contribution consists of an equivalent representation of the algebraic constraints in the form of some appropriate sliding manifolds. This interpretation of the given algebraic restrictions makes it possible to apply the well-established sliding mode control (SMC) analysis/design. And, this development is exactly the topic under investigation in the above article. Let us recall that the SMC usually implies strong stability and robustness properties of the resulting systems. Moreover, the SMC approach also provides a basis for some effective computational methods associated with the feedback-type design of controllers. The authors use this fact and apply a decentralized SMC algorithm to simulations of the deformable surfaces. Moreover, they also propose a numerically stable solution procedure for the associated Jacobian inversion problem. The published article addresses an interesting and important subject of the modern control engineering and also studies some related aspects of the computational control science. The above-mentioned main point of the article, namely, the