An Adaptive Sliding Mode Observer for A Complex Network of Dynamical Systems

Abstract

A novel approach for reconstructing the entire state information of all the individual nodes of a complex network dynamical system, at a supervisory level, is proposed in this paper. The nodes of the network are assumed to belong to a class of systems with a known linear part and unknown but bounded nonlinearities or uncertainties in certain channels of the system. Adaptive sliding mode observers are designed for the purpose of enhancing autonomy in the network of dynamical systems. The synthesis of the sliding mode observer, formulated as a system of LMIs, depends entirely on the dynamics of an individual node of the network. The efficacy of the proposed methodology is demonstrated by considering a network of Chua oscillators.

Observer Design for a class of complex networks with unknown topoloy

“…As long as the interconnections satisfy the necessary rank condition on the relation in which states they enter the dynamics of the agents and which states are measured, the network dynamics can be transformed to the UIO form. Compared to a recent approach of [Menon and Edwards, 2011] that applies an SMO to a network with linear interconnections to treat the nonlinearities as disturbances, the proposed dissipativity-based approach can deal with a wider class of systems since the nonlinearity can be explicitly taken into account. Compared to the SMO the proposed observer can deal with unbounded unknown inputs and the design simplifies to solving an LMI while it can be difficult to find a sufficiently large observer gain for the SMO.…”

“…Remark 4 : Compared to the approach of [Menon and Edwards, 2011], that applies a Sliding Mode Observer (SMO) to deal with the nonlinearities as unknown inputs, the method proposed in this paper can deal with a wider class of systems because the nonlinearities can explicitly be taken into account. Furthermore, by considering the interconnections as unknown input, the approach can deal with arbitrary complex interconnections.…”

“…6]. Recently, an observer for systems with unknown but bounded nonlinearities and linear time-varying (nonswitching) interconnections was proposed in [Menon and Edwards, 2011]. Unless this study provided promising results, it is not clear how it could be extended to the case of networks with known or unknown nonlinear interconnections and possibly time-varying topology.…”