Stabilization of Networked Control Systems With Sparse Observer-Controller Networks

Abstract

In this paper we provide a set of stability conditions for linear time-varying networked control systems with arbitrary topologies using a piecewise quadratic switching stabilization approach with multiple quadratic Lyapunov functions. We use this set of stability conditions to provide a novel iterative lowcomplexity algorithm that must be updated and optimized in discrete time for the design of a sparse observer-controller network, for a given plant network with an arbitrary topology. We employ distributed observers by utilizing the output of other subsystems to improve the stability of each observer. To avoid unbounded growth of controller and observer gains, we impose bounds on the norms of the gains.

Consensus of multi‐agent systems with fixed inner connections

“…As a similar topic in multi‐agent systems, consensus has also been investigated and applied in satellite formation, sensor networks, and air traffic control . Combining the 2 problems in a unified model not only is of theoretical interest but also plays an important role in many engineering applications . Real‐world networks are usually coupled with hard‐wired links; hence, it is sometimes not possible to achieve specific performance like consensus or tracking.…”

“…The 2 problems are similar in essence, but there does not seem to be any work considering these 2 problems simultaneously. In Razeghi‐Jahromi and Seyedi, the stability problem is solved with the direct Lyapunov method for spatially networked systems, without considering the consensus matter. In Duan et al, the decentralized control is used for some coupled special networks, but the results applicable to general networks are limited.…”

Sparse Observer-Based Sliding Mode Control For Networked Control Systems

“…This can be effective only when the interconnections between the subsystems are not strong. When the interconnections are strong, utilizing the distributed control frameworks has been considered to ensure stability of the overall system (Razeghi-Jahromi and Seyedi, 2015). An outstanding research implemented on the sliding mode control (SMC) has been decentralized SMC for the large-scale interconnected systems; see Yan et al (2004Yan et al ( , 2006; Qureshi and Abido (2014); Mahmoud and Qureshi (2012) and the references therein.…”

“…Note that recently several work in the literature focus on the design of sparsely distributed controller/observer networks; see e.g. Razeghi-Jahromi and Seyedi (2015); Lin et al (2011). The objective of this paper is to extend this idea to the field of Discrete-time SMC (DSMC) problems.…”

“…However, this may result in a non-convex condition. Also, Razeghi-Jahromi and Seyedi (2015) have considered the problem of finding the sparsest control/observer network that satisfies a set of stability conditions, obtained through a Lyapunov direct scheme. In this paper, as the second step, we will search for a sparse control/observer network structure with the least possible number of links satisfying the given stability condition.…”