Sparsely distributed sliding mode control for interconnected systems

Abstract

This paper proposes a framework for the design of sparsely distributed output feedback discrete-time sliding mode control (ODSMC) for interconnected systems. The major target here is to develop an observer based discrete-time sliding mode controller employing a sparsely distributed control network structure in which local controllers exploit some other sub-systems' information as well as its own local information. As the local controllers/observers have access to some other sub-systems' states, the control performance will be improved and the applicability region will be widened compared to the decentralised structure. As the first step, a stability condition is derived for the overall closed-loop system obtained from applying ODSMC to the underlying interconnected system, by assuming a priori known structure for the control/observer network. The developed LMI based controller design scheme provides the possibility to employ different information patterns such as fully distributed, sparsely distributed and decentralised patterns. In the second step, we propose a methodology to identify a sparse control/observer network structure with the least possible number of communication links that satisfies the stability condition given in the first step. The boundedness of the obtained overall closed-loop system is analysed and a bound is derived for the augmented system state which includes the closed-loop system state and the switching function.

Distributed extended state observer design and output feedback anti‐disturbance control for nonlinear interconnected systems: A dynamic memory event‐triggered mechanism

“…Remark 6. When designing the observer, the above minimizing the summation of 𝜃 i𝑗 is actually same as minimizing the number of L i𝑗 ≠ 0(i ≠ 𝑗) in previous studies [13,17,18]. In addition, by utilizing the method of exhaustion, under the worst cases, the sparse observer network can be found only by solving ∑  i=1 2  i times of convex optimization problem.…”

“…Therefore, research on distributed control strategies for ISs has become increasingly popular in recent years. A distributed output feedback sliding mode control scheme was presented for ISs in Argha et al [13], wherein a sparsely distributed controller/observer network is introduced. Distributed fault estimation and fault-tolerant static output feedback control were investigated in Zhang et al [14].…”

“…In the aforementioned references [13][14][15][16][17][18], the control schemes were implemented in a time-triggered manner. However, unnecessary data transmission may result in a communication channel overload and reduce communication efficiency [19].…”

“…1. Distinguished from the ISs with a single disturbance in previous studies [13,17,18,29], multi-source disturbances are considered in this paper. A distributed extended state observer is designed to estimate the unknown disturbances and system states; based on the observer output, an output feedback anti-disturbance controller with DC is constructed, which can compensate and attenuate two kinds of disturbances.…”

“…2. Compared with the distributed control based on the sparse network proposed in previous studies [13,17,18], this paper proposes a DMET output feedback anti-disturbance controller that can reduce data transmission. 3.…”