Decentralized Sampled-Data Fuzzy Observer Design for Nonlinear Interconnected Systems

Abstract

This paper presents the decentralized sampled-data fuzzy observer design techniques for nonlinear interconnected systems, which are assumed to be composed of fuzzy subsystems and unknown interconnections. To design the decentralized fuzzy observer, the estimation error dynamics is obtained and the performance function is defined. Based on the estimation error dynamics and the performance function, the continuous-time decentralized fuzzy observer is firstly proposed to minimize the interconnection bound to attenuation degree ratio (IAR). Also, the decentralized sampled-data fuzzy observers are designed by using the approximate discretization and the exact discrete-time design approaches, respectively. Each proposed observer design technique is formulated into the optimal problems with the linear matrix inequalities (LMIs). Finally, several simulation examples show the validity and superiority of proposed observer design techniques by comparing with the conventional techniques.Index Terms-Decentralized sampled-data fuzzy observer, nonlinear interconnected systems, interconnection bound to attenuation degree ratio, approximate discretization, exact discrete-time design.1063-6706 (c)

A novel approach of decentralized H∞$H_{\infty }$ fuzzy filtering for nonlinear large‐scale systems with uncertain interconnections

“…Especially, these approaches have been frequently used in digital redesign [22,23,31], which has high practicality. Also, the approximate discretization and exact discrete-time design approaches have been applied in the sampled-data fuzzy controller design of many practical applications, such as power systems [43], UAVs [44], active suspensions [45] and so on.…”

“…However, the interconnection problem of large-scale systems has not been considered at all. • In [44], the decentralized fuzzy filtering has been guaranteed for large-scale systems, it still does not address the uncertainty problem of interconnection • In [45], the fuzzy observer considering the uncertain interconnection problem has been proposed, but is has not extended to filter design.…”

“…The main limitations of previous papers are highlighted as follows: In [43], the fuzzy filters have been presented for non‐linear systems with sampled‐data output and missing measurements. However, the interconnection problem of large‐scale systems has not been considered at all. In [44], the decentralized fuzzy filtering has been guaranteed for large‐scale systems, it still does not address the uncertainty problem of interconnection In [45], the fuzzy observer considering the uncertain interconnection problem has been proposed, but is has not extended to filter design. …”

Adaptive Observer-Based Decentralized Sliding Mode Control for Connected Systems in the Presence of Unknown Interconnection and Bounded Disturbance

“…By designing a reducedorder observer to estimate unmeasurable stats, in Hua et al (2015) a decentralized output feedback adaptive neural network tracking control has been proposed for stochastic connected systems. Koo et al (2015) state that a sampled data observer has been designed such that each observer is solved as an optimization problem by the LMI approach. However, there is a lack of connection information.…”

Design of a Fault Tolerant Sampled-Data Fuzzy Observer With Exponential Time-Varying Gains

“…As a controller and an observer can be designed simultaneously, the observer-based approach is applicable to not only asymptotically stable systems but also unstable systems. Recently, a pioneer study of designing an observer for oscillating systems without a controller was conducted in [15]. As a practical application of the fuzzy observer approach, authors in [16] studied the fuzzy observer-based attitude and heading reference system composed of inertial sensors.…”