**A Decentralized Approach Based on Unknown Input Observers for**

** Actuator Fault Detection and Isolation of**

a Class of Interconnected Nonlinear Systems

a Class of Interconnected Nonlinear Systems

**Amir ABBASI ^{1}, Javad POSHTAN^{2*}, Ali MOAREFIANPOUR^{1}**

**Department of Electrical Engineering, Science and Research Branch,**

^{1 }Islamic Azad University, Tehran, Iran

**Iran University of Science and Technology,**

^{2}Narmak, Tehran, 16846-13114, Iran

jposhtan@iust.ac.ir

^{* }*Corresponding author*

**Abstract: **This paper presents a novel decentralized scheme for actuator fault detection and isolation of a class of large-scale interconnected nonlinear systems. For each of the interconnected subsystems, a local nonlinear unknown input observer (UIO) is designed without the need to communicate with other agents. The interconnected terms are treated as unknown inputs, hence all subsystems are decoupled completely and the information of other subsystems is not needed for fault detection and isolation. In addition to the interconnections, an exogenous disturbance which contains both system and measurement noise is approximately decoupled. To facilitate the observer design, sufficient condition for existence of the designed observer is formulated in terms of a set of linear matrix inequalities (LMIs) and optimal gain matrices are obtained. A simulation example of an automated highway system demonstrates the effectiveness of the proposed methodology.

**Keywords:** Unknown Input Observer (UIO), Large-Scale System, Decentralized Fault detection and Isolation.

**>>Full text**

**CITE THIS PAPER AS**:

Amir ABBASI, Javad POSHTAN*, Ali MOAREFIANPOUR, **A Decentralized Approach Based on Unknown Input Observers for Actuator Fault Detection and Isolation of a Class of Interconnected Nonlinear Systems**, *Studies in Informatics and Control*, ISSN 1220-1766, vol. 25(4), pp. 453-460, 2016.

**Introduction**

With the advancement of last decades’ technology, large-scale systems have been developed in many fields such as telecommunication, industrial processes, power generation, space structures, and transportation. To ensure safe and reliable operations of such systems, the design of fault detection and isolation (FDI) schemes is crucial. Due to the special structure of large-scale interconnected systems such as uncertainty, complexity, interconnection among subsystems, and high dimensionality, non-centralized FDI schemes have been developed for these systems. In these schemes, local diagnosers can be designed using local modes of subsystems; however, choosing a scheme depends on tasks of local diagnosers and the type of information exchange [25].

In decentralized schemes, a local diagnoser can detect and isolate faults only in its underlying subsystem. Nonetheless, communication with other local diagnosers is not always needed.

It should also be considered that the need for exchanging information among local diagnosers may cause an increase in costs and moreover, appropriate mechanisms should be considered such as transmission delays and network access [4]. To diagnose other subsystems, distributed schemes are much more practical [13].

As each fault can influence several subsystems, the interconnections among subsystems is a challenge for FDI of interconnected systems. To decouple subsystems completely, abilities of unknown input observers (UIOs) for dealing with the effect of interdependencies among subsystems has been considered for decentralized state estimation; see for example [8-9,19]. In [6], a bank of decentralized observers was designed so that each observer includes the model of the entire system. A distributed FDI scheme based on the UIOs for networks of interconnected second-order linear time-invariant systems was proposed in [18]. In [22], a distributed FDI for large networked systems with uncertainties based on UIOs was designed such that is resilient to network model uncertainties but cannot relax all limitations on interconnections. FDI of singular delayed LPV systems using UIOs was considered in [7].

As most systems can be described as a class of Lipschitz nonlinear systems [10], this paper focuses on a class of large-scale interconnected systems which satisfy the Lipschitz condition and investigates abilities of UIOs in these systems. In [24], a scheme for decentralized actuator fault diagnosis was proposed based on a sliding mode unknown input observer for an automated highway system. Despite having the ability to estimate the fault, the need for the knowledge of the interconnections and fault range, computing numerous constants and coordinate transformation are the drawbacks of aforementioned method. A decentralized actuator fault detection scheme was proposed in [25] where interconnection terms are not assumed unknown and the Lipschitz condition should be satisfied. Moreover, some information of other subsystems is needed. In [26], for an automated highway system a distributed FDI scheme was proposed with the assumption of satisfying the Lipschitz condition and exact knowledge of interconnection terms. For a local diagnoser, If FDI of other subsystems is not needed, choosing a decentralized scheme would be more proper. As a result, without the knowledge of interconnection terms, FDI can be performed. A distributed fault detection method for second-order multi-agent systems was considered in [20] under the assumption that the system has zero mean white noise sequences and faults were treated as unknown inputs using UIOs. In [11], a distributed formation control of networked Euler–Lagrange systems was designed in which the dynamic of each agent was described by Euler-Lagrange equation and fault diagnosis was performed. Fault detection for high-order nonlinear multi-agent systems was proposed in [12], which the unknown nonlinear functions are treated as unknown input. Here interdependencies are considered as unknown inputs and all subsystems are decoupled completely. This makes easier the fault detection and isolation and there is not any limitation on interconnections. However, there may be the noise and disturbance in the system and a special structure of UIO is needed to decouple the disturbance and interconnections simultaneously. In this regard, inspired by the UIO designed in [18] and an LMI approach in [2], a decentralized UIO is designed with the ability of decoupling the interconnections and attenuating the exogenous disturbance. The structure of UIO was defined in [3] is similar to later works (for example [5,14-16]) despite the adding abilities of fault estimation and noise filtration. Compared to [5,14-16], here we design UIO in decentralized form and all variables are obtained using LMI technique without the need to compute or try any constant.

The rest of the paper is organized as follows. Section 2 introduces the problem formulation and some definitions and assumptions are given in this section. Section 3 proposes a design procedure of a decentralized observer and related lemmas and theorem. A new decentralized FDI scheme based on UIOs is presented in Section 4. In Section 5, the simulation results of an automated highway system investigate the performance of the proposed scheme.

**REFERENCES**

- BOYD, S. P., L. EL GHAOUI, E. FERON, V. BALAKRISHNAN, V.,
**Linear Matrix Inequalities in System and Control Theory**SIAM: Philadelphia,1994. - CHEN, W., M. SAIF,
**Unknown Input Observer Design for a Class of Nonlinear Systems: an LMI Approach,**IEEE Am. Ctrl. Conf., 2006, pp. 834-839. - DAROUACH, M., M. ZASADZINSKI, S. J. XU,
**Full-order Observers for Linear Systems with Unknown Inputs,**IEEE Trans. Aut. Ctrl., 39(3), 1994, pp. 606-609. - DAVOODI, M. R., K. KHORASANI, H. A. TALEBI, H. R. MOMENI,
**Distributed Fault Detection and Isolation Filter Design for a Network of Heterogeneous Multiagent Systems,**IEEE Trans. Ctrl. Syst. Tech., 22(3), 2014, pp. 1061-1069. - DELSHAD, S. S., A. JOHANSSON, M. DAROUACH, T. GUSTAFSSON,
**Robust State Estimation and Unknown Inputs Reconstruction for a Class of Nonlinear Systems: Multiobjective Approach,**Automatica, 64, 2016, pp. 1-7. - DING, S. X., P. ZHANG, C. CHIHAIA, W. LI, Y. WANG, E. L. DING,
**Advanced Design Scheme for Fault Tolerant Distributed Networked Control Systems,**IFAC Proc. Vol., 41(2), 2008, pp. 13569-13574. - HASSANABADI, A. H., M. SHAFIEE, V. PUIG,
**UIO Design for Singular Delayed LPV Systems with Application to Actuator Fault Detection and Isolation,**J. Syst. Sc., 47(1), 2016, pp. 107-121. - HEYDARI, M., M. A. DEMETRIOU,
**Adaptive Distributed Unknown Input Observers for Interconnected Linear Descriptor Systems,**J. Syst. Sc., 2016, pp. 1-8. - HOU, M., P. C. MÜLLER,
**Design of Decentralized Linear State Function Observers,**Automatica, vol. 30(11), 1994, pp. 1801-1805. - KHALIL, H. K., J. W. GRIZZLE,
**Nonlinear Systems (Vol. 3),**New Jersey: Prentice hall, 1996. - LIU, L., J. SHAN,
**Distributed Formation Control of Networked Euler–Lagrange Systems with Fault Diagnosis,**Franklin Inst., 352(3), 2015, pp. 952-973. - LIU, X., X. GAO, J. HAN,
**Observer-based Fault Detection for High-order Nonlinear Multi-agent Systems**, J. Franklin Inst., 353(1), 2016, pp. 72-94. - LIU, X., X. GAO, J. HAN,
**Robust Unknown Input Observer based Fault Detection for High-order Multi-agent Systems with Disturbances,**ISA Trans., 61, 2016, pp. 15-28. - LIU, X., Z. GAO,
**Unknown Input Observers for Fault Diagnosis in Lipschitz Nonlinear Systems**, IEEE International Conference on Mechatronics and Automation, 2015, pp. 1555-1560. - MOHAMED, K., M. CHADLI, M. CHAABANE,
**Unknown Inputs Observer for a Class of Nonlinear Uncertain Systems: An LMI Approach,**J. Aut. and Comp., 9(3), 2012, pp. 331-336. - MONDAL, S., G. CHAKRABORTY, K. BHATTACHARYY,
**LMI Approach to Robust Unknown Input Observer Design for Continuous Systems with Noise and Uncertainties,**J. Ctrl, Aut. and Syst., 8(2), 2010, pp. 210-219. - REPPA, V., M. M. POLYCARPOU, C. G. PANAYIOTOU,
**Decentralized Isolation of Multiple Sensor Faults in Large-scale Interconnected Nonlinear Systems,**IEEE Trans. Aut. Ctrl, 60(6), 2015, pp. 1582-1596. - SHAMES, I., TEIXEIRA, A.M., SANDBERG, H., JOHANSSON, K.H.,
**Distributed Fault Detection for Interconnected Second-order Systems**, Automatica, 47(12), 2011, pp. 2757-2764. - SHI, J., X. HE, Z. WANG, D. ZHOU,
**Distributed Fault Detection for a Class of Second-order Multi-agent Systems: An Optimal Robust Observer Approach.**IET Control Theory & Apps., 8(12), 2014, pp. 1032-1044. - SHI, J., X. HE, Z. WANG, D. ZHOU,
**Distributed Fault Detection for a Class of Second-order Multi-agent Systems: An Optimal Robust Observer Approach,**IET Control Theory & Applications, 2013, 8(12), pp. 1032-1044. - SPOONER, J. T., K. M. PASSINO,
**Fault-tolerant Control for Automated Highway Systems**, IEEE Trans. Veh. Tech. 46(3), 1997, pp. 770-785. - TEIXEIRA, A., I. SHAMES, H. SANDBERG, K. H. JOHANSSON,
**Distributed Fault Detection and Isolation Resilient to Network Model Uncertainties,**IEEE Trans. Cyber., 44(11), 2014, pp. 2024-2037. - WANG, Y., L. XIE, C. E. De SOUZA,
**Robust Control of a Class of Uncertain Nonlinear Systems**, Syst. & Ctrl. Let., 19(2), 1992, pp. 139-149. - YAN, X. G., C. EDWARDS,
**Robust Decentralized Actuator Fault Detection and Estimation for Large-scale Systems using a Sliding Mode Observer,**J. Ctrl., 81(4), 2008, pp. 591-606. - ZHANG, X.,
**Decentralized Fault Detection for a Class of Large-scale Nonlinear Uncertain Systems,**IEEE Am. Ctrl. Conf., 2010, pp. 5650-5655. - ZHANG, X., Q. ZHANG,
**Distributed Fault Detection and Isolation in a Class of Large-scale Nonlinear Uncertain Systems**, IFAC Proc. Vols., 44(1), 2011, pp. 4302-4307.