Active Fault Diagnosis via Reachable Set Separation using Interval Methods

This paper presents an optimization-based approach for active fault isolation in linear time invariant systems subject to additive disturbances which are bounded in intervals. We model the evolution of the system states and outputs using interval dynamics with the input signals also bounded within given intervals. The proposed approach is based on determining a sequence of control actions to minimize a function which quantifies the overlap of output intervals, while taking into account the prescribed input bounds. The resulting optimization problem is nonconvex, yet the cost function has Lipschitz-continuous gradient and the constraints are simple, which allows us to solve them efficiently. A numerical example is used to illustrate the implementation and suitability of the proposed optimization approach for active fault isolation.

[1]  Niels Kjølstad Poulsen,et al.  Active Fault Diagnosis Based on Stochastic Tests , 2008, Int. J. Appl. Math. Comput. Sci..

[2]  Richard D. Braatz,et al.  Input design for guaranteed fault diagnosis using zonotopes , 2014, Autom..

[3]  Miroslav Simandl,et al.  On infinite horizon active fault diagnosis for a class of non-linear non-Gaussian systems , 2014, Int. J. Appl. Math. Comput. Sci..

[4]  Davide Martino Raimondo,et al.  Active fault diagnosis: A multi-parametric approach , 2017, Autom..

[5]  Richard D. Braatz,et al.  Active fault diagnosis using moving horizon input design , 2013, 2013 European Control Conference (ECC).

[6]  M. V. Iordache,et al.  Diagnosis and Fault-Tolerant Control , 2007, IEEE Transactions on Automatic Control.

[7]  Richard D. Braatz,et al.  A hybrid stochastic-deterministic input design method for active fault diagnosis , 2013, 52nd IEEE Conference on Decision and Control.

[8]  Ivo Punčochář,et al.  A Survey of Active Fault Diagnosis Methods , 2018 .

[9]  Richard D. Braatz,et al.  A Hybrid Stochastic-Deterministic Approach For Active Fault Diagnosis Using Scenario Optimization , 2014 .

[10]  D K Smith,et al.  Numerical Optimization , 2001, J. Oper. Res. Soc..

[11]  Leonidas J. Guibas,et al.  Zonotopes as bounding volumes , 2003, SODA '03.

[12]  Miroslav Simandl,et al.  Constrained Active Fault Detection and Control , 2015, IEEE Transactions on Automatic Control.

[13]  Henrik Niemann,et al.  A Setup for Active Fault Diagnosis , 2006, IEEE Transactions on Automatic Control.

[14]  Stephen L. Campbell,et al.  Auxiliary signal design for robust active fault detection of linear discrete-time systems , 2011, Autom..

[15]  Thomas Parisini,et al.  Distributed Fault-Tolerant Control of Large-Scale Systems: An Active Fault Diagnosis Approach , 2020, IEEE Transactions on Control of Network Systems.

[16]  Richard D. Braatz,et al.  Constrained zonotopes: A new tool for set-based estimation and fault detection , 2016, Autom..

[17]  Pantelis Sopasakis,et al.  A simple and efficient algorithm for nonlinear model predictive control , 2017, 2017 IEEE 56th Annual Conference on Decision and Control (CDC).

[18]  Goele Pipeleers,et al.  Embedded nonlinear model predictive control for obstacle avoidance using PANOC , 2018, 2018 European Control Conference (ECC).

[19]  Vicenç Puig,et al.  Robust fault detection using zonotope‐based set‐membership consistency test , 2009 .

[20]  Goele Pipeleers,et al.  A Penalty Method Based Approach for Autonomous Navigation using Nonlinear Model Predictive Control , 2018, 1805.02524.