Sub-Optimal Geometric Distance Algorithm for Active Fault Detection and Diagnosis: Reduced Nominal Performance Degradation Approach


This work presents a sub-optimal alternative formulation for a concave minimization problem used in the design of auxiliary inputs for active fault detection and diagnosis. The proposed method is developed in the framework of ellipsoidal reach sets and guaranteed fault diagnosis within a given time horizon. Moreover, the method enables the design of auxiliary inputs in the null input space of the nominal system, thereby reducing the nominal performance degradation. Its properties are investigated for a second-order system and an over-actuated aircraft to demonstrate the method’s numerical efficiency and the auxiliary input’s efficacy in separating the reach sets for the nominal-faulty and faulty-faulty cases.

This is a preview of subscription content, access via your institution.

Fig. 1
Fig. 2


  1. Boyd, S., El Ghaoui, L., Feron, E., & Balakrishnan, V. (1994). Linear matrix inequalities in system and control theory. Philadelphia, Pennsylvania: Society for Industrial and Applied Mathematics.

  2. Campbell, S. L., & Nikoukhah, R. (2004). Auxiliary signal design for failure detection. Princeton: Princeton University Press.

    Google Scholar 

  3. Durieu, C., Walter, É., & Polyak, B. (2001). Multi-Input Multi-Output ellipsoidal state bounding. Journal of Optimization Theory and Applications, 111(2), 273–303.

    MathSciNet  Article  Google Scholar 

  4. Glavaški, S. & Elgersma, M. (2001). Active aircraft fault detection and isolation. In Proceedings of the 2001 autotestcon-IEEE systems readiness technology conference (pp. 692–705).

  5. Grant, M. & Boyd, S. (2014). CVX: MATLAB software for disciplined convex programming, version 2.0. Accessed 28 November 2018

  6. Halder, A. (2018). On the parameterized computation of minimum volume outer ellipsoid of Minkowski Sum of ellipsoids. In Proceedings of the 2018 IEEE conference on decision and control (CDC) (pp. 4040–4045).

  7. Heirung, T. A. N., & Mesbah, A. (2019). Input design for active fault diagnosis. Annual Reviews in Control, 47, 35–50.

    MathSciNet  Article  Google Scholar 

  8. Horst, R., & Tuy, H. (1996). Global optimization: Deterministic approaches. New York: Springer.

    Google Scholar 

  9. Jordan, T. L., Langford, W. M., & Hill, J. S. (2005). Airborne subscale transport aircraft research testbed-Aircraft model development. In Proceedings of the AIAA guidance, navigation, and control conference and exhibit.

  10. Kerestecioglu, F. (1993). Change detection and input design in dynamical systems. Manchester: Research Studies Press.

    Google Scholar 

  11. Kim, K. K. K., Raimondo, D. M., & Braatz, R. D. (2013). Optimum input design for fault detection and diagnosis: Model-based prediction and statistical distance measures. In Proceedings of the 2013 European control conference (ECC) (pp. 1940–1945).

  12. Kurzhanskiy, A. A., & Varaiya, P. (2007). Ellipsoidal techniques for reachability analysis of discrete-time linear systems. IEEE Transactions on Automatic Control, 52(1), 26–38.

    MathSciNet  Article  Google Scholar 

  13. Marseglia, G. R., & Raimondo, D. M. (2017). Active fault diagnosis: A multi-parametric approach. Automatica, 79, 223–230.

    MathSciNet  Article  Google Scholar 

  14. Nguyen, N., Precup, N., Urnes, J., Nelson, C., Lebofsky, S., Ting, E., & Livne, E. (2014). Experimental investigation of a flexible wing with a variable camber continuous trailing edge flap design. In Proceedings of the 32nd AIAA applied aerodynamics conference.

  15. Niemann, H. & Poulsen, N. K. (2015). Active fault diagnosis in sampled-data systems. In Proceedings of the 9th IFAC symposium on fault detection, supervision and safety for technical processes (SAFEPROCESS) (pp. 883–888).

  16. Nikoukhah, R. (1998). Guaranteed active failure detection and isolation for linear dynamical systems. Automatica, 34(11), 1345–1358.

    MathSciNet  Article  Google Scholar 

  17. Paulson, J. A., Raimondo, D. M., Findeisen, R., Braatz, R. D., & Streif, S. (2014). Guaranteed active fault diagnosis for uncertain nonlinear systems. In Proceedings of the 2014 European control conference (ECC) (pp. 926–931).

  18. Punčochář, I. & Škach, J. (2018). A survey of active fault diagnosis methods. In Proceedings of the 10th IFAC symposium on fault detection, supervision and safety for technical processes (pp. 1091–1098).

  19. Raimondo, D. M., Braatz, R. D., & Scott, J. K. (2013). Active fault diagnosis using moving horizon input design. In Proceedings of the 2013 European control conference (ECC) (pp. 3131–3136).

  20. Scott, J. K., Findeisen, R., Braatz, R. D., & Raimondo, D. M. (2014). Input design for guaranteed fault diagnosis using zonotopes. Automatica, 50(6), 1580–1589.

    MathSciNet  Article  Google Scholar 

  21. Sekunda, A., Niemann, H., & Poulsen, N. K. (2016). Active fault detection based on a statistical test. In Proceedings of the 3rd conference on control and fault-tolerant systems (SysTol) (pp. 511–518).

  22. Šimandl, M., & Punčochář, I. (2009). Active fault detection and control: Unified formulation and optimal design. Automatica, 45(9), 2052–2059.

    MathSciNet  Article  Google Scholar 

  23. Toh, k. C., Todd, M. J., & Tütüncü, R. H. . (1999). SDPT3-A MATLAB software package for semidefinite programming, Version 1.3. Optimization Methods and Software, 11(1), 545–581.

  24. Wang, J., Ge, W., Wu, H., & Zhou, J. (2016). Active fault detection based on residual ellipsoid. In Proceedings of the 35th Chinese control conference (CCC) (pp. 6784–6789).

  25. Zhang, X. J. (1989). Auxiliary signal design in fault detection and diagnosis (lecture notes in control and information sciences). New York: Springer.

    Google Scholar 

Download references


This work was supported in part by CAPES (grant 88882.446995/2019-01) and CNPQ (grant 306900/2018-1).

Author information



Corresponding author

Correspondence to Mario H. Chaves.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Chaves, M.H., Kienitz, K.H. Sub-Optimal Geometric Distance Algorithm for Active Fault Detection and Diagnosis: Reduced Nominal Performance Degradation Approach. J Control Autom Electr Syst (2021).

Download citation


  • Guaranteed diagnosis
  • Input design
  • Ellipsoidal sets
  • Fault detection