Functional Diagnosis of Digital State Automation Networks

The problem of functional diagnosis of digital devices forming a network of state automata is considered. This task for the network components is supposed to be solved, and the corresponding diagnostic devices for them are provided. The possibility of their population transformation into the tools for the entire network diagnostics is shown. The result of the transformation with the restrictions on the number of components with errors is simplified in compare with the original population. A procedure is proposed allowing to find analytical expressions defining an auxiliary control and an error discriminator for the most probable case of error localization (all errors are concentrated in a certain component of the network). The first part of the article provides a solution of the functional diagnosis problem for the case when the parity functions of all components are scalar, and the class of detectable errors is given by unit multiplicity. Next, the result generalizes for the case of vector functions, where multiple errors can occur. The procedure minimizes the sought for functional diagnosis devices with respect to the order when preserving the initial detecting ability within any network component. The obtained results are illustrated by an example of construction of functional diagnosis equipment for ranging signal processing device in broadband short-range radio engineering navigation system.

1. Hartmanis J., Stearns R. The Algebraic Structure Theory of Sequential Machines. New York, Prentice Hall, 1966, 211 p.

2. Parkhomenko P. P., Sogomonyan E. S. Osnovy tekhnicheskoy diagnostiki. V 2 kn. Kn. 2: Optimizatsiya algoritmov diagnostirovaniya, apparaturnyye sredstva [Fundamentals of Technical Diagnostics. Book 2: Optimization of Diagnostic Algorithms, Hardware Tools; ed by P. P. Parkhomenko]. Moscow, Energiya, 1981, 320 p. (In Russian)

3. Isidori A. Nonlinear Control Systems. London, Springer, 1995, 549 p.

4. Patton R., Clark R., Frank P. Fault Diagnosis in Dynamic Systems: Theory and Application. Englewood Cliffs, NJ, USA, Prentice-Hall, 1989, 594 p.

5. Zhang Y., Jiang J. Bibliographical Review on Reconfigurable Fault-Tolerant Systems. Annu. Rev. Control. 2008, vol. 32, no. 2, pp. 229–252.

6. Podkopayev B. P. Algebraicheskaya teoriya funktsional'nogo diagnostirovaniya dinamicheskikh sistem. V 2 ch. Ch. 2: Sistemnye algebry, algebraicheskaya model' funktsional'nogo diagnostirovaniya, realizatsiya modeli funktsional'nogo diagnostirovaniya [Algebraic Theory of Functional Diagnosis of Dynamic Systems. Pt. 2: System Algebras, Algebraic Model of Functional Diagnosis, Realization of the Functional Diagnosis Model]. SPb, Izd-vo SPbGETU "LETI", 2013, 132 p. (In Russian)

7. Kaldmäe A., Kotta Ü., Shumsky A., Zhirabok A. Measurement Feedback Disturbance Decoupling in Discrete-Time Nonlinear Systems. Automatica. 2013, vol. 49, no. 9, pp. 2887–2891.

8. Katz R. Max-Plus (A,B)-invariant Spaces And Control of Timed Discrete-Event Systems. IEEE Trans. on Automatic Control. 2007, vol. 52, no. 2, pp. 229–241.

9. Shcherbakov N. S., Podkopayev B. P. Strukturnaya teoriya apparatnogo kontrolya tsifrovykh avtomatov [Structural Theory of Digital Automation Hardware Control] Moscow, Mashinostroyeniye, 1982, 191 p. (In Russian)

10. Kaldmäe A., Kotta Ü., Shumsky A., Zhirabok A. Measurement Feedback Disturbance Decoupling In Discrete-Event Systems. Int. J. Robust Nonlinear Control. 2015, vol. 25, no. 17, pp. 3330–3348.

11. Miller R. F. Switching Theory. Vol. 1. Combinatorial Circuits. N. Y., 1965, 416 p.

12. Cheng D. Disturbance Decoupling of Boolean Control Networks. IEEE Trans. on Automatic Control. 2011, vol. 56, no. 10, pp. 2–10.

13. Yang M., Li R., Chu T. Controller Design for Disturbance Decoupling of Boolean Control Networks. Automatica. 2013, vol. 49, no. 1, pp. 273–277.

14. Podkopayev B. P. Algebraicheskaya teoriya funktsional'nogo diagnostirovaniya dinamicheskikh sistem. CH. 1: Sistemy, diagnostirovaniye sistem, sistemnyye algebry [Algebraic Theory of Functional Diagnosis of Dynamic Systems. Part 1: Systems, Diagnostic Systems, System Algebras]. SPb, Elmor, 2007, 132 p. (In Russian)

15. Shumsky A., Zhirabok A. Nonlinear Diagnostic Filter Design: Algebraic and Geometric Points of View. Int. J. of Applied Mathematics and Computer Science. 2006, vol. 16, no. 1, pp. 101–113.