Problems of differential and topological diagnostics. Part 8. Aircraft movement and algorithms for its diagnosis

M. V. Shamolin

Vestnik Samarskogo universiteta. Estestvennonaučnaâ seriâ, Tome 28 (2022) no. 1-2, pp. 32-45

Résumé

This work is the eighth work of the cycle on differential and topological diagnostics. In it, a qualitative and numerical mathematical experiment is carried out to diagnose the control system of an aircraft during its planning from altitudes close to orbital, with an initial velocity close to the first cosmic velocity. And we have shown that the proposed diagnostic algorithms work successfully when searching for various kinds of reference faults, in particular, malfunctions of control signal sensors from a gyrostabilized platform, malfunctions close to to the reference ones, for trajectory measurements with an error, as well as in the case of continuous express diagnostics. At the same time, a certain diagnostic algorithm is built and used in accordance with the previously developed methodology.

Détail

Keywords: problem of differential diagnostics, direct (indirect) control system, diagnostics, a priori list of faults.

Bibliographie

[1] Shamolin M.V., “Problems of differential and topological diagnostics. Part 1. Motion equations and classification of malfunctions”, Vestnik Samarskogo universiteta. Estestvennonauchnaia seriia = Vestnik of Samara University. Natural Science Series, 25:1 (2019), 32–43 (In Russ.) | DOI | MR | Zbl

[2] Shamolin M.V., “Problems of differential and topological diagnostics. Part 2. Problem of differential diagnostics”, Vestnik Samarskogo universiteta. Estestvennonauchnaia seriia = Vestnik of Samara University. Natural Science Series, 25:3 (2019), 22–32 (In Russ.) | DOI | MR | Zbl

[3] Shamolin M.V., “Problems of differential and topological diagnostics. Part 3. The checking problem”, Vestnik Samarskogo universiteta. Estestvennonauchnaia seriia = Vestnik of Samara University. Natural Science Series, 25:4 (2019), 36–47 (In Russ.) | DOI | MR | Zbl

[4] Shamolin M.V., “Problems of differential and topological diagnostics. Part 4. The case of exact trajectorial measurements”, Vestnik Samarskogo universiteta. Estestvennonauchnaia seriia = Vestnik of Samara University. Natural Science Series, 26:1 (2020), 52–68 (In Russ.) | DOI | MR | Zbl

[5] Shamolin M.V., “Problems of differential and topological diagnostics. Part 5. The case of trajectorial measurements with error”, Vestnik Samarskogo universiteta. Estestvennonauchnaia seriia = Vestnik of Samara University. Natural Science Series, 26:3 (2020), 30–39 | DOI | MR | Zbl

[6] Shamolin M.V., “Problems of differential and topological diagnostics. Part 6. Statistical solving of the problem of differential diagnostics”, Vestnik Samarskogo universiteta. Estestvennonauchnaia seriia = Vestnik of Samara University. Natural Science Series, 27:1 (2021), 74–80 (In Russ.) | DOI | MR | Zbl

[7] Shamolin M.V., “Problems of differential and topological diagnostics. Part 7. Differential diagnostics in some systems of direct and indirect control”, Vestnik Samarskogo universiteta. Estestvennonauchnaia seriia = Vestnik of Samara University. Natural Science Series, 27:3 (2021), 31–45 (In Russ.) | DOI | MR | Zbl

[8] Borisenok I.T., Shamolin M.V., “Resolving a problem of differential diagnostics”, Fundamental and Applied Mathematics, 5:3 (1999), 775–790 (In Russ.) | MR | Zbl

[9] Shamolin M.V., Certain problems of differential and topological diagnostics, 2nd edition, revised and enlarged, Ekzamen, M., 2007 (In Russ.)

[10] Shamolin M.V., “Foundations of Differential and Topological Diagnostics”, J. Math. Sci., 114:1 (2003), 976–1024 | DOI | MR | Zbl

[11] Parkhomenko P.P., Sagomonian E.S., Foundations of Technical Diagnostics, Energiya, M., 1981 (In Russ.)

[12] Mironovskii L.A., “Functional diagnosis of dynamical systems”, Automation and Remote Control, 1980, no. 8, 96–121 (In Russ.)

[13] Okunev Yu.M., Parusnikov N.A., Structural and Algorithmic Aspects of Modeling for Control Problems, Izd-vo MGU, M., 1983 (In Russ.)

[14] Chikin M.G., “Phase-constrained systems”, Automation and Remote Control, 1987, no. 10, 38–46 (In Russ.) | MR | Zbl

[15] Zhukov V.P., “On the sufficient and necessary conditions for the asymptotic stability of nonlinear dynamical systems”, Automation and Remote Control, 55:3 (1994), 321–330 (English; Russian original) | MR | Zbl

[16] Zhukov V.P., “On the sufficient and necessary conditions for robustness of the nonlinear dynamic systems in terms of stability retention”, Automation and Remote Control, 69:1 (2008), 27–35 (English; Russian original) | DOI | MR | Zbl

[17] Zhukov V.P., “Reduction of Stability Study of Nonlinear Dynamic Systems by the Second Lyapunov Method”, Automation and Remote Control, 66:12 (2005), 1916–1928 (English; Russian original) | DOI | MR | Zbl

[18] Borisenok I.T., Shamolin M.V., “Solving the problem of differential diagnostics by the method of statistical tests”, Vestnik Moskovskogo Universiteta. Seriya 1. Matematika. Mekhanika = Moscow University Mechanics Bulletin, 2001, no. 1, 29–31 (in Russian) | MR | Zbl

[19] Beck A., Teboulle M., “Mirror Descent and Nonlinear Projected Subgradient Methods for Convex Optimization”, Operations Research Letters, 31:3, May (2003), 167–175 | DOI | MR | Zbl

[20] Ben-Tal A., Margalit T., Nemirovski A., “The Ordered Subsets Mirror Descent Optimization Method with Applications to Tomography”, SIAM Journal on Optimization, 12:1 (2001), 79–108 | DOI | MR | Zbl

[21] Su W., Boyd S., Candes E., “A Differential Equation for Modeling Nesterov's Accelerated Gradient Method: Theory and Insights”, The Journal of Machine Learning Research, 2016, no. 17(153), 1–43 https://www.researchgate.net/publication/311221666_A_differential_equation_for_modeling_Nesterov | Zbl

[22] Shamolin M.V., “Diagnostics of Gyro-Stabilized Platform, Included in the Aircraft Motion Control System”, Elektronnoe modelirovanie = Electronic Modeling, 33:3 (2011), 121–126 (In Russ.)

[23] Shamolin M.V., “Diagnostics of Aircraft Motion in Planning Descent Mode”, Elektronnoe modelirovanie = Electronic Modeling, 32:5 (2010), 31–44 (In Russ.)

[24] Fleming W.H., “Optimal Control of Partially Observable Diffusions”, SIAM Journal of Control, 6:2 (1968), 194–214 | DOI | MR | Zbl

[25] Choi D.H., Kim S.H., Sung D.K., “Energy-efficient Maneuvering and Communication of a Single UAV-based Relay”, IEEE Transactions on Aerospace and Electronic Systems, 50:3 (2014), 2119–2326 | DOI

[26] Ho D.-T., Grotli E.I., Sujit P.B., Johansen T.A., Sousa J.B., “Optimization of Wireless Sensor Network and UAV Data Acquisition”, Journal of Intelligent Robotic Systems, 78:1 (2015), 159–179 | DOI

[27] Ceci C., Gerardi A., Tardelli P., “Existence of Optimal Controls for Partially Observed Jump Processes”, Acta Applicandae Mathematicae, 74:2 (2002), 155–175 | DOI | MR | Zbl

[28] Rieder U., Winter J., “Optimal Control of Markovian Jump Processes with Partial Information and Applications to a Parallel Queueing Model”, Mathematical Methods of Operations Research, 70 (2009), 567–596 | DOI | MR | Zbl

[29] Chiang M., Tan C.W., Hande P., Lan T., “Power control in wireless cellular networks”, Foundations and Trends in Networking, 2:4 (2008), 381–533 | DOI

[30] Altman E., Avrachenkov K., Menache I., Miller G., Prabhu B.J., Shwartz A., “Power control in wireless cellular networks”, IEEE Transactions on Automatic Control, 54:10 (2009), 2328–2340 | DOI | MR | Zbl

[31] Ober R.J., “Balanced Parameterization of Classes of Linear Systems”, SIAM Journal on Control and Optimization, 29:6 (1991), 1251–1287 | DOI | MR | Zbl

[32] Ober R.J., McFarlane D., “Balanced Canonical Forms for Minimal Systems: A normalized Coprime Factor Approach”, Linear Algebra and Its Applications, 122–124 (1989), 23–64 | DOI | MR | Zbl