Aircraft Motion Adaptive Control with the Non-Linear Dynamic Inversion and Machine Learning

Aeronautical and Space-Rocket Engineering


Аuthors

Dhiman G. *, Stepanova E. Y.**, Tiumentsev Y. V.***, Tskhai R. A.****

Moscow Aviation Institute (National Research University), 4, Volokolamskoe shosse, Moscow, А-80, GSP-3, 125993, Russia

*e-mail: Gd9617@mail.ru
**e-mail: lady.alena-he2015@yandex.ru
***e-mail: yutium@gmail.com
****e-mail: RomanTskhai106@yandex.ru

Abstract

There are several actively developing approaches to the nonlinear dynamic systems (DC) control, which are aimed at shortcomings surmounting of the conventional methods based on linearization. Particularly, one of the most popular options of this conventional linearization employs Taylor expansion of the functions, which describe the dynamic system, leaving only the linear part of the obtained expansion. The topmost drawback of this option consists in the fact that it is being elaborated for certain fixed conditions of the dynamic system functioning, while these conditions may be wide-ranging. This fact forces us to select, in one way or another, a finite set of such conditions, i.e., the calculated operating modes of the dynamic system, and then switch between the control laws obtained for these modes. This approach is called the “gain scheduling” (GS).
However, both stability and required control quality for the control laws obtained within the framework of the GS approach by the linear model is being guaranteed only in  the small neighborhood of each of the set modes, the size of this neighborhood herewith is as a rule unknown. With large deviations from the calculated mode, the requirements for the regulation quality may not be met, and moreover the system may be unstable.
In recent decades, several nonlinear control methodologies have emerged for the shortcomings overcoming of such conventional approaches to the dynamic systems linearization. One of the most popular methodologies of this kind is known as the feedback linearization (FBL). The FBL approach uses an accurate model of the dynamic system, for which its nonlinearities are fully or partially compensated for by the feedback and applying transformation of the state variables characterizing the dynamic system. The result is a linear system, moreover, this linearization will be accurate, unlike the approximate one based on the Taylor expansion, and will apply to the entire range of DS operating conditions, rather than to any single design regime. The resulting system can be operated using conventional linear control methods.
When using the FBL-approach to solve problems related to the aircraft motion control, it is most often referred to as nonlinear dynamic inversion (NDI). The NDI approach and its modifications are employed to solve the problems related to various classes of aircraft, including airplanes, helicopters, unmanned aerial vehicles, and spacecraft.
In its original formulation, the NDI approach has a number of drawbacks that may complicate its application for solving applied problems, including aircraft motion control problems. The main drawback is that it requires precise knowledge of the nonlinear dynamics of the system under consideration, represented by a corresponding model. This requirement cannot be always met. For example, for atmospheric aircraft (airplanes, helicopters, etc.), such factors as aerodynamic forces and moments acting on the aircraft play an important role in their motion model. These factors are being typically characterized by incomplete and inaccurate knowledge of their specific values. In addition, they can change during flight due to various types of abnormal situations (equipment failures and structural damage, icing of lifting and control surfaces, exposure to heavy rainfall, etc.).
To overcome these shortcomings of the NDI scheme, it is worth-while to consider modifications that would compensate for the aircraft properties uncertainty caused by both incomplete and inaccurate knowledge of these properties or their changes inflight. To solve this problem, it is necessary to provide the NDI with adaptability, which will allow it to remain operable in situations where the control object model used is not entirely adequate. One possible solution to this problem, which is discussed in our article, is introducing a loop for additional compensation of the error arising from tracking the specified input signal into the source NDI scheme. Three options of the compensator have been implemented by the feedforward neural networks, including a multi-perceptron, a sigma-pi network, and a Kolmogorov-Arnold network.
As a test problem demonstrating the effectiveness of the proposed approach, we consider processing of a given sequence of changes in the angular pitch rate. A sequence of step changes in this aircraft state variable is used as the reference signal.
The results of computational experiments presented in the article allow evaluating performance of the adaptive NDI variant for compensating for uncertainties caused by the inaccurate knowledge of the control object properties, as well as in the event of abnormal situations. It is shown that the neural network compensator application allows solving this task successfully, whereas without such compensator, the NDI scheme loses its performance.

Keywords:

longitudinal angular motion, adaptive control, nonlinear dynamic inversion, neural network compensator, multi-perceptron, sigma-pi network, Kolmogorov-Arnold network

References

  1.  Leith DJ, Leithead WE. Survey of gain-scheduling analysis and design. International Journal of Control. 2000;73(11):1001–1025. DOI: 10.1080/002071700411304
  2. Khalil HK. Nonlinear systems. 3rd ed. Upper Saddle River, New Jersey: Prentice Hall; 2002. 766 p. 
  3. Kim DP. Theory of automatic control. Vol. 2. Multidimensional, nonlinear, optimal and adaptive systems. Moscow: Fizmatlit; 2004. 464 p. (In Russ.).
  4.  Stevens BL, Lewis FL, Johnson EN. Aircraft control and simulation: Dynamics, Controls design and autonomous systems. 3rd ed. John Wiley & Sons, Inc; 2016. 764 p. DOI: 10.1002/9781119174882
  5.  Enns D, Bugajski D, Hendrick R, et al. Dynamic inversion: an evolving methodology for flight control design. International Journal of Control. 1994;59(1):71–91. DOI: 10.1080/00207179408923070
  6.  Miller CJ. Nonlinear dynamic inversion baseline control law: Architecture and performance predictions. AIAA Guidance, Navigation, and Control Conference (August 08-11, 2011; Portland, Oregon, USA). DOI: 10.2514/6.2011-6467
  7. Efremov AV, Shcherbakov AI. Comparative Analysis of Modern Approaches to the Aircraft Control Systems Synthesis. Aerospace MAI Journal. 2025;32(4):192-200. (In Russ.). URL: https://vestnikmai.ru/eng/publications.php?ID=186680
  8.  Horn JF. Non-linear dynamic inversion control design for rotorcraft. Aerospace. 2019;6(3):38. DOI: 10.3390/aerospace6030038
  9.  Soneson GL, Horn JF, Zheng A. Simulation testing of advanced response types for ship-based rotorcraft. Journal of the American Helicopter Society. 2016;61(3). DOI: 10.4050/JAHS.61.032011
  10.  Bijnens B, Chu QP, Voorsluijs GM, et al. Adaptive feedback linearization flight control for a helicopter UAV. AIAA Guidance, Navigation, and Control Conference (August 15-18, 2005; San Francisco, California). AIAA–2005–6284. DOI: 10.2514/6.2005-6284
  11.  Ducard G, Geering HP. Airspeed control for unmanned aerial vehicles: A nonlinear dynamic inversion approach. 16th Mediterranean Conference on Control and Automation (June 25–27, 2008; Ajaccio, France), pp. 676–681. DOI: 10.1109/MED.2008.4602202
  12.  da Costa RR, Chu QP, Mulder JA. Reentry flight controller design using nonlinear dynamic inversion. Journal of Spacecraft and Rockets. 2003;40(1):64-71. DOI: 10.2514/2.3916
  13.  Valasek J, Ito D, Ward DT. Robust dynamic inversion controller design and analysis for the X-38. AIAA Guidance, Navigation, and Control Conference (August 06-09, 2001; Montreal, Canada). DOI: 10.2514/6.2001-4380
  14.  Zhang Y, de Visser CC, Chu QP. Aircraft damage identification and classification for database-driven online flight-envelope prediction. Journal of Guidance, Control, and Dynamics. 2018;41(2):449–460. DOI: 10.2514/1.G002866
  15.  Cao Y, Tan W, Xu Z. Aircraft icing: An ongoing threat to aviation safety. Aerospace Science and Technology. 2018;75:353–385. DOI: 10.1016/j.ast.2017.12.028
  16.  Cao Y, Wu Z, Xu Z. Effects of rainfall on aircraft aerodynamics. Progress in Aerospace Sciences. 2014;71;85–127. DOI: 10.1016/j.paerosci.2014.07.003
  17.  Stevens BL, Lewis FL, Johnson EN. Aircraft control and simulation: Dynamics, Controls Design, and Autonomous Systems. 3rd ed. Wiley-Blackwell; 2016. 722 p.
  18. Dhiman G, Tiumentsev YuV, Tskhay RA. Combined use of dynamic inversion and reinforcement learning for optimal adaptive control of supersonic transport airplane motion. Journal of Computer and Systems Sciences International. 2025;64(1):136-152. (In Russ.).
  19.  Enns D, Bugajski D, Hendrick R, et al. Dynamic inversion: An evolving methodology for flight control design. International Journal of Control. 1994;59(1):71–91. DOI: 10.1080/00207179408923070
  20.  Lombaerts TJJ, Looye GHN. Design and flight testing of nonlinear autoflight control laws. AIAA Guidance, Navigation, and Control Conference (August 13–16, 2012; Minneapolis, MN). DOI: 10.2514/6.2012-4982
  21.  Johnson EN, Turbe MA. Modeling, control, and flight testing of a small ducted fan aircraft. AIAA Guidance, Navigation, and Control Conference ( August 15-18, 2005, San Francisco, California). AIAA 2005-6281. DOI: 10.2514/1.16380
  22.  Bosworth JT. Flight results of the NF-15B Intelligent Flight Control System (IFCS) aircraft with adaptation to a longitudinally destabilized plant. AIAA Guidance, Navigation, and Control Conference (August 18-21, 2008; Honolulu, HI, USA). DOI: 10.2514/6.2008-6985
  23.  Haykin S. Neural networks: A comprehensive foundation. 2nd ed. Prentice Hall; 2006. 842 p.
  24. Shibzukhov ZM. ΣΠ–neural networks: an introduction. XI Vserossiiskaya nauchno-tekhnicheskaya konferentsiya “Neiroinformatika–2009” (January 27-30, 2009): Lektsii po neiroinformatike. Moscow: MIFI; 2009. p. 66–88.
  25. Liu Z, Wang Y, Vaidya S, et al. KAN: Kolmogorov-Arnold Networks. arXiv:2404.19756v4. 2024. 27 p. DOI: 10.48550/arXiv.2404.19756
  26. Acquatella P, van Ekeren W, Chu Q. PI(D) tuning for flight control systems via incremental nonlinear dynamic inversion. IFAC-PapersOnLine. 20th World Congress of the IFAC (July 9-14, 2017; Toulouse, France). 2017;50(1):8175-8180. DOI: 10.1016/j.ifacol.2017.08.1265

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