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All Journal Bulletin of Electrical Engineering and Informatics
Abdiramanov Orisbay Galymdzhanovich
L.N. Gumilyov Eurasian National University
Electrical & Electronics Engineering

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Chaos and strange attractors in linear spacecraft attitude control via gradient-velocity Lyapunov Beisenbi Mamyrbek Aukebaevich; Abdiramanov Orisbay Galymdzhanovich; Saltanat Beisenbina Erkinovna; Nurbayeva Marzhan Nurbaykyzy; Basheyeva Zhuldyz Orynbassarovna
Bulletin of Electrical Engineering and Informatics Vol 15, No 4: August 2026
Publisher : Institute of Advanced Engineering and Science

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.11591/eei.v15i4.10299

Abstract

This paper investigates the generation of deterministic chaos in nonlinear spacecraft control systems using the gradient–velocity method of Lyapunov vector functions. Unlike traditional Lyapunov-based approaches, which lack a universal method for constructing functions, the proposed approach provides explicit algebraic inequalities that determine the conditions for chaotic behaviour. A nonlinear spacecraft model with linear control laws is analysed, incorporating actuator dynamics and measurement uncertainties. Numerical simulations demonstrate the transition between robustly stable and chaotic regimes under variations of system parameters. The results are validated through phase portraits and transient responses, and further supported by quantitative chaos indicators such as Lyapunov exponents and bifurcation analysis. The study shows that when robust stability boundaries are preserved, the system remains periodically stable, whereas violation of these conditions leads to deterministic chaos with the formation of strange attractors. Compared with existing methods, the gradient–velocity approach offers a systematic framework applicable to high-dimensional nonlinear systems. The proposed methodology can be extended to the synthesis of spacecraft attitude control systems, where maintaining stability under uncertainty is critical. This work contributes to the theoretical understanding and practical mitigation of chaos in aerospace applications.
Co-Authors Basheyeva Zhuldyz Orynbassarovna Beisenbi Mamyrbek Aukebaevich Nurbayeva Marzhan Nurbaykyzy Saltanat Beisenbina Erkinovna