Chaos and strange attractors in linear spacecraft attitude control via gradient-velocity Lyapunov

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.