Reliable parameter estimation of nonlinear chaotic systems and PMSMs with the stellar oscillation optimizer

Accurate parameter identification is a critical prerequisite for reliable modeling, analysis, and control of nonlinear dynamical systems. This study introduces the stellar oscillation optimizer (SOO), a recently proposed metaheuristic inspired by the oscillatory behavior of stars, and investigates its effectiveness in estimating system parameters through a unified optimization framework. The identification problem is formulated as the minimization of a trajectory–mismatch cost function, where candidate solutions are iteratively refined by the oscillatory dynamics of SOO. To comprehensively evaluate its performance, four benchmark systems were considered: three canonical chaotic models (Lorenz, Chen, and Rössler) and a practical engineering case represented by a permanent-magnet synchronous motor (PMSM). The outcomes were benchmarked against several state-of-the-art algorithms, including Kirchhoff’s law algorithm (KLA), Tianji’s horse racing optimization (THRO), puma optimizer (PO), and hiking optimization algorithm (HOA), under a standardized protocol. The results show that SOO consistently achieves numerically convergent solutions with machine-precision-level residuals under deterministic and noise-free simulation settings, while maintaining strong robustness across independent runs. In chaotic benchmarks, the reported residuals approach floating-point limits, which indicates stable numerical convergence rather than guaranteed physical identifiability under real measurement conditions. On the PMSM model, SOO demonstrates accurate and repeatable parameter estimation within the adopted simulation framework.