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    <subfield code="a">In the rapidly developing landscape of control engineering within electrical and  electronics engineering, the study addresses critical challenges posed by the escalating  complexity of system designs. As technology continues to advance, the demand for  effective methodologies to design, analyse, and synthesize complex system models  becomes vital. In response to this imperative, researchers have increasingly turned to  optimization-based approaches, with the Sine Cosine Algorithm (SCA) emerging as a  prominent solution. However, existing limitations in terms of convergence accuracy and  local optima stagnation have prompted the introduction of innovative improvements in  this study. The Nonlinear Sine Cosine Algorithm (NSCA) is introduced as a key  extension, incorporating a versatile nonlinear decreasing gain into the transition  parameter mechanism. This enhancement offers a tailored balance between exploration  and exploitation, aligning with the specific requirements of complex electrical and  electronics engineering problems. Moreover, the Nonlinear Sine Cosine Algorithm-Safe  Experimentation Dynamic (NSCA-SED) introduces a hybridization of multi-agent and  single-agent algorithms, presenting a dynamic approach with random perturbation to  navigate search trajectories effectively, and release design parameters that might be  trapped in local optima. The empirical assessment of these proposed methods  encompasses a diverse set of 23 benchmark functions, demonstrating their efficacy  comparable to well-established metaheuristic algorithms such as as the Grey Wolf  Optimizer (GWO), Multi-Verse Optimization (MVO), Sine Cosine Algorithm (SCA),  Ant Lion Optimizer (ALO), Moth-Flame Optimization Algorithm (MFO), and  Grasshopper Optimization Algorithm (GOA). The applications extend beyond  established optimization problems, addressing contemporary experiments in control  engineering, including Model Order Reduction, Nonlinear System Identification, and  Data-driven Control. Simulation results underscore the robustness and superiority of the  NSCA and NSCA-SED algorithms in these contexts, showcasing improvements ranging  from 13.97% to 97.17% for Model Order Reduction, 17.76% to 99.37% for Nonlinear  System Identification, and 84.51% to 89.47% for Data-driven Control when compared to  the standard SCA. In summary, this study not only contributes advancements to  optimization algorithms but also directly addresses and enhances methodologies in  electrical and electronics engineering. By overcoming the limitations of existing  approaches, the NSCA and NSCA-SED algorithms stand as valuable tools in the  collection of control engineers, facilitating the design and optimization of complex  systems in contemporary electrical and electronics applications.</subfield>
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