## 1 Introduction  
The power system is becoming extremely challenging in terms of load demand changes and electricity quality, making loads highly unpredictable and uncertain, which has resulted in fluctuations in grid frequency and subsequently influenced the stability of the power system [1, 2]. It is crucial to maintain the stability and reliability of interconnected power systems, preventing frequency deviations that can lead to power outages and damage to equipment [3, 4, 5]. For frequency and grid stabilization, Automatic Generation Control (AGC) is employed to adjust the output power of generators based on real-time conditions, ensuring that the power system can quickly return to a steady state after disturbances [6]. Load frequency control (LFC) [1, 7] is proposed to regulate system frequency and manage power exchanges with neighboring areas. This mechanism is designed to maintain system frequency stays within acceptable boundaries and improve stability and reliability in power distribution, even as the power demand fluctuates [5]. Load disturbances are a constant presence, leading to deviations in the nominal system frequency and causing variations in the scheduled tie-line power flow between interconnected areas [3; 4]. LFC systems based on Area Control Error (ACE) signals, which employ Proportional-Integral (PI) controllers [3; 4], have been developed to enhance the dynamic response of power systems [5]. To address the uncertainties of the dynamic model and the nonlinearity of certain components (such as the governor and actuators, e.g., turbine), many related studies apply optimization algorithms to search for optimal controllers, such as meta-heuristic algorithms [8], ant algorithm [9], fuzzy logic [10; 11], particle swarm optimization (PSO) [12] and genetic algorithm [13], neural networks [14], and deep learning [15]. The multi-area power systems, created by interconnecting several single-area systems, aim to improve the overall reliability and stability. They require the careful management of load and generation imbalances across different regions to maintain optimal performance [16; 17; 18; 19; 20]. Some control strategies, such as Active Disturbance Rejection Control, Sliding-Mode Control, and Model Predictive Control, have been applied to multi-area power systems, showcasing their advantages in handling disturbances introduced by renewable energy sources [21; 22; 23]. Furthermore, PSO has been used to tune PID controller parameters for LFC, demonstrating competitive performance in nonlinear scenarios [24]. Comparative studies of Genetic Algorithm, Simulated Annealing, and PSO for multi-area LFC systems further emphasize the potential of algorithms in enhancing control strategies [25]. However, a significant gap in the existing research is the lack of consideration of degraded components in the LFC of power systems. Degraded components, such as aging infrastructure and the wear and tear of mechanical parts, can significantly impact the performance and reliability of LFC systems [26]. Conventional control for LFC systems involves designing a fixed controller to manage load disturbances across various runtime conditions throughout the system's lifetime [27; 28; 29]. However, since key components are aged, aging failures can degrade system performance [30]. Consequently, the degradation of key components can lead to diminished power generation precision and less accurate frequency measurements, impairing the reliability and stability of the LFC system [31; 4]. Extensive experiments have shown that the component is incapable of delivering satisfactory performance once its degradation reaches a pre-defined threshold [32; 33; 34; 35]. Many research studies describe actuator degradation using various models, such as a constant value, uniform distribution over predefined intervals, multi-state process, Gamma process, inverse Gaussian distribution, Wiener process, and dependent Markov chains [36; 37; 30; 34; 38].