# Hybrid Fuzzy-DDPG Approach for Efficient MPPT in Partially Shaded Photovoltaic Panels
## 2 Materials and Methods
### Reinforcement Learning Fuzzy-DDPG  
Reinforcement learning (RL), as discussed in [35], is a machine learning paradigm in which an agent learns to make optimal decisions by interacting with an environment. This process is typically formulated as a Markov Decision Process (MDP), which is characterized by key components:  
* State (S): Represents the current situation or context of the agent. At each time step, the agent observes the state of the environment. * Action (A): The agent selects an action from a set of possible actions based on the current state. * Transition Probability (P): P(s'!s, a) denotes the probability of transitioning to state s' after taking action a in state s. This captures the dynamics of the environment. * Reward (R): R(s, a, s') represents the immediate reward received by the agent after taking action a in state s and transitioning to state s'. * Discount Factor (\(\gamma\)): A value between 0 and 1 that determines the importance of future rewards. A higher discount factor prioritizes long-term rewards. * Policy (\(\pi\)): A mapping from states to actions, defining the agent's behavior. The policy can be deterministic, \(\pi(s)=a\), or stochastic, \(\pi(a|s)=P(a|s)\). The primary objective in RL is to find an optimal policy that maximizes the expected cumulative discounted reward, formally expressed as follows:  
\[R(\pi)=\mathbb{E}_{\pi}\left[\sum_{t=0}^{\infty}\gamma^{t}\,r(s_{t},a_{t},s_{t+1 })\right]. \tag{7}\]  
In continuous state spaces, the exponential growth of the state-action pair complexity--often referred to as the curse of dimensionality--renders traditional tabular methods impractical. This challenge necessitates the use of function approximation techniques, where neural networks and other parametric models are employed to estimate value functions or to directly parameterize policies. Such approaches have led to the development of advanced RL methods including Deep Q-Networks (DQN), policy gradient methods, and actor-critic architectures like Deep Deterministic Policy Gradient (DDPG) [36]. Beyond these foundational aspects, modern RL methods have evolved to incorporate strategies such as curriculum learning and adaptive exploration [37], which further enhance training stability and convergence. In our study, RL is applied to dynamically adjust the duty cycle of a DC-DC converter in a photovoltaic system under partial shading conditions. This formulation not only addresses the inherent non-stationarity and high-dimensionality of the environment but also demonstrates how RL, when combined with fuzzy logic enhancements, provides a robust and adaptive framework for achieving Maximum Power Point Tracking in complex, real-world settings. In the context of Maximum Power Point Tracking for photovoltaic systems under partial shading conditions, the RL agent learns to adjust the duty cycle of a DC-DC converter to maximize the power output of the PV system. Partial shading occurs when some parts of a PV array receive less sunlight than others, leading to multiple peaks in the power-voltage curve. Traditional MPPT methods can get stuck at local maxima, resulting in suboptimal power generation. RL offers a promising solution to this problem by learning to navigate the complex power landscape and find the global maximum power point. Traditional RL algorithms like Q-learning [38] and SARSA are designed for discrete state and action spaces. Extensions to continuous spaces often involve function approximation techniques, such as tile coding [39], radial basis functions (a common function approximation technique, though not directly referenced in the current search results), or neural networks (neural networks are widely used in RL, see for example [40]). However, these approximations can suffer from instability and divergence issues [41]. Policy gradient methods, which directly optimize the policy, are naturally suited for continuous action spaces. Algorithms like REINFORCE and actor-critic methods have been developed to handle such scenarios.