Fuzzy-Partitioned Multi-Agent TD3 for Photovoltaic Maximum Power Point Tracking under Partial Shading

Maximum power point tracking (MPPT) under partial shading is a nonconvex, rapidly varying control problem that challenges multi-agent policies deployed on photovoltaic modules. We present Fuzzy–MAT3D, a fuzzy-augmented multi-agent TD3 (Twin-Delayed Deep Deterministic Policy Gradient) controller trained under centralized training/decentralized execution (CTDE). On the theory side, we prove that differentiable fuzzy partitions of unity endow the actor–critic maps with global Lipschitz regularity, reduce temporal-difference target variance, enlarge the input-to-state stability (ISS) margin, and yield a global $L_{\infty }$$\gamma$-contraction of fixed-policy evaluation (hence, non-expansive with $\kappa =\gamma <1$). We further state a two-time-scale convergence theorem for CTDE-TD3 with fuzzy features; a PL/last-layer-linear corollary implies point convergence and uniqueness of critics. We bound the projected Bellman residual with the correct contraction factor (for $L^{\infty }$ and $L^2\left(\rho \right)$ under measure invariance) and quantified the negative bias induced by $min\{Q_1,Q_2\}$; an N-agent extension is provided. Empirically, a balanced common-random-numbers design across seven scenarios and 20 seeds, analyzed by ANOVA and CRN-paired tests, shows that Fuzzy–MAT3D attains the highest mean MPPT efficiency ( $92.0$±$4.0$ ), outperforming MAT3D and Multi-Agent Deep Deterministic Policy Gradient controller (MADDPG). Overall, fuzzy regularization yields higher efficiency, suppresses steady-state oscillations, and stabilizes learning dynamics, supporting the use of structured, physics-compatible features in multi-agent MPPT controllers. At the level of PV plants, such gains under partial shading translate into higher effective capacity factors and smoother renewable generation without additional hardware.