Adaptive Dynamic Programming With Unscented Kalman Filtering for Nonlinear Hysteresis Compensation in Magnetic Shielding Systems

Active magnetic compensation (AMC) systems are essential in precision industries, such as battery diagnostics and nondestructive testing. However, the inherent hysteretic nonlinearity of ferromagnetic shielding materials limits compensation accuracy: model-free methods struggle to capture path-dependent magnetization memory, while conventional optimal control faces fundamental challenges because hysteresis violates the Markovian assumption. This article proposes a physics-informed observer-based adaptive dynamic programming (ADP) framework with three key contributions. First, the non-Markovian nature of hysteretic AMC dynamics, which prevents direct application of Bellman’s optimality principle, is resolved by incorporating irreversible magnetization from the Jiles–Atherton (J–A) model as an augmented state variable, extending ADP applicability to memory-dependent systems. Second, the unmeasurability of this internal magnetization state is addressed through an augmented Unscented Kalman Filter that embeds J–A hysteresis dynamics into its prediction step, providing the ADP controller with complete state information. Third, closed-loop stability of the estimation-control architecture is established via Lyapunov-based input-to-state stability analysis under bounded estimation uncertainty. Experimental validation demonstrates 66.7% reduction in residual field mean absolute error compared to proportional–integral–derivative, 72.6% improvement over pseudopartial-derivative algorithm, and 24.7% enhancement over conventional ADP under multifrequency disturbances representative of industrial operating conditions.