A Dual-Weighting and Adaptive Regularization Framework for Takagi–Sugeno Identification of Nonlinear Dynamic Systems from Closed-Loop Sensor Data

In sensor-based monitoring and control systems, dynamic models are often identified from data collected in closed loop (where the noisy sensor measurements that drive the controller are also regressors). Feedback links regressors to disturbances, which violates one of the basic assumptions of least squares and leads to biased—and sometimes highly unstable—estimates. This difficulty is worsened in Takagi–Sugeno (TS) models, as they involve global coupling: poorly excited regions can dominate the model. In this work, we address this by proposing Dual-Weighted Takagi–Sugeno Identification (DW-TSI), a framework that combines dual weighting with adaptive regularization. We achieve this through a rule-wise weighted least-squares formulation that decomposes the global problem into local subproblems, weighting each sample by its membership activation and preserving the interpretability of the local submodels in state space; an adaptive ridge term then scales the penalty of each rule inversely with its cumulative activation, ensuring that conditioning is reinforced exactly where the sensor data are weakest. The framework is extensively validated on an open-loop unstable physical aero-pendulum, identified using only closed-loop angular measurements. Unlike classical TS models, DW-TSI maintains boundedness in a multi-step autonomous simulation, and it approximates subspace identification (N4SID) accurately. A sensor noise injection study further shows that the proposed estimator degrades gracefully in the presence of measurement noise, whereas unregularized TS estimation collapses. These models can be deployed for sensor-based feedback control without any retuning.