Identification-Based Zero-Sum Tracking Control for Linear Composite Systems with Unmeasured Disturbances

This paper develops an identification-based implementation of zero-sum tracking control for a linear composite plant with an unmeasured shared disturbance. Weak-form regression estimates unknown coefficients from sampled states, the applied input, and a known reference, with an instrumental-variable projection compared against ordinary weak least squares. A common identified model supplies the regulator equations and a full-system game Riccati equation retaining both disturbance channels. A square-completion identity gives the exact-model saddle interpretation under explicit admissibility conditions. A separate uncertainty-dependent stability margin and tracking bound retain the effect of reference mismatch. Two simulation models are tested under five disturbance laws, recording noise, parameter changes and weak excitation. A deterministic tracking adaptation of a recent two-loop game-PI algorithm is additionally implemented, with its required extra disturbance record. It achieves more accurate noiseless gains, while IV-game passes 80/80 paired noisy-trial screens versus 35/80 for this comparator under the specified protocol. Warm, paired offline timings are also reported. The unequal sensor information, supplied initial policies and rejected candidates are explicitly documented. These results support the stated acquisition protocol, but not exact identification under arbitrary hidden disturbances, universal superiority, or hardware real-time guarantees.