The interturbine burner (ITB) engine, which is introduced between high and low pressure turbines (LPTs), is a relatively new concept for increasing specific thrust and lowering high altitude specific fuel consumption (SFC) than engine with afterburner (AB). Although ITB engines have outstanding performance improvements, they also present a challenge to the design of control laws for ITB engines under unknown matching mechanisms and multiple constraints. This study proposes a self-scheduling control law design method for ITB engine mode transition that considers ITB ignition and flameout characteristics, as well as cooling air volume. This method derives the control law based on the global optimal algorithm and shapley additive explanation (SHAP)-value analysis method, which avoids manual analysis and reduces the number of adjustment of variable geometric components. An ITB transient model is established to verify the control laws under the transition of ignition and flameout modes. During the mode transition process of opening and closing the ITB, the flow fluctuation of the precritical point and rear-critical point does not exceed 2%, and the comprehensive thrust fluctuation index composed of three typical state points does not exceed 5%. Through simulation analysis with constrained constraints, at most one variable geometry component is adjusted.