The transient-state acceleration control of aircraft engines has consistently been a focal point in the field of aircraft engine control research. To address the controller design problem of transient-state acceleration in aircraft engines based on switched linear systems, a data-driven optimization control algorithm is proposed. First, the optimization control problem for the transient-state acceleration process of aircraft engines is mathematically described. Subsequently, the Bellman optimal criterion in optimal control is utilized to derive the invariance of a value function at switching instants, providing an initial value for the optimization of the next subsystem. The optimization problem is then transformed into solving a Lyapunov equation using the principles of dynamic programming, and an iterative adaptive dynamic programming (ADP) algorithm is introduced to obtain optimal feedback control gains, which makes the solution of Lyapunov equation approach the optimal solution infinitely. Finally, simulation validation is conducted on a switched linear system for the transient-state acceleration of a specific aircraft engine. The effectiveness and superiority of the proposed algorithm are verified by comparing to traditional proportion integral differential (PID) control algorithms and active disturbance rejection control (ADRC).