Abstract:Abstract: A new method was proposed for identifying the time history of the input excitation based on dynamic programming in time domain. Using the state-space formulation and the least square error method, the objective function is established between measured and identified system responses. Then Bellman's Principle of Optimality is commonly used for the minimization of the objective function to estimate the excitation forces, finally the dynamic programming method of identification formulations are deduced. The numerical example is provided to verify the proposed model, and satisfactory results are achieved even the measurement noise is taken into the measurement system responses.