Conventionally, the finite-horizon linear quadratic tracking (FHLQT) problem relies on solving the time-varying Riccati equations and the time-varying non-causal difference equations as the system dynamics is known. In this paper, with unknown system dynamics being considered, a Q-function-based model-free method is developed to solve the FHLQT problem. First, an augmented system consisting of the controlled system and the desired trajectory system is formulated, and the FHLQT problem transforms to the finite-horizon linear quadratic regulator (FHLQR) problem with the augmented system. Then, a time-varying Q-function which depends explicitly on the control input is defined. With the defined time-varying Q-function, a model-free finite-horizon control method is developed to approximate the solutions of the time-varying Riccati equations of the transformed FHLQR problem. At last, simulation studies are carried out to verify the validity of the developed method.

传统上，有限视界线性二次跟踪 (FHLQT) 问题依赖于求解时变 Riccati 方程和时变非因果差分方程，因为系统动力学是已知的。本文在考虑未知系统动力学的情况下，开发了一种基于Q函数的无模型方法来解决 FHLQT 问题。首先，制定了由受控系统和期望轨迹系统组成的增广系统，并利用增广系统将FHLQT问题转化为有限水平线性二次调节器（FHLQR）问题。然后，定义明确依赖于控制输入的时变Q函数。用定义的时变Q-函数，开发了一种无模型的有限范围控制方法来逼近变换后的 FHLQR 问题的时变 Riccati 方程的解。最后通过仿真研究验证了所开发方法的有效性。