This study is aimed at answering the famous question of how the approximation
errors at each iteration of Approximate Dynamic Programming (ADP) affect the
quality of the final results considering the fact that errors at each iteration
affect the next iteration. To this goal, convergence of Value Iteration scheme
of ADP for deterministic nonlinear optimal control problems with undiscounted
cost functions is investigated while considering the errors existing in
approximating respective functions. The boundedness of the results around the
optimal solution is obtained based on quantities which are known in a general
optimal control problem and assumptions which are verifiable. Moreover, since
the presence of the approximation errors leads to the deviation of the results
from optimality, sufficient conditions for stability of the system operated by
the result obtained after a finite number of value iterations, along with an
estimation of its region of attraction, are derived in terms of a calculable
upper bound of the control approximation error. Finally, the process of
implementation of the method on an orbital maneuver problem is investigated
through which the assumptions made in the theoretical developments are verified
and the sufficient conditions are applied for guaranteeing stability and near
optimality.

本研究探讨了近似动态规划中每次迭代的近似误差如何影响最终结果的质量，研究表明可以基于一些已知量和可验证的假设获得一定范围内的最优解，同时通过计算控制近似误差的上界得到系统稳定的充分条件，最后在轨道机动问题中验证了理论研究的假设并应用了稳定性与优化的条件。