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本文通过对动力学系统模型和对带有约束条件的优化控制问题的分析，以系统的动力学优化控制问题为对象，进一步将带有对称编码的遗传算法应用于带有约束条件的优化问题的求解中．根据系统的终点和初始状态，提出了泛横向对称编码和泛纵向对称编码理论，为进一步拓展对称编码理论的应用空间提供了理论基础．在讨论了单输入和双输入的系统模型后，由定理１、定理２和定理３描述了对称编码自动满足系统的终点和初始状态约束的特点，这一理论的初步应用成果表明，以对称编码理论为核心的遗传算法的性能远好于普通的遗传算法，并可望其在机器学习、神经网络技术等领域中得到进一步应用．
In this paper, through the analysis of the dynamic system model and the optimization control problem with constraints, taking the system dynamics optimization control problem as an object, the genetic algorithm with symmetric coding is further applied to the optimization problem with constraints Solve. According to the end point and the initial state of the system, a pan-horizontal symmetric coding and a pan-longitudinal symmetric coding theory are proposed, which provides a theoretical basis for further expanding the application space of symmetric coding theory. After discussing single-input and double-input system models, the theorem 1, the theorem 2 and the theorem 3 describe that the symmetric coding automatically satisfies the characteristics of the system’s end point and the initial state constraints. The preliminary application results of this theory show that the symmetric coding The performance of the theory-based genetic algorithm is far better than that of the ordinary genetic algorithm, and it is expected to be further applied in the fields of machine learning and neural network technology.