In this paper, we propose an iterative framework to solve optimal control for nonlinear proportional state-delay systems. The successive convexification technique is first implemented to convert the original nonlinear problem into a sequence of linear-quadratic problems. And a symplectic pseudospectral method, where the multi-interval pseudospectral scheme is applied with a proportional mesh, to solve the transformed problems is then developed based on the first-order necessary conditions. Each linear-quadratic problem is finally transformed into a system of linear algebraic equations with a sparse coefficient matrix. Due to the benefit of the successive convexification technique and the multi-interval pseudospectral method, initial guess on costate variables is avoided and converged solutions can be obtained with an exponential convergent rate. The proposed iterative framework is validated by four examples with distinct features, highlighting its numerical precision and efficiency. And either exponential or linear convergence property can be exhibited by tuning the approximation degree or the mesh number.

在本文中，我们提出了一个迭代框架来解决非线性比例状态延迟系统的最优控制。首先实施连续凸化技术，将原始非线性问题转换为一系列线性二次问题。然后基于一阶必要条件发展了一种辛伪谱方法，其中应用比例网格的多区间伪谱方案来解决变换问题。每个线性二次问题最终都转化为具有稀疏系数矩阵的线性代数方程组。由于连续凸化技术和多区间伪谱方法的好处，避免了对共态变量的初始猜测，并且可以以指数收敛速度获得收敛解。所提出的迭代框架通过四个具有不同特征的示例进行了验证，突出了其数值精度和效率。并且可以通过调整逼近度或网格数来表现指数或线性收敛特性。