基于模拟退火算法的最优控制问题全局优化

参数化后的最优控制问题是一类高维非光滑非线性约束优化问题，传统的非线性规划算法求解时存在着收敛性差、局部收敛等问题。针对上述问题，该文采用多重参数化方法处理最优控制问题，非可微精确罚函数方法处理约束条件，引入了具有良好全局收敛性的模拟退火算法求解参数化后的最优控制问题。典型的时间最优和燃料最优控制问题的求解结果表明：模拟退火算法有着可靠的全局收敛性，优于遗传算法以及序列二次规划等经典优化算法。

Global Optimization of Optimal Control Problems Based on Simulated Annealing

The parameterized problem of optimal control problem is always a non-convex, high-dimension nonlinear constrained one, and the classical nonlinear programming algorithms are subject to poor convergence and local solution for solving the parameterized optimal control problem.In order to overcome these problems, the optimal control problem was conversed into a parameter optimization one by multiple parameterized methods, and the indifferentiable accurate penalty function was to deal with constraints.The simulated annealing with good global convergence ability was adopted to solve the parameter optimization problem. The numerical results from the solution to the two classical optimal control problems including a time-optimal problem and a fuel-optimal problem show that the simulated annealing has high global convergence reliability, and its performance is superior to the genetic algorithm and the classical optimization algorithms such as sequential quadratic programming.