求解最优控制问题的一类单调时间离散格式OA
A Monotonic Time-Discretized Scheme for Optimal Control Problems
近期,Breitenbach和Borzì 构造了一类求解常微分方程最优控制问题的序列二次Hamilton(sequential quad-ratic Hamiltonian,SQH)方法.他们证明了该迭代方法在连续时间情形下的单调收敛性.然而,该迭代方法在离散时间情形下的收敛性质尚未被解决.该文构造了一类中点时间离散格式,并证明了其能保持SQH迭代的单调收敛性.数值实验验证了该方法的有效性及收敛性.
Recently,Breitenbach and Borzì proposed a sequential quadratic Hamiltonian method for solving op-timal control problems.They proved the monotonic convergence of the algorithm in the continuous time case.However,the properties of the discrete version of the iterative procedure have not been tackled yet.A midpoint time-discretized scheme preserving the monotonic properties of the sequential quadratic Hamiltonian method was presented.Numerical experiments show the effectiveness and convergence of the proposed algorithm.
向清清;陈浩
重庆师范大学 数学科学学院,重庆 401331重庆师范大学 数学科学学院,重庆 401331
数理科学
最优控制问题序列二次Hamilton方法单调时间离散格式收敛性
optimal control problemsequential quadratic Hamiltonian methodmonotonic time-discretized schemeconvergence
《应用数学和力学》 2026 (2)
230-242,13
重庆市自然科学基金(CSTB2025NSCQ-GPX1015)
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