论文标题
非convex随机最佳控制问题连续近似的全局收敛
Global Convergence of Successive Approximations for Non-convex Stochastic Optimal Control Problems
论文作者
论文摘要
本文着重于找到控制域的随机最佳控制问题的近似解决方案，而状态轨迹受控制的随机微分方程的约束。与控制有关的扩散使传统的连续近似方法（MSA）不足以降低每次迭代中成本功能的价值。如果不增加执行哈密顿最小化的额外术语，则通过我们的新型误差估计值涉及更高阶段的向后伴随方程，MSA就足够了。在对系数的某些凸度假设（在控制域上没有凸度假设）下，随着迭代次数倾向于无限，成本功能的值降至全局最小值。特别是，一类广义线性二次系统可用收敛速率。
This paper focuses on finding approximate solutions to stochastic optimal control problems with control domains being not necessarily convex, where the state trajectory is subject to controlled stochastic differential equations. The control-dependent diffusions make the traditional method of successive approximations (MSA) insufficient to reduce the value of cost functional in each iteration. Without adding extra terms over which to perform the Hamiltonian minimization, the MSA becomes sufficient by our novel error estimate involving a higher order backward adjoint equation. Under certain convexity assumptions on the coefficients (no convexity assumptions on the control domains), the value of the cost functional descends to the global minimum as the number of iterations tends to infinity. In particular, a convergence rate is available for a class of generalized linear-quadratic systems.
