A Novel Cellular Method for the Solution of Nonlinear Stochastic Optimal Control Problems

本研究计画针对非线性随机最优控制问题，提出一种新的求解方法，称为短时高斯胞映射法。 随机非线性最优控制问题可以发现在土木工程结构受到地震，海浪，风荷载激励，在精密机械，制造过程和机器人，并在武装车辆（陆地或空中），目标跟踪系统和制导系统在战斗或粗糙的环境中运行。 对于复杂的非线性系统，在随机激励作用下，获得最优控制解的有效方法很少。该方法已被应用到一些非常具有挑战性的非线性振子在高斯白色噪声激励下，并已被证明是有效的和准确的分析复杂的非线性随机系统。本计画进一步发展此方法于非线性随机最优控制问题。本研究的结果提供的能力，更有效地和准确地预测和控制非线性系统的随机激励的响应，以更好地评估系统的可靠性在恶劣的随机环境下，并开发新的策略，用于控制状态约束随机系统。

This research project deals with a new method, called the short-time Gaussian cell mapping method for solving nonlinear stochastic optimal control problems. Stochastic nonlinear optimal control problems can be found in civil engineering structures subject to earthquake, ocean waves, and wind loading excitations, in precision machines, manufacturing processes and robots, and in armed vehicles (land or air), target tracking systems and guidance systems operated in combat or rough environments. Few effective methods exist for obtaining optimal control solutions of complex nonlinear systems to random excitations. The method has been applied to some very challenging nonlinear oscillators under Gaussian white noise excitations and has been proven to be effective and accurate in analyzing complex nonlinear stochastic systems. This project develops this method further for nonlinear stochastic optimal control problems. The results of this research provide the capability to more efficiently and accurately predict and control the response of nonlinear systems subject to stochastic excitations, to better assess the reliability of the system under harsh random environments, and to develop new strategies for controlling the state-constrained stochastic system.