We address the design of optimal control strategies for high-dimensional stochastic dynamical systems. Such systems may be deterministic nonlinear systems evolving from random initial states, or systems driven by random parameters or random noise. The objective is to provide a validated new computational capability for optimal control which will be achieved more efficiently than current state-of-the-art methods. The new framework utilizes direct single or multi-shooting discretization, and is based on efficient vectorized gradient computation with adaptable memory management. The algorithm is demonstrated to be scalable to high-dimensional nonlinear control systems with random initial condition and unknown parameters. Numerical applications are presented and discussed for stochastic path planning problems involving models of unmanned aerial and ground vehicles, and for distributed control of a nonlinear advection-reaction-diffusion equation.

我们解决高维随机动力学系统的最优控制策略设计问题。这样的系统可以是从随机初始状态演变而来的确定性非线性系统，也可以是由随机参数或随机噪声驱动的系统。目的是提供一种经过验证的最佳控制新计算能力，该能力将比当前最新技术更有效地实现。新框架利用直接的单次或多次射击离散化，并且基于具有自适应内存管理的高效矢量化梯度计算。该算法被证明可扩展到具有随机初始条件和未知参数的高维非线性控制系统。