Temporal Deep Unfolding for Nonlinear Stochastic Optimal Control⁎⁎It turned out that the expanded version of this conference paper appeared first (Kishida and Ogura, 2022).

Intrinsically, many real control problems are mathematically challenging. Thus, we often relax the original problem to obtain a tractable problem. In this paper, we consider a computational technique to solving a nonlinear stochastic optimal control problem in a direct manner. Our computational approach employs the idea of the recently developed technique, called deep unfolding. Deep unfolding is a deep learning method that is model-based, used to accelerate iterative algorithms. For the finite-horizon optimal control problem, we regard each state transition of the discrete-time dynamical system with control inputs and disturbances as an iteration step. Then, we unfold those state transitions into the layers to construct a deep neural network so that each of those layers contains a trainable parameter of the control input. This produces a computational graph. Once the computational graph is fixed, the control inputs are computed by training the deep neural network. This open-loop method is then integrated into model predictive control to close the loop. The advantages of our computational technique are not only the ability of handling nonlinear state transitions and non-Gaussian disturbances, but also its simplicity. The feasibility and benefit of the proposed technique are demonstrated by numerical experiments using a continuous stirred tank reactor model, which is highly nonlinear.