A new scalable algorithm for computational optimal control under uncertainty

Abstract

We address the design and synthesis 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 processes. 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.

23 pages, 17 figures

References in corpus (4)

• TensorFlow: A system for large-scale machine learning
• Polynomial approximation of high-dimensional Hamilton-Jacobi-Bellman equations and applications to feedback control of semilinear parabolic PDEs
• The Numerical Approximation of Nonlinear Functionals and Functional Differential Equations
• Stability analysis of hierarchical tensor methods for time-dependent PDEs

Cited by in corpus (7)

• On some neural network architectures that can represent viscosity solutions of certain high dimensional Hamilton--Jacobi partial differential equations
• Neural network architectures using min-plus algebra for solving certain high dimensional optimal control problems and Hamilton-Jacobi PDEs
• Optimal Control of ensembles of dynamical systems
• Overcoming the curse of dimensionality for some Hamilton--Jacobi partial differential equations via neural network architectures
• Lax-Oleinik-type formulas and efficient algorithms for certain high-dimensional optimal control problems
• Average Optimal Control of Uncertain Control-Affine Systems
• Hopf-type representation formulas and efficient algorithms for certain high-dimensional optimal control problems