Distributionally Robust Surrogate Optimal Control for Large-Scale Dynamical Systems

This paper explores tractable robust optimal control of nonlinear systems with large state spaces. Conventional applications of surrogate modeling for control replace the underlying dynamical model with a data-driven surrogate function. For large-scale systems, this approach possesses a host of shortcomings. We address these challenges by presenting a novel robust surrogate optimization framework for finite-time and receding horizon optimal control. Rather than modeling the entire state transition function, we define a surrogate model which maps the initial state and time series of control inputs to an approximate objective function value. We also define surrogate models which predict time series of relevant constraint functions. Since the bulk of the relevant information is encoded in the initial state, we apply a principal component analysis to project the state onto a reduced basis, allowing surrogate models with tractable parameterizations. To guarantee constraint satisfaction, we use φ-divergence to formulate distributionally robust chance constraints which are satisfied for worst-case realizations of the test data modeling error distribution. We validate our approach using a case study of optimal lithium-ion battery fast charging using a large-scale electrochemical battery model.