July 8, 2022
Journal Article

Differentiable Predictive Control: Deep Learning Alternative to Explicit Model Predictive Control for Unknown Nonlinear Systems

Abstract

We present differentiable predictive control (DPC) as a deep learning-based alternative to the explicit model predictive control (MPC) for unknown nonlinear systems. The structure of the proposed neural architecture is inspired by the structure of an MPC, by i) using a prediction model capturing controlled system dynamics, ii) receding horizon optimal control action predictions, and iii) enforcing inequality constraints via penalty methods. In the DPC framework, a neural state-space model is learned from time-series measurements of the system dynamics. The control policy is then optimized via gradient descent approach by differentiating the closed-loop system dynamics model fully parametrized by deep neural networks. The proposed architecture allows to train the control policy tracking the distribution of reference signals and handle time-varying inequality constraints imposed on states and control actions. We experimentally demonstrate that it is possible to train generalizing constrained optimal control policies purely based on the observations of the dynamics of the unknown nonlinear system. The proposed control method is applied to a laboratory device in embedded implementation using a Raspberry-Pi platform. We compare the control performance of the proposed method against explicit MPC and report pivotal efficiency gains in online computational demands, memory requirements, policy complexity, and construction time. In particular, we show that our method scales linearly compared to exponential scalability of the explicit MPC solved via multiparametric programming, hence, opening doors for applications in nonlinear systems with a large number of variables, longer prediction horizons, and faster sampling rates that are beyond the reach of classical methods.

Published: July 8, 2022

Citation

Drgona J., K. Kis, A.R. Tuor, D.L. Vrabie, and M. Klauco. 2022. Differentiable Predictive Control: Deep Learning Alternative to Explicit Model Predictive Control for Unknown Nonlinear Systems. Journal of Process Control 116. PNNL-SA-162137. doi:10.1016/j.jprocont.2022.06.001