Differentiable Predictive Control: An MPC Alternative for Unknown Nonlinear Systems using Constrained Deep Learning

We present an alternative to model predictive control (MPC) for unknown nonlinear systems in low-resource embedded device settings. The structure of the presented data-driven control policy learning method, Differentiable Predictive Control (DPC), echos the structure of classical 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. However, contrary to MPC, the presented control architecture does not require the system dynamics model to synthesize the control policy. Instead, a dynamics model is learned end-to-end from time-series measurements of the system dynamics in the off-policy setup. The control policy is then optimized via gradient descent by differentiating the closed-loop system dynamics model. The proposed architecture allows to train the control policy to track the distribution of reference signals and handle time-varying inequality constraints. 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 micro-controller. We demonstrate superior reference tracking control performance compared to classical explicit MPC and a baseline PI controller, and pivotal efficiency gains in online computational demands, memory requirements, policy complexity, and construction. Beyond improved control performance, the DPC 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 and fast sampling rates which are beyond the reach of classical explicit MPC.