Tractable Data-Driven Model Predictive Control Using One-Step Neural Networks Predictors

Abstract

Model Predictive Control (MPC) is a popular control strategy that relies on the availability of a prediction model to estimate future system trajectories over a finite time horizon. Recently, researchers have introduced Neural Networks (NNs) into the MPC framework for the development of data-driven prediction models. In MPC, the control actions are computed by solving iteratively, at each time-step, an optimization problem subject to state and input constraints. Finding the optimal solution to such a problem is a crucial challenge in the data-driven setting, due to the complexity and black-box nature of data-driven models such as NNs. This paper addresses this challenge by proposing a hierarchical deep NN formed by a set of cascading one-step NN predictors whose combination constitutes an interpretable prediction model over the entire prediction horizon. Thanks to the proposed NN architecture, it is shown that the resulting optimal control problem is tractable, as it can be solved by employing efficient iterative algorithms, and interpretable, so that input and state constraints can be enforced seamlessly. The effectiveness of the proposed method is validated through numerical simulations. Note to Practitioners—Model Predictive Control (MPC) is a widely used methodology in the industry which typically relies on the availability of a model in the form of step response, transfer function or state-space models. In some cases, the explicit model might not be available or its accuracy may be not sufficient for the required closed-loop performance. This paper aims to develop a simple and practical framework for deploying a model-free data-driven MPC solution based on deep learning. This objective is pursued by suggesting a novel approach using simple neural networks in a cascading interpretable structure. Such networks are used to predict the one-step evolution of the system, and their cascade represents the MPC prediction model over an arbitrary long prediction horizon. We characterize such a neural model focusing on its interpretability and tractability, deriving the resulting optimal control problem to be solved in a receding horizon strategy. We then show that the MPC optimization can be solved efficiently using highly efficient iterative algorithms that can be implemented in practice. Numerical simulations involving the use of the Alternating Direction Method of Multipliers (ADMM) algorithm show its effectiveness for both linear and nonlinear systems.