Nonlinear Data-Driven Predictive Control Using Deep Subspace Prediction Networks

Indirect data-driven predictive control (DPC) algorithms for nonlinear systems typically employ multi-step predictors, which are identified from input-output data using neural networks. In this paper we put forward a unifying multi-step prediction network architecture, i.e., the deep subspace prediction network (DSPN). We then prove that the DSPN architecture specialized to multi-layer-perceptron neural networks recovers the linear predictor corresponding to subspace predictive control for a sufficient number of hidden layer neurons. Hence, we establish a well-posed generalization of subspace predictive control for nonlinear systems. Moreover, we develop a regularized DSPN architecture that embeds a linear subspace predictor to improve extrapolation properties for non-training data. Simulation results on a benchmark inverted pendulum show that nonlinear DPC based on DSPN achieves high control performance for both noiseless and noisy data.