Approximate moving horizon estimation and robust nonlinear model predictive control via deep learning

Abstract Optimization-based methods for output-feedback control enable dealing with multiple-input and multiple-output nonlinear systems in the presence of uncertainties and constraints. The combination of moving horizon estimation (MHE) and nonlinear model predictive control (NMPC) can be especially powerful because of its general formulation but its implementation requires solving two optimization problems at every sampling instant, which can be challenging due to hardware or time constraints. We propose to take advantage of the expressive capabilities of deep neural networks to approximate the solution of the MHE and NMPC problems. By substituting the MHE and NMPC with their learning-based counterparts, the required online computations are significantly reduced. We also propose to use sensitivity analysis to compute an approximate upper-bound of the maximum one-step divergence from the optimal performance caused by the approximation error. The efficacy of the proposed learning-based approach is illustrated with simulation results of a semi-batch reactor for industrial polymerization.