Nonlinear Model Predictive Control with Latent Force Models

Abstract

This paper shows how model predictive control of a nonlinear system with a time-dependent autocorrelated disturbance can be realized in a computationally efficient way. To this end, the disturbance is modeled as a Gaussian process that can be reformulated as a linear state space model driven by white Gaussian noise. This disturbance model is combined with a first-principles physical system model resulting in a latent force model. In this way, the current states and the disturbance can be estimated using the unscented Kalman filter. Moreover, the disturbance model can be used to predict future values of the disturbance, which is necessary for predictive control. In order to further reduce the computational effort of the algorithm, a separate predictor for the linear disturbance subsystem is outlined. The predicted disturbance and the estimated states are used to formulate the optimization problem of a model predictive controller. The proposed approach is evaluated numerically using the example of a two-dimensional overhead crane. It is shown that the algorithm is real-time capable with computation times in the sub-millisecond range.