(734i) Predictive Control of Solar Collector Energy System with Gaussian Process Priors of Uncertain Solar Irradiance

In this work, we study the application of the receding horizon optimal control for solar collector energy system governed by coupled nonlinear hyperbolic partial differential equations [1]. The optimal solution is calculated by using the calculus of variations approach. Solar irradiance is the only dominant source to provide heat to the system and suppose that current time solar irradiance can be measured by a solar irradiance measuring device such as pyranometer. In order to apply nonlinear model predictive control (MPC) techniques [2], the prediction of solar irradiance in future certain time horizon is necessary. In this work, we consider the multi-step ahead prediction of solar irradiance (time series) using non-parametric Gaussian process (GP) regression parametrized by mean and covariance function [3]. k-step ahead forecasting of a discrete-time non-linear dynamic system can be performed by doing repeated one-step ahead predictions. k-step ahead prediction method works as follows: it predicts only one time step ahead, using the estimate of the output of the current prediction, as well as previous outputs (up to the lag L), as the input to the prediction of the next time step, until the prediction k steps ahead is made. In the simulation part, the integration of GP model of solar irradiance and MPC is performed to achieve optimal outlet temperature trajectory tracking.

[1] Xu, Xiaodong, Yuan Yuan, and Stevan Dubljevic. "Receding horizon optimal operation and control of a solar‐thermal district heating system." AIChE Journal (2017)

[2] Van Pham, Thang, Didier Georges, and Gildas Besancon. "Predictive control with guaranteed stability for water hammer equations." IEEE transactions on automatic control 59.2 (2014): 465-470.

[3] Rasmussen, Carl Edward. "Gaussian processes in machine learning." Advanced lectures on machine learning. Springer, Berlin, Heidelberg, 2004. 63-71.