Spatiotemporal learning-based stochastic MPC with applications in aero-engine control

Abstract

To deal with the issue of model uncertainty, extensive stochastic MPC methods have been investigated, where the uncertainties are typically assumed to follow given statistical distributions. However, in practical scenarios, the statistical properties of model uncertainties may depend on certain hyperparameters varying both temporally and spatially. For instance, in the applications of aero-engine control, different types of uncertainties may occur under different operational conditions, such as flight altitudes and Mach numbers, which are dynamically changing. Traditionally, the stochastic MPC methods may not be able to handle these types of uncertainties directly. Therefore, we propose a spatiotemporal learning-based stochastic model predictive control algorithm to study the stochastic optimal control problem with dynamically changing uncertainties, by constructing spatiotemporal Gaussian processes (GPs) to approximate the uncertainties based on measurement data. Since the spatiotemporal GPs may be difficult to evaluate with long processing time series, we present a state–space representation of GPs to employ computationally efficient Kalman filtering. Then, we derive a computationally tractable control strategy by parameterizing the controller and reformulating the cost and chance constraints, and analyze the corresponding recursive feasibility and closed-loop stability. Finally, the proposed algorithm is applied to the compressor control of the aero-engine, and the comparisons with other MPC controllers are demonstrated to show the effectiveness of our methods.