Improving the Accuracy of Sample-based Model Predictive Control via Sample-based Newton-like method with Approximated Hessian and Gradient by Quadratic Regression

Model predictive control (MPC) is garnering attention in various fields owing to its attractive characteristics such as its direct use in non-linear dynamic models, and application in multivariable constrained optimal control problems. In particular, an advanced method called sample-based MPC demonstrates several excellent characteristics and aims to resolve challenging practical examples. In this study, we present the results of a sample-based MPC controlling extremely challenging tasks that the existing gradient-based MPC fails to manage appropriately. However, the sample-based MPC exhibits an unresolved fatal defect owing to its probabilistic features. The most well-known defect caused by these features is the irregular waveform of the estimated optimal control input such as that in Brownian motion under steady-state conditions. Thus, we propose a Newton-like method based on quadratic regression that incorporated a sample-based MPC scheme. As the proposed method does not require prior derivation of the first and second derivatives of the cost (or objective) function, it can improve the defects without interfering with the excellent characteristics of the sample-based MPC.