Guaranteed Gaussian Process Predictive Control for Lipschitz Nonlinear System with Input and State Constraints

Though model predictive control can systematically handle the control problem of multi-input multi-output system under state and input constraints, it heavily depends upon the model of the controlled system. The non-parametric nature of the Gaussian Process endows it with the flexibility of modeling various practical systems and, more importantly, the ability to provide the level of confidence in its predictions, which makes it preferable to the model predictive control. Therefore, in this paper, these two approaches are combined into a whole scheme, called the Gaussian Process Predictive Control, which can make the system avoid some relatively uncertain areas, through incorporating the variance into the objective function. Then with some mild assumptions, the closed system stability and recursive feasibility is guaranteed theoretically, and validated by a standard simulation example.