Explicit stochastic Nonlinear Predictive Control based on Gaussian process models

Nonlinear Model Predictive Control (NMPC) algorithms are based on various nonlinear models. Recently, an on-line optimization approach for stochastic NMPC based on a Gaussian process model was proposed. A significant advantage of the Gaussian process models is that they provide information about prediction uncertainties, which would be of help in NMPC design. On the other hand, an explicit solution to the stochastic NMPC problem based on Gaussian process model would allow efficient on-line computations as well as verifiability of the implementation. This paper suggests an approximate multi-parametric Nonlinear Programming approach to explicit solution of stochastic NMPC problems for constrained nonlinear systems based on Gaussian process model. In particular, the reference tracking problem is considered. The approach builds an orthogonal search tree structure of the state space partition and consists in constructing a feasible PWL approximation to the optimal control sequence.