Nonlinear Model Predictive Control (NMPC) involves the solution at each sampling instant of a finite horizon optimal control problem subject to nonlinear system dynamics, and state and input constraints. Mathematical models of engineering systems usually contain some amount of uncertainty. In the robust NMPC problem formulation, the model uncertainty is taken into account. This paper presents an approximate multi-parametric Nonlinear Programming approach to explicit solution of feedback stochastic MPC problems for constrained nonlinear systems in the presence of stochastic uncertainty. It is assumed that the discrete probability distribution of the uncertainty is known. The mathematical expectation of the cost function is minimized subject to state and input constraints. The approximate explicit approach constructs a piecewise nonlinear approximation to the optimal sequence of feedback control policies. It is demonstrated by explicit feedback stochastic NMPC for a cart moving on a plane and attached to the wall via a spring.
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