Stochastic Model Predictive Control: An Alternative Approach for the Online Implementation

M. Nechtelberger and A. Hofer (Austria)


Model Predictive Control, open loop optimal control, sto chastic linear time variant system, online implementation, quadratic programming


Model Predictive Control also called Receding Horizon Control with quadratic cost function and linear constraints is a very widely used multivariable control design tech nique. In the presence of uncertainty, the standard MPC formulation is not necessarily the best solution possible. In this paper, linear stochastic systems are investigated under optimal open loop control. By taking the uncertainty ex plicitly into account in the MPC scheme, an increase of performance is possible, because the optimal solution of the standard MPC scheme applied to the stochastic plant is in general just a suboptimal solution of the stochas tic MPC control. This paper shows that in the presence of input constraints the stochastic MPC formulation can be written as quadratic optimization problem (QP) of very small dimension that grows only linearly with the predic tion horizon N. Thus, an efficient online implementation exists.

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