Robust model predictive control based on interval predictor estimation

Abstract

When considering three uncertainties in one state space equation, the interval predictors are constructed for state estimation and prediction output respectively through our own algebraic computations. After applying this interval predictor of prediction output into robust model predictive control strategy, one min-max optimisation problem is solved to obtain the optimal control input. Max operation is used to embody that the prediction output is not a constant value, but one interval. Using the parabola property of the cost function in max operation, we derive that the max operation is one piecewise quadratic function, whose expansion needs more knowledge about some unknown variables. To avoid these knowledge about unknown variables, all control input and prediction output are regarded as decision variables simultaneously, then this robust model predictive control can be formulated as a quadratic programming problem with inequality constrained condition.