Min–Max MPC based on an upper bound of the worst case cost with guaranteed stability. Application to a pilot plant

Min–Max MPC (MMMPC) offers the possibility to consider disturbances and uncertainties in the mathematical model used to predict the future trajectory of the system. The explicit consideration of disturbances and uncertainties in order to obtain a more robust control performance complicates the practical implementation of MMMPC due to the high computational burden required to compute the control law. The computational complexity of the optimization problem can be reduced by using approximate solutions or upper bounds of the worst case cost of the objective function. A computationally efficient MMMPC strategy based on such an upper bound was presented in a previous work also published in this journal (see Section 1). One of the main drawbacks of that strategy is the lack of a stability guarantee. In this paper it is shown that input-to-state practical stability of the MMMPC strategy can be guaranteed if a certain initial condition and a semi-feedback approach are used. Furthermore, the MMMPC strategy is validated in experiments with a continuous stirred tank reactor in which the temperature of the reactor is controlled. The behavior of the system and the controller are illustrated by means of experimental results.