Robustness of Model Predictive Control Algorithms for Systems with Hard Constraints

The inclusion of hard constraints on inputs, outputs or other associated variables in a Model Predictive Control algorithm is the major attraction of this type of control laws. The presence of such constraints results in an on-line optimization problem that produces a nonlinear controller, even when the plant and model dynamics are assumed linear. The Contraction Mapping Principle has been applied to the operator mapping the state of the system (plant + controller) at sampling point k to that at k + 1 to obtain nominal and robust stability conditions for the nonlinear system. These conditions can be used to analyze the stability properties of the MPC algorithms and to obtain design insights by examining their variation during simulations of the system. Simple examples demonstrate the effectiveness of these conditions in capturing the nonlinear characteristics of the control system. The robustness conditions are also applied to a 2 × 2 subsystem of the Shell Standard Control Problem, which with its hard constraint specifications and the multiple performance objectives, is the kind of problem for which the use of an on-line optimizing control algorithm like Quadratic Dynamic Matrix Control (QDMC) seems to be an appropriate approach.