Handling State and Output Constraints in MPC Using Time-dependent Weights

A popular method for handling state and output constraints in a model predictive control (MPC) algorithm is to use 'soft constraints', in which penalty terms are added directly to the objective function. Improved closed loop performance can be obtained for plants with nontninimum phase zeros by modifying the MPC formulation to include suitably-designed time-dependent weights on the penalty terms associated with the state and output constraints. When the penalty terms are written in terms of the 'worst-ease' l-infinity norm, incorporating the appropriate time dependence into the weights provides much better closed loop performance. The approach is illustrated using two multivariable plants with nonminimum phase transmission zeros, where the time-dependent weights cause the open loop predictions to coincide with closed loop predictions, which results in a reduction of output constraint violations.