Optimal control under hard and soft inequality constraints for non positive response systems

The authors have previously defined "non-positive response systems" as a subclass of non-minimum phase systems. Undesirable behaviour is noticed when such systems operate in the neighborhood of inequality type constraints on outputs. A stabilizing control was built for such systems in the light of model predictive control techniques. This paper shows two methods for coping with perturbation effects. It explains the necessity of changing the form of a hard output constraint. In the first method, if violated due to unknown perturbations, an inequality type hard constraint is temporarily modified in order to be able to bring the system back into its admissible domain. The second method introduces a soft constraint type over the receding horizon criterion and thus deals with the penalty function approach.