Stability of Barrier Model Predictive Control

In the last decades, industrial problems have tried to take into account constraints explicitly in the design of the control law. Model Predictive Control is one way to do so and has been extensively studied. However, most papers related to constrained Model Predictive Control often omit to consider nondifferentiable constraints and stability is not ensured when constraints are not satisfied. The aim of this paper is to propose a formulation of the cost function of a Model Predictive Control to ensure stability in face with input and state nondifferentiable constraints. For this purpose, a set where all constraints are satisfied is defined by means of the invariant set theory. Once this set is defined, the system is enforced to reach it and stay in, while guaranteeing stability thanks to the choice of a well suited Lyapunov function based on the cost function.