A Model Predictive Control scheme with Ultimate Bound for Economic Optimization

This paper presents a Model Predictive Control (MPC) scheme for nonlinear continuous-time systems where an economic stage cost, which is not a measure of the distance to a desired set point, is combined with a classic stabilizing stage cost. The associated control strategy leads to a closed-loop behavior that compromises, in a seamless way, between the convergence of the closed-loop state trajectory to a given steady-state and the minimization of the economic cost. More precisely, we derive a set of sufficient conditions under which the closed-loop state trajectory is ultimately bounded around the desired steady-state, with the size of the bound being proportional to the strength of the economic cost. Numerical results show the effectiveness of the proposed scheme on a target estimation and tracking control problem.