Shrinking economic MPC of constrained nonlinear systems: An event‐triggered constraint relaxation approach

Abstract This article proposes a novel event‐triggered economic model predictive control (EMPC) scheme with shrinking prediction horizon of nonlinear systems subject to the constraints on the state and control. Some auxiliary positive‐definite functions at economic optimal equilibrium points are defined for economic performance functions. The optimal value function of the auxiliary function is used to design an adjustable stability constraint, which is imposed on the original EMPC optimization problem. The stability constraint is relaxed to design the triggered scheme avoiding Zeno behavior, while the prediction horizon is shrinked in different degrees by judging whether the last state within the triggered interval is in the terminal region. The involved parameter can be used to achieve a sensible compromise between system performance and computational complexity. The sufficient conditions guaranteeing the recursive feasibility and stability of the EMPC are derived. Finally, the effectiveness of the algorithm is illustrated by a continuously stirred tank reactor example.