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

• Published in: International journal of robust and nonlinear control Vol. 34; no. 15; pp. 10424 - 10436
• Main Authors: Tian, Yu, He, Defeng, Mu, Jianbin
• Format: Journal Article
• Language: English
• Published: Hoboken, USA John Wiley & Sons, Inc 01.10.2024; Wiley Subscription Services, Inc
• Subjects: Algorithms; Constraints; Continuously stirred tank reactors; Control systems; Design optimization; economic optimization; event‐triggered control; model predictive control; Nonlinear control; Nonlinear systems; Performance prediction; Predictive control; Stability
• ISSN: 1049-8923; 1099-1239
• DOI: 10.1002/rnc.7521

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.