This paper proposes a novel varying horizon economic model predictive control (EMPC) scheme without terminal constraints for constrained nonlinear systems with additive disturbances and unknown economic costs. The general regression learning framework with mixed kernels is first used to reconstruct the unknown cost. Then an online iterative procedure is developed to adjust the horizon adaptively. Again, an elegant horizon-dependent contraction constraint is designed to ensure the convergence of the closed-loop system to a neighborhood of the desired steady state. Moreover, sufficient conditions ensuring recursive feasibility and input-to-state stability are established for the system in closed-loop with the EMPC. The merits of the proposed scheme are verified by the simulations of a continuous stirred tank reactor and a four-tank system in terms of robustness, economic performance and online computational burden.
Xiong et al. (Mon,) studied this question.