Such an online optimization-based control scheme can find wide applications in various fields such as process industries (Rawlings, 2000, Venkat et al., 2008), smart grid (Hassine, Naouar, & Mrabet-Bellaaj, 2017), networked systems (Wu et al., 2016, Yang et al., 2017), and mechatronic systems (Li et al., 2017a, Shen et al., 2018). The basic principle of MPC is to, at each step, solve a finite horizon constrained optimization problem formulated based on the current system state to stabilize dynamic systems. Model predictive control (MPC) or receding horizon control (RHC) has attracted increasing interest in both academia and industry in recent years.
Finally, numerical comparison results on two examples of dynamic systems are reported to demonstrate the effectiveness of the developed strategy. We establish the conditions of ensuring the recursive feasibility and asymptotic stability of the closed-loop system. Moreover, by appropriately tuning the sliding mode parameters, the conventional terminal constraints and large prediction horizon typically used in the literature are no longer required. Thanks to it, the proposed MPC strategy can stabilize the constrained nonlinear system of which the corresponding linearization around the equilibrium is non-stabilizable. This SMC law developed for the linearized model helps compensate the model mismatch between the linearization and the original nonlinear system model. In this paper, a terminal cost characterized by an implicit sliding mode control (SMC) law is proposed for developing a stabilizing constrained MPC scheme. Yet, they inherently and largely limit the size of the feasible region and restrict the use of MPC to practical applications.
It is well-known that terminal state constraints play an instrumental role in ensuring the feasibility and stability of the nonlinear model predictive control (MPC).
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