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摘要: 针对未知但有界扰动下约束非线性系统, 提出一种新的鲁棒经济模型预测控制(Economic model predictive control, EMPC)策略, 保证闭环系统对扰动输入具有输入到状态稳定性(Input-to-state stability, ISS). 基于微分对策原理, 分别优化经济目标函数和关于最优经济平衡点的鲁棒稳定性目标函数, 其中经济最优性与鲁棒稳定性是具有冲突的两个控制目标. 利用鲁棒稳定性目标最优值函数构造EMPC优化的隐式收缩约束, 建立鲁棒EMPC的递推可行性和闭环系统关于最优经济平衡点相对于有界扰动输入到状态稳定性结果. 最后以连续搅拌反应器为例, 对比仿真验证本文策略的有效性.Abstract: This paper proposes a novel robust economic model predictive control (EMPC) scheme of constrained nonlinear systems with unknown but bounded disturbances, with guaranteed input-to-state stability (ISS) of the closed-loop system with respect to the disturbance. Based on the principle of differential game, economic objective functions and robust stability objective functions on economically optimal equilibrium points are optimized simultaneously, which are two conflicting control goals. The optimal value function of the robust objective is used to design an implicit contractive constraint of the EMPC optimization, which guarantees ISS of the closed-loop system at the equilibrium point with respect to the disturbance. Some sufficient conditions for recursive feasibility and ISS with respect to the disturbance are presented. Finally, an example of a continuously stirred tank reactor is utilized to illustrate the effectiveness of the proposed scheme.
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图 2 持续扰动
$w(k)=0.1436\sin(k/2) $ 的仿真结果Fig. 2 Simulation results under continuous disturbance
$w(k)=0.1436\sin(k/2) $ 
图 3 持续扰动
$w(k)=0.1436\exp(-k/10) $ 的仿真结果Fig. 3 Simulation results under continuous disturbance
$w(k)=0.1436\exp(-k/10) $ 
图 5 不同初始状态的闭环系统相轨迹
Fig. 5 Phase trajectories of the closed-loop system from different initial states
表 1 平均经济性能和收敛过渡时间
Table 1 Average economic performance and transient time
$\lambda $ $w(k)= 0.1436\sin ( {k/} 2 )$ $w(k)=0.1436\exp( - {{k/} }10)$ ${J_{{\rm{ave}}} } $ ${J_{{\rm{ave}}} } $ ${ {{T} }_{ {\text{tr} } } }$ 0.1 −3.4361 −3.3953 49Ts 0.3 −3.4464 −3.4019 54Ts 0.5 −3.4553 −3.4083 58Ts 0.7 −3.4623 −3.4143 65Ts 0.9 −3.4712 −3.4194 74Ts 
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