性能维持的增广可行域Tube鲁棒经济模型预测控制

针对未知但有界扰动作用下的约束线性系统,提出一种性能维持的增广可行域Tube经济模型预测控制(tube economic model predictive control,TEMPC)策略.首先考虑经济性能优化目标和鲁棒稳定控制目标,构造TEMPC优化问题的隐式收缩约束,并对系统状态和控制约束进行紧缩Tube设计,给出增广可行域优化问题的数学描述;然后,引入线性分解增广名义终端状态和终端罚函数,扩大优化问题的初始可行域,在此基础上应用终端“三要素”和收缩原理,建立TEMPC策略的递推可行性和闭环系统关于最优经济平衡点有界稳定性的充分性条件,进而证明闭环性能在原初始可行域上的不变性;最后,通过对比仿真结果验证所提出策略的有效性和优越性.

Performance-preserved tube economic model predictive control with enlarged feasibility regions

This paper presents a performance-preserved tube economic model predictive control (TEMPC) scheme with enlarged feasibility regions for constrained linear systems subject to unknown but bounded disturbances. Firstly, using economic cost optimization objectives and robust stability control objectives, an inexplicitly contractive constraint of the TEMPC optimization problem is designed. Secondly, optimization problem with enlarged feasibility regions is formulated by the design of the tightening tubes on the system constraints on the state and control. Furthermore, the nominal terminal states and penalty functions are enlarged by adopting linear-decomposition, which increases the size of the initial feasible regions of the optimization problem. Then, using terminal triplet elements and the contractive principle, the sufficient conditions are established for guaranteeing the recursive feasibility of the TEMPC scheme and bounded stability of the closed-loop system with respective to the optimally economic equilibrium point. Moreover, the closed-loop performance is shown to be preserved in the original initial feasible region. Finally, the comparison simulation results verify the effectiveness and merits of the proposed scheme.