Robust stability properties of soft constrained MPC
Robust stability properties of soft constrained MPC
复制标题
软约束MPC的鲁棒稳定性特性
DOI：
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发表时间：
2010
期刊：
影响因子：
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通讯作者：
M. Morari
中科院分区：
文献类型：
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作者：
M. Zeilinger;C. Jones;M. Morari
在模型预测控制中，硬状态约束的执行可能过于保守甚至不可行，特别是在存在干扰的情况下。这项工作提出了一种软约束 MPC 方法，即使对于不稳定的系统也能提供闭环稳定性。采用两种类型的软约束：通过引入两种不同类型的松弛变量来放松沿水平线的状态约束，通过将目标从原点移动到可行的稳态来软化终端约束。所提出的方法显着扩大了吸引区域，并在可以强制执行所有状态约束时保留最佳行为。显示了所提出的控制律下标称系统的渐近稳定性，并分析了系统在加性扰动下的输入状态稳定性和鲁棒稳定性特性。
In Model Predictive Control, the enforcement of hard state constraints can be overly conservative or even infeasible, especially in the presence of disturbances. This work presents a soft constrained MPC approach that provides closed-loop stability even for unstable systems. Two types of soft constraints are employed: state constraints along the horizon are relaxed by the introduction of two different types of slack variables and the terminal constraint is softened by moving the target from the origin to a feasible steady-state. The proposed method significantly enlarges the region of attraction and preserves the optimal behavior whenever all state constraints can be enforced. Asymptotic stability of the nominal system under the proposed control law is shown, as well as input-to-state stability of the system under additive disturbances and the robust stability properties are analyzed.