Robust constrained model predictive control using linear matrix inequalities
Robust constrained model predictive control using linear matrix inequalities
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DOI：
10.1109/acc.1994.751775
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发表时间：
1994-06
期刊：
影响因子：
--
通讯作者：
M. Kothare;V. Balakrishnan;M. Morari
中科院分区：
文献类型：
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作者：
M. Kothare;V. Balakrishnan;M. Morari
模型预测控制（MPC）当前设计技术的主要缺点是它们无法明确处理模型不确定性。在本文中，作者通过在MPC问题的公式表述中直接纳入对对象不确定性的描述来解决MPC中的鲁棒性问题。通过允许离散时间对象的状态空间矩阵任意时变且属于一个多面体，在时域中表达对象的不确定性。使无穷时域目标函数的上界最小化并满足输入和输出约束的反馈控制律的存在性问题被归结为关于线性矩阵不等式（LMI）的凸优化问题。结果表明，对于由多面体描述的对象不确定性，可行的滚动时域状态反馈控制设计是鲁棒稳定的。
The primary disadvantage of current design techniques for model predictive control (MPC) is their inability to explicitly deal with model uncertainty. In this paper, the authors address the robustness issue in MPC by directly incorporating the description of plant uncertainty in the MPC problem formulation. The plant uncertainty is expressed in the time-domain by allowing the state-space matrices of the discrete-time plant to be arbitrarily time-varying and belonging to a polytope. The existence of a feedback control law minimizing an upper bound on the infinite horizon objective function and satisfying the input and output constraints is reduced to a convex optimization over linear matrix inequalities (LMIs). It is shown that for the plant uncertainty described by the polytope, the feasible receding horizon state feedback control design is robustly stabilizing.