Quadratic costs do not always work in MPC
Quadratic costs do not always work in MPC
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DOI：
10.1016/j.automatica.2017.04.058
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发表时间：
2017-08-01
期刊：
影响因子：
6.4
通讯作者：
Worthmann, Karl
中科院分区：
文献类型：
--
作者：
Mueller, Matthias A.;Worthmann, Karl
我们考虑无终端成本和约束的模型预测控制(MPC)。首先，我们严格地证明了基于二次阶段代价的预测控制可能失效，即不存在预测时间长度使得虽然系统是有限时间可控的，但预测控制闭环系统的(受控)平衡点是渐近稳定的。因此，只要采用纯二次代价，无限水平最优控制问题的稳定性一般不能在预测控制中保持。这说明了用阶段费用作为设计参数来实现渐近稳定的必要性。此外，我们放宽了在没有终端成本和约束的情况下用于预测控制的标准可控性假设，以减轻其验证。(C)2017爱思唯尔有限公司。保留所有权利。
We consider model predictive control (MPC) without terminal costs and constraints. Firstly, we rigorously show that MPC based on quadratic stage costs may fail, i.e., there does not exist a prediction horizon length such that a (controlled) equilibrium is asymptotically stable for the MPC closed loop although the system is, e.g., finite time controllable. Hence, stability properties of the infinite horizon optimal control problem are, in general, not preserved in MPC as long as purely quadratic costs are employed. This shows the necessity of using the stage cost as a design parameter to achieve asymptotic stability. Furthermore, we relax the standard controllability assumption employed in MPC without terminal costs and constraints to alleviate its verification. (C) 2017 Elsevier Ltd. All rights reserved.