Robust Nonlinear Model Predictive Control with Constraint Satisfaction: A Relaxation-based Approach
Robust Nonlinear Model Predictive Control with Constraint Satisfaction: A Relaxation-based Approach
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DOI：
10.3182/20140824-6-za-1003.02420
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发表时间：
2014
期刊：
影响因子：
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通讯作者：
S. Streif;M. Kögel;Tobias Bäthge;R. Findeisen
中科院分区：
文献类型：
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作者：
S. Streif;M. Kögel;Tobias Bäthge;R. Findeisen
摘要提出了一种保证鲁棒约束满足的非线性模型预测控制方案。该方案适用于多项式或有理系统，并保证状态，终端和输出约束鲁棒满足，尽管不确定和有界干扰，参数和状态测量或估计。此外，对于适当选择的终端集，在一个时间实例的潜在优化问题的可行性保证了约束鲁棒地满足所有未来的时间实例。该方案利用了一个半无限优化问题转化为一个双层优化问题：外部程序确定一个输入最小化标称非线性系统的性能指标，而几个内部程序证明鲁棒约束满足。我们使用凸松弛来处理内部程序中的非线性动力学问题。最后给出了一个仿真例子来说明该方法。
Abstract A nonlinear model predictive control scheme guaranteeing robust constraint satisfaction is presented. The scheme is applicable to polynomial or rational systems and guarantees that state, terminal, and output constraints are robustly satisfied despite uncertain and bounded disturbances, parameters, and state measurements or estimates. In addition, for a suitably chosen terminal set, feasibility of the underlying optimization problem at a time instance guarantees that the constraints are robustly satisfied for all future time instances. The proposed scheme utilizes a semi-infinite optimization problem reformulated as a bilevel optimization problem: The outer program determines an input minimizing a performance index for a nominal nonlinear system, while several inner programs certify robust constraint satisfaction. We use convex relaxations to deal with the nonlinear dynamics in the inner programs efficiently. A simulation example is presented to demonstrate the approach.