Optimization with few violated constraints and its application in controls

很少违反约束的优化是标准优化的一种变体，其中可能会违反少量的约束。当某些约束因建模不确定性和/或测量误差而不可靠时，它尤其有用。在这个方案中，我们证明了几个控制问题可以在极少违反约束的情况下在最优化框架内得到解决。一个例子是在存在孤立点的情况下具有收敛和数值效率的鲁棒系统辨识算法。然而，与标准优化不同的是，很少有违反约束的优化在文献中受到关注，并且几乎没有可用的结果。在论证了对控制问题进行少违反约束优化的必要性之后，我们给出了我们的初步结果，包括问题的建立、初步分析和一个求解少违反约束优化问题的数值算法。实验证明，该算法具有较低的计算复杂度。初步结果是非常有希望的。然后，在方案中概述了算法及其应用方面的详细研究计划。

Optimization with few violated constraints is a variant of the standard optimization in which a small number of constraints may be violated. It is especially useful when some of constraints are not reliable due to modeling uncertainty and/or measurement errors. In this proposal, we show that several control problems can be solved within the framework of opti-mization with few violated constraints. One example is a convergent and numerically efficient algoritlini for robust system identification in the presence of outliers.Unlike the standard optimization, however, optimization with few violated constraints has received little attention in the literature and few results are available. After demonstrating a need for optimization with few violated constraints for controls, we present our preliminary results in the proposal which include the problem set up, preliminary analysis and a numerical algorithm for solving optimization with few violated constraints. The algorithm is proven to have a low computational complexity. Preliminary results are very promising. Then, a detailed research plan in terms of the algorithm and its application is outlined in the proposal.