Semidefinite Programming Approximation for a Matrix Optimization Problem over an Uncertain Linear System
Year: 2023
Type: preprint
Abstract: A matrix optimization problem over an uncertain linear system on finite horizon (abbreviated as MOPUL) is studied, in which the uncertain transition matrix is regarded as a decision variable. This problem is in general NP-hard. By using the given reference values of system outputs at each stage, we develop a polynomial-time solvable semidefinite programming (SDP) approximation model for the problem. The upper bound of the cumulative error between reference outputs and the optimal outputs of the approximation model is theoretically analyzed. Two special cases associated with specific applications are considered. The quality of the SDP approximate solutions in terms of feasibility and optimality is also analyzed. Results of numerical experiments are presented to show the influences of perturbed noises at reference outputs and control levels on the performance of SDP approximation.
Source: arXiv (Cornell University)
Authors: Xu, Jintao, Fang, Shu-Cherng, Xing, Wenxun
Institutions: Tsinghua University, North Carolina State University
Language: English
Subfield: Numerical Analysis
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Award: 凸二次约束二次规划问题的鲁棒灵敏度分析研究
OpenAlex ID: W4387075495