Necessary and Sufficient Conditions for Two Quadratic Equalities to Hold With Applications

• 成果类型: Article
• 署名作者: Zhang, Tianliang; Zhang, Weihai
• 署名单位: Qingdao University of Technology; Nanjing University of Science & Technology; Shandong University of Science & Technology
• 刊物名称: IEEE TRANSACTIONS ON AUTOMATIC CONTROL
• ISSN/ISSBN: 0018-9286
• DOI: 10.1109/TAC.2023.3284536
• 发表日期: 2023
• 页码: 8082-8086
• 关键词: Hamilton-Jacobi equation (HJE); Moore-Penrose pseudoinverse; quadratic equality; stochastic H-infinity control; stochastic linear quadratic (LQ) control

摘要

This note gives necessary and sufficient conditions for two quadratic equalities to hold based on Moore-Penrose pseudoinverse. The obtained results generalize the well-known identity x(T )Ax + x(T)b + b(T)x =(x + A(-1)b)(T )A(x + A(-1)b) - b(T)A(-1)b to the case of the nonexistence of A-1 . As applications, the previous results on indefinite stochastic linear quadratic optimal control can be easily retrieved, and some consequences on stochastic H-infinity control and nonlinear optimal control can be improved.