Different-Level Dynamic Quadratic Minimization Using Square Root Matrix Based Zhang Equivalency

For quadratic minimization (QM), it is usually assumed that the solution objective is time-invariant and at the same level. However, the QM is always time-varying (i.e., naturally and implicitly dynamic) and may be at different levels (i.e., explicitly dynamic) in practice. In this paper, different from the general QM, a novel different-level dynamic QM (DLDQM) is proposed and investigated. First, the DLDQM solving is split up into two general time-varying QM (TVQM) solving. Then, a solution model is thus proposed and investigated for the DLDQM, by applying square root matrix based Zhang equivalency and Moore-Penrose (MP) generalized inverse. In addition, it is worth pointing out that solving the DLDQM is a new and important attempt of this research. Finally, illustrative numerical experiments are conducted with numerical results presented and analyzed.