A new approach of analyzing time-varying dynamical equation via an optimal principle

In this paper, an innovative design approach is proposed to solve time-varying dynamical equation, including matrix inverse equation and Sylvester equation. Based on the precondition of the existing solution of time-varying dynamical equation, different from previous approach to solve unknown matrix, an optimal design principle is used to solve the unknown variables. A performance index is introduced based on the inherent properties of the time-varying dynamical equation and Euler equation. The solution of time-varying dynamical equation is converted to an optimal problem of performance index. Furthermore, convergence and sensitivity to additive noise are also analyzed, and simulation results confirm that the method is feasible and effective. Especially, in simulations we design a tunable positive parameter in the dynamic optimization model. The tunable parameter is not only helpful to accelerate its convergence but also reduce its sensitivity to additive noise. Meanwhile the comparative simulation results are shown for the convergence accuracy and robustness of this method.