Solving Time-Varying Nonsymmetric Algebraic Riccati Equations With Zeroing Neural Dynamics

The problem of solving algebraic Riccati equations (AREs) and certain linear matrix equations which arise from the ARE frequently occur in applied and pure mathematics, science, and engineering applications. In this article, by considering the nonsymmetric ARE (NARE) as a general form of ARE, the time-varying NARE (TV-NARE) problem is proposed and investigated. As a particular case of TV-NARE, the time-invariant NARE (TI-NARE) problem is investigated too. Then, by employing the zeroing (or Zhang) neural dynamics (ZND) design, a ZND TV-NARE (ZNDTV-NARE) model and a ZND TI-NARE (ZNDTI-NARE) model are proposed and investigated. Also, by combining the ZNDTV-NARE model with the frozen-time Riccati equation (FTRE) approach to optimal control of linear time-varying (LTV) systems based on the state-dependent Riccati equation (SDRE) process, a hybrid ZND FTRE control (HZND-FTREC) model is developed and investigated. The effectiveness of the proposed dynamical systems is proven in ten numerical experiments, three of which include applications to LTV and nonlinear systems.