A Novel Solution for Solving Time-Varying Algebraic Riccati Equations and Its Application to Sound Source Tracking

Abstract

Solving time-varying algebraic Riccati equations (TVAREs) is crucial in sound source tracking and optimal control. It is worth noting that previous studies have focused primarily on solving static algebraic Riccati equations (AREs) or interference-free TVAREs. Nonetheless, in real-world solution systems, AREs are often time-varying and subject to a variety of external disturbances. To address these problems, we propose two strong initial state discrete noise-resistant zeroing neurodynamics (SDRZND) algorithms for determining the solutions to TVAREs. First, we introduce a bounded smoothing of the strong initial state coefficient to accelerate algorithm convergence while avoiding the additional impulse noise that nonsmoothed coefficients in the discrete algorithm might generate. Then, an integral feedback term is designed and integrated with this coefficient to enhance the algorithm’s robustness. Subsequently, to further improve the algorithm’s flexibility, we introduce a variable time step, leading to the SDRZND-Euler (SDRZND-E) and SDRZND-Taylor–Zhang (SDRZND-TZ) algorithms presented in this article. Lastly, the effectiveness, noise resistance, and practicality of these algorithms are verified through theoretical analysis, numerical simulations, and sound source tracking experiments.