2017/09/15 by Bin Zhou, Zhou, Bin
Engineering · Mathematics · #Advanced Control Systems Optimization #Dynamical Systems (math.DS) #FOS: Mathematics #Numerical methods for differential equations #Optimization and Control (math.OC) #Stability and Control of Uncertain Systems
paper · pdf · doi:10.48550/arxiv.1709.05033
openalex publication_date 2017/09/15 · openalex created_date 2017/09/25 · openalex updated_date 2026/07/28
We study in this paper the linear quadratic optimal control (linear quadratic regulation, LQR for short) for discrete-time complex-valued linear systems, which have shown to have several potential applications in control theory. Firstly, an iterative algorithm was proposed to solve the discrete-time bimatrix Riccati equation associated with the LQR problem. It is shown that the proposed algorithm converges to the unique positive definite solution (bimatrix) to the bimatrix Riccati equation with appropriate initial conditions. With the help of this iterative algorithm, LQR problem for the antilinear system, which is a special case of complex-valued linear system, was carefully examined and three different Riccati equations based approaches were provided, namely, bimatrix Riccati equation, anti-Riccati equation and normal Riccati equation. The established approach is then used to solve the LQR problem for discrete-time time-delay system with one step state delay and a numerical example was used to illustrate the effectiveness of the proposed methods.