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.
Characterizations of the Aubin property of the KKT-mapping in composite optimization by SC derivatives and quadratic bundles
Johann Radon Institute for Computational and Applied Mathematics (RICAM)（约翰·拉登计算与应用数学研究所）；Institute of Information Theory and Automation, Czech Academy of Sciences（捷克科学院信息与自动化研究所）
Geometric Conditions for Lossless Convexification in Linear Optimal Control with Discrete-Valued Inputs: Real-Time Implementation for Spacecraft Rendezvous
Stochastic Optimal Linear Quadratic Regulation Control of Discrete-time Systems with Delay and Quadratic Constraints
School of Control Science and Engineering, Shandong University（山东大学控制科学与工程学院）；College of Electrical Engineering and Automation, Shandong University of Science and Technology（山东科技大学电气工程学院）
