Risk-Constrained LQR Design Framework for Non-Gaussian Interconnected Systems Defined Over a Digraph

Abstract

This article studies the risk-constrained linear–quadratic regulation (Rc-LQR) for a class of interconnected systems (ISs) with non-Gaussian noise. The IS is of a weakly connected topology. The standard linear–quadratic regulation (LQR) controller is optimal in expectation for the quadratic cost and, thus, is called risk-neutral LQR (Rn-LQR) controller. However, the Rn-LQR system may suffer from low-probability yet statistically significant/risky events. The Rc-LQR controller can well trade between the standard LQR performance and the risk cost. The Rc-LQR control problem has been studied for the traditional single systems in the literature. The extension of the Rc-LQR to the ISs has not been reported. The information constraint induced by the system topology complicates the Rc-LQR design of the non-Gaussian ISs. In this article, an orthogonal projection method is proposed to handle the information constraint of the subsystem controller for the non-Gaussian ISs. Then, the Rc-LQR of the non-Gaussian ISs can be successfully designed. Finally, the effectiveness of the proposed methods is illustrated by simulations.