Approximate solution to optimal linear quadratic Gaussian control over non-acknowledgment networks

Abstract

This paper investigates the solution of the optimal linear quadratic Gaussian control (LQG) problem for systems with packet losses over non-acknowledgment networks. The acknowledgment refers to acknowledgment signals, which are sent by the actuator to notify the controller whether the control packets are successfully received or not. Systems without acknowledgment for packet losses are usually called user-diagram-protocol-like (UDP-like) systems. It is known that for general UDP-like systems, there is no analytical solution to the optimal LQG problem and the computational efforts of numerical solutions will exponentially grow with time. By using a moment-preserving Gaussian approximation approach, this paper develops an efficient algorithm to approximately estimate system states. Based on approximate state estimates, an analytical solution to the optimal LQG problem for general UDP-like systems is obtained by using a dynamic programming approach. It is an approximate solution, and it becomes an exact solution under special conditions. Some simulation examples are given to illustrate the effectiveness of the proposed methods.