Analysis of Networked Structural Control With Packet Loss

Thao H. T. Truong, Peter J. Seiler, Lauren E. Linderman

Abstract: This brief considers the analysis of networked structural control systems with measurement loss. This is modeled as a sampled-data system that integrates the discrete-time operation of the controller with a fast-sampling approximation of the continuous-time structural (plant) dynamics. Random measurement loss in each channel due to the use of the wireless transmission is modeled as a Bernoulli process. This leads to a discrete-time, Markov jump linear model for the feedback system. An H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> -norm analysis is proposed to assess the stability and the performance of the structural control. An example of a three-story building model is used to illustrate this approach. The H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> -norm results are shown to be in agreement with the numerical simulations. The analysis can, thus, be used to assess various design choices. For example, the relationship between the probability of signal loss and the H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> -norm depends on the method used to handle the signal loss. Moreover, the analysis shows that, for a jump controller setup using steady-state Kalman gains, the system can become unstable at very small probabilities of signal loss.