Optimal LQG Control of Networked Systems Under Traffic-Correlated Delay and Dropout
Dipankar Maity, Mohammad H. Mamduhi, Sandra Hirche, Karl Henrik Johansson
Abstract
Transmission delay and packet dropout are inevitable network-induced phenomena that severely compromise the control performance of network control systems. The real-time network traffic is a major dynamic parameter that directly influences delay and reliability of transmission channels, and thus, acts as an unavoidable source of induced coupling among all network sharing systems. In this letter, we analyze the effects of traffic-induced delay and dropout on the finite-horizon quality-of-control of an individual stochastic linear time-invariant system, where quality-of-control is measured by an expected quadratic cost function. We model delay and dropout of the channel as generic stochastic processes that are correlated with the real-time network traffic induced by the rest of network users. This approach provides a pathway to determine the required networking capabilities to achieve a guaranteed quality-of-control for systems operating over a shared-traffic network. Numerical evaluations are performed using realistic stochastic models for delay and dropout. As a special case, we consider exponential distribution for delay with its rate parameter being traffic-correlated, and traffic-correlated Markov-based packet drop model.