Stochastic optimal control of unknown linear networked control system using Q-learning methodology

In this paper, the Bellman equation is utilized forward-in-time for the stochastic optimal control of Networked Control System (NCS) with unknown system dynamics in the presence of random delays and packet losses which are unknown. The proposed stochastic optimal control approach, referred normally as adaptive dynamic programming, uses an adaptive estimator (AE) and ideas from Q-learning to solve the infinite horizon optimal regulation control of NCS with unknown system dynamics. Update laws for tuning the unknown parameters of the adaptive estimator (AE) online to obtain the time-based Q-function are derived. Lyapunov theory is used to show that all signals are asymptotically stable (AS) and that the approximated control signals converge to optimal control inputs. Simulation results are included to show the effectiveness of the proposed scheme.