Robust power control of single sink optical networks with time-delays

We study the stability of game-theoretic based power control algorithms on multi-link optical networks in the presence of time-delays and uncertainties. The control algorithms, originally developed in the absence of time-delays and uncertainties, adjust the signal powers at the transmitters to solve the optical signal-to-noise ratio (OSNR) optimization problem. This minimizes the bit error rate of the signal channels. We apply the game-theoretic framework to a perturbed OSNR model in the presence of time-delays. Uncertainties in the OSNR model appear as norm-bounded uncertainties in the noise powers, system gains, and channel powers. The time-delays are due to signal propagation between the channel sources and OSNR output. We restrict our analysis to single sink network topologies. A primal-dual control scheme ensures convergence to the Nash equilibrium, and OSNR optimization. The resultant closed-loop system has two time-scales. Robust stability in the presence of time-delays is established via singular perturbation theory modified for Lyapunov-Krasovskii theory.