Nem Stefanovic

A control theoretic approach to noncooperative game design

This paper investigates design of noncooperative games from a control theoretic perspective. Pricing mechanisms are used as a design tool to ensure that the Nash equilibrium of a broad class of noncooperative games satisfies certain global objectives such as welfare maximization. The class of games considered provide a theoretical basis for a variety of decentralized resource allocation and control problems including network congestion control, wireless uplink power control, and optical power control. The game design problem is analyzed under full and limited information assumptions for dynamic systems and nonseparable utility functions. Stability properties of the game and pricing dynamics are studied under the assumption of timescale separation and in two separate time-scales. Thus, sufficient conditions are derived, which allow the designer to place the Nash equilibrium solution or to guide the system trajectory to a desired region or point. The obtained results are illustrated with examples.

Brief paper: An analysis of stability with time-delay of link level power control in optical networks

We study the effects of time-delay on the stability of optical networks. A link level power control scheme adjusts the OSNR value of the signals toward channel OSNR optimization. We utilize the OSNR model from [Pavel, L. (2006). A noncooperative game approach to OSNR optimization in optical networks. IEEE Transactions on Automatic Control, 51(5), 848-852] along with its game-theoretic based control algorithm. Time-delay is incorporated into the closed loop system, for the general network case where every link has a unique time-delay. We derive sufficient conditions for stability under arbitrary time-delays and network configurations. The results are verified via extensive simulations.

Link level power control of optical networks with time-delay

We analyze the effects of time-delay in optical communication networks. A link level power control scheme adjusts the OSNR value of the signals toward channel OSNR optimization. We utilize the model from L. Pavel (2006) along with its game-theoretic based control algorithm. We incorporate time-delay into the closed loop system, for the general case where every link has a unique time-delay. We derive sufficient conditions for stability under arbitrary time-delays and network configurations.

A Lyapunov-Krasovskii stability analysis for game-theoretic based power control in optical links

We analyze the stability of a game-theoretic based power control algorithm for optical links in the presence of time-delays. The control objective is to achieve optimal optical signal to noise ratio (OSNR) values for the signal channels. The control algorithms regularly adjust the signal powers entering the link based on a game-theoretic model. Each signal power is modeled as a player, whose goal is to maximize its own utility function. The utility function increases with an increasing OSNR value, and hence requires an increasing signal power. The trade-off is that if one player increases its OSNR value, this adversely affects the OSNR values of all of the other players. In addition to the signal powers, a dynamic price parameter is fed back to the power control algorithms. Time-delay is present for both the channel pricing parameter and the OSNR feedbacks in the link. We study the stability of the closed-loop, time-delay system. The work utilizes singular perturbation theory modified to handle Lyapunov-Krasovskii techniques.

Brief paper: A stability analysis with time-delay of primal-dual power control in optical links

Primal-dual power control algorithms in optical networks must be designed properly to remain stable in the presence of time-delays. Control algorithms at the signal transmitters continuously update their channel powers in response to dynamic pricing information from the network links. The control algorithms optimize the optical signal-to-noise ratios (OSNRs) of the channels in a distributive and non-cooperative manner. We consider the case of a single link with multiple channels and a constant time-delay. These results also apply to single sink general network configurations if the time-delay represents the longest round-trip time in the network. We derive sufficient conditions for the stability of the closed loop system based on a tunable parameter in the control algorithm. The work combines singular perturbation theory with Lyapunov-Razumikhin time-delay techniques. We verify our results through simulations based on realistic network parameters.

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

Abstract Optical networks provide high data transmission rates which require optimal power control algorithms to ensure the proper delivery of the signals. Time-delays may destabilize the control algorithms. We study the stability of game-theoretic based primal–dual control algorithms applied to multi-link single-sink optical networks. We present a perturbed optical signal-to-noise ratio (OSNR) model with time-delays. By optimizing the OSNR values, we reduce the bit error rates of the channels. We modify singular perturbation theory to include Lyapunov–Krasovskii stability theory with multiple time-delays and uncertainties. Simulations show the stabilization of perturbed systems at the expense of transient convergence time.

L/sub 2/ nonlinear control of EDFA system with amplified spontaneous emission

Current control methods for Erbium doped fiber amplifier (EDFA) devices lack a systematic approach to provide specified performance over the entire state space. Linearization techniques are combined with heuristic switching to attain operation around specific operating points. In this paper, a more inclusive model that takes amplified spontaneous emission (ASE) into account is developed. Furthermore, a nonlinear L2 control scheme is developed that eliminates the necessity of switching between multiple linear control approximations and replaces them by one nonlinear controller that is valid over the entire state space (or average inversion level)

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.

Application of robust L 2 control to erbium doped fiber amplifier: Input and state uncertainty

We extend the results of our previous work (2005) to increase the robustness of an L2 nonlinear controller applied to an erbium doped fiber amplifier (EDFA). We consider the rejection of input and state uncertainties to a full information (FI) extended state space model of the EDFA. The generic robust stabilization problem is solved and the concept of state uncertainty is shown to be associated to parametric uncertainty in the EDFA model. We compare the improved robust L2 controller to the standard L2 controller in our previous work (2005)