Distributive Power Control Algorithm for Multicarrier Interference Network over Time-Varying Fading Channels - Tracking Performance Analysis and Optimization

Distributed power control over interference limited network has received an increasing intensity of interest over the past few years. Distributed solutions (like the iterative water-filling, gradient projection, etc.) have been intensively investigated under \emph{quasi-static} channels. However, as such distributed solutions involve iterative updating and explicit message passing, it is unrealistic to assume that the wireless channel remains unchanged during the iterations. Unfortunately, the behavior of those distributed solutions under \emph{time-varying} channels is in general unknown. In this paper, we shall investigate the distributed scaled gradient projection algorithm (DSGPA) in a $K$ pairs multicarrier interference network under a finite-state Markov channel (FSMC) model. We shall analyze the \emph{convergence property} as well as \emph{tracking performance} of the proposed DSGPA. Our analysis shows that the proposed DSGPA converges to a limit region rather than a single point under the FSMC model. We also show that the order of growth of the tracking errors is given by \mathcal{O}\(1 \big/ \bar{N}\), where $\bar{N}$ is the \emph{average sojourn time} of the FSMC. Based on the analysis, we shall derive the \emph{tracking error optimal scaling matrices} via Markov decision process modeling. We shall show that the tracking error optimal scaling matrices can be implemented distributively at each transmitter. The numerical results show the superior performance of the proposed DSGPA over three baseline schemes, such as the gradient projection algorithm with a constant stepsize.Comment: To Appear on the IEEE Transaction on Signal Processin

Switcher-random-walks: a cognitive-inspired mechanism for network exploration

Semantic memory is the subsystem of human memory that stores knowledge of concepts or meanings, as opposed to life specific experiences. The organization of concepts within semantic memory can be understood as a semantic network, where the concepts (nodes) are associated (linked) to others depending on perceptions, similarities, etc. Lexical access is the complementary part of this system and allows the retrieval of such organized knowledge. While conceptual information is stored under certain underlying organization (and thus gives rise to a specific topology), it is crucial to have an accurate access to any of the information units, e.g. the concepts, for efficiently retrieving semantic information for real-time needings. An example of an information retrieval process occurs in verbal fluency tasks, and it is known to involve two different mechanisms: -clustering-, or generating words within a subcategory, and, when a subcategory is exhausted, -switching- to a new subcategory. We extended this approach to random-walking on a network (clustering) in combination to jumping (switching) to any node with certain probability and derived its analytical expression based on Markov chains. Results show that this dual mechanism contributes to optimize the exploration of different network models in terms of the mean first passage time. Additionally, this cognitive inspired dual mechanism opens a new framework to better understand and evaluate exploration, propagation and transport phenomena in other complex systems where switching-like phenomena are feasible.Comment: 9 pages, 3 figures. Accepted in "International Journal of Bifurcations and Chaos": Special issue on "Modelling and Computation on Complex Networks

Distributed Averaging via Lifted Markov Chains

Motivated by applications of distributed linear estimation, distributed control and distributed optimization, we consider the question of designing linear iterative algorithms for computing the average of numbers in a network. Specifically, our interest is in designing such an algorithm with the fastest rate of convergence given the topological constraints of the network. As the main result of this paper, we design an algorithm with the fastest possible rate of convergence using a non-reversible Markov chain on the given network graph. We construct such a Markov chain by transforming the standard Markov chain, which is obtained using the Metropolis-Hastings method. We call this novel transformation pseudo-lifting. We apply our method to graphs with geometry, or graphs with doubling dimension. Specifically, the convergence time of our algorithm (equivalently, the mixing time of our Markov chain) is proportional to the diameter of the network graph and hence optimal. As a byproduct, our result provides the fastest mixing Markov chain given the network topological constraints, and should naturally find their applications in the context of distributed optimization, estimation and control

Cluster-based feedback control of turbulent post-stall separated flows

We propose a novel model-free self-learning cluster-based control strategy for general nonlinear feedback flow control technique, benchmarked for high-fidelity simulations of post-stall separated flows over an airfoil. The present approach partitions the flow trajectories (force measurements) into clusters, which correspond to characteristic coarse-grained phases in a low-dimensional feature space. A feedback control law is then sought for each cluster state through iterative evaluation and downhill simplex search to minimize power consumption in flight. Unsupervised clustering of the flow trajectories for in-situ learning and optimization of coarse-grained control laws are implemented in an automated manner as key enablers. Re-routing the flow trajectories, the optimized control laws shift the cluster populations to the aerodynamically favorable states. Utilizing limited number of sensor measurements for both clustering and optimization, these feedback laws were determined in only $O(10)$ iterations. The objective of the present work is not necessarily to suppress flow separation but to minimize the desired cost function to achieve enhanced aerodynamic performance. The present control approach is applied to the control of two and three-dimensional separated flows over a NACA 0012 airfoil with large-eddy simulations at an angle of attack of $9^\circ$, Reynolds number $Re = 23,000$ and free-stream Mach number $M_\infty = 0.3$. The optimized control laws effectively minimize the flight power consumption enabling the flows to reach a low-drag state. The present work aims to address the challenges associated with adaptive feedback control design for turbulent separated flows at moderate Reynolds number.Comment: 32 pages, 18 figure