Stochastic Behavior of the Nonnegative Least Mean Fourth Algorithm for Stationary Gaussian Inputs and Slow Learning

Some system identification problems impose nonnegativity constraints on the parameters to estimate due to inherent physical characteristics of the unknown system. The nonnegative least-mean-square (NNLMS) algorithm and its variants allow to address this problem in an online manner. A nonnegative least mean fourth (NNLMF) algorithm has been recently proposed to improve the performance of these algorithms in cases where the measurement noise is not Gaussian. This paper provides a first theoretical analysis of the stochastic behavior of the NNLMF algorithm for stationary Gaussian inputs and slow learning. Simulation results illustrate the accuracy of the proposed analysis.Comment: 11 pages, 8 figures, submitted for publicatio

Multi-hop Diffusion LMS for Energy-constrained Distributed Estimation

We propose a multi-hop diffusion strategy for a sensor network to perform distributed least mean-squares (LMS) estimation under local and network-wide energy constraints. At each iteration of the strategy, each node can combine intermediate parameter estimates from nodes other than its physical neighbors via a multi-hop relay path. We propose a rule to select combination weights for the multi-hop neighbors, which can balance between the transient and the steady-state network mean-square deviations (MSDs). We study two classes of networks: simple networks with a unique transmission path from one node to another, and arbitrary networks utilizing diffusion consultations over at most two hops. We propose a method to optimize each node's information neighborhood subject to local energy budgets and a network-wide energy budget for each diffusion iteration. This optimization requires the network topology, and the noise and data variance profiles of each node, and is performed offline before the diffusion process. In addition, we develop a fully distributed and adaptive algorithm that approximately optimizes the information neighborhood of each node with only local energy budget constraints in the case where diffusion consultations are performed over at most a predefined number of hops. Numerical results suggest that our proposed multi-hop diffusion strategy achieves the same steady-state MSD as the existing one-hop adapt-then-combine diffusion algorithm but with a lower energy budget.Comment: 14 pages, 12 figures. Submitted for publicatio

Application of optimization techniques to the design of a flutter suppression control law for the DAST ARW-2

The design of a candidate flutter suppression (FS) control law for the symmetric degrees of freedom for the DAST ARW-2 aircraft is discussed. The results illustrate the application of several currently employed control law design techniques. Subsequent designs, obtained as the mathematical model of the ARW-2 is updated, are expected to employ similar methods and to provide a control law whose performance will be flight tested. This study represents one of the steps necessary to provide an assessment of the validity of applying current control law synthesis and analysis techniques in the design of actively controlled aircraft. Mathematical models employed in the control law design and evaluation phases are described. The control problem is specified by presenting the flutter boundary predicted for the uncontrolled aircraft and by defining objectives and constraints that the controller should satisfy. A full-order controller is obtained by using Linear Quadratic Gaussian (LQG) techniques. The process of obtaining an implementable reduced-order controller is described. One example is also shown in which constrained optimization techniques are utilized to explicitly include robustness criteria within the design algorithm

Design of a candidate flutter suppression control law for DAST ARW-2

A control law is developed to suppress symmetric flutter for a mathematical model of an aeroelastic research vehicle. An implementable control law is attained by including modified LQC (Linear Quadratic Gaussian) design techniques, controller order reduction, and gain scheduling. An alternate (complementary) design approach is illustrated for one flight condition wherein nongradient-based constrained optimization techniques are applied to maximize controller robustness

Distributed Coupled Multi-Agent Stochastic Optimization

This work develops effective distributed strategies for the solution of constrained multi-agent stochastic optimization problems with coupled parameters across the agents. In this formulation, each agent is influenced by only a subset of the entries of a global parameter vector or model, and is subject to convex constraints that are only known locally. Problems of this type arise in several applications, most notably in disease propagation models, minimum-cost flow problems, distributed control formulations, and distributed power system monitoring. This work focuses on stochastic settings, where a stochastic risk function is associated with each agent and the objective is to seek the minimizer of the aggregate sum of all risks subject to a set of constraints. Agents are not aware of the statistical distribution of the data and, therefore, can only rely on stochastic approximations in their learning strategies. We derive an effective distributed learning strategy that is able to track drifts in the underlying parameter model. A detailed performance and stability analysis is carried out showing that the resulting coupled diffusion strategy converges at a linear rate to an $O(\mu)-$neighborhood of the true penalized optimizer