Choon Yik Tang

Zero-Gradient-Sum Algorithms for Distributed Convex Optimization: The Continuous-Time Case

This paper presents a family of continuous-time distributed algorithms called Zero-Gradient-Sum (ZGS) algorithms, which solve unconstrained, separable, convex optimization problems over undirected networks with fixed topologies. The ZGS algorithms are derived using a Lyapunov function candidate that exploits convexity, and get their name from the fact that they yield nonlinear networked dynamical systems whose states slide along an invariant, zero-gradient-sum manifold and converge asymptotically to the unknown minimizer. We also present a systematic way to construct ZGS algorithms, show that a subset of them converge exponentially, and obtain lower bounds on their convergence rates in terms of the convexity characteristics of the problem and the network topology, including its algebraic connectivity. Finally, we show that some of the well-studied continuous-time distributed consensus algorithms are special cases of ZGS algorithms and discuss the ramifications.

Gossip Algorithms for Convex Consensus Optimization Over Networks

In many applications, nodes in a network wish to achieve not only a consensus, but an optimal one. To date, a family of subgradient algorithms have been proposed to solve this problem under general convexity assumptions. This paper shows that, with a few additional mild assumptions, a fundamentally different, non-gradient-based algorithm with appealing features can be constructed. Specifically, we develop Pairwise Equalizing (PE), a gossip-style, distributed asynchronous iterative algorithm for achieving unconstrained, separable, convex consensus optimization over undirected networks with time-varying topologies, where each component function is strictly convex, continuously differentiable, and has a minimizer. We show that PE is easy to implement, bypasses limitations facing the subgradient algorithms, and produces a switched, nonlinear, networked dynamical system that is deterministically and stochastically asymptotically convergent. Moreover, we show that PE admits a common Lyapunov function and reduces to the well-studied Pairwise Averaging and Randomized Gossip Algorithm in a special case.

Nonlinear Dual-Mode Control of Variable-Speed Wind Turbines With Doubly Fed Induction Generators

This paper presents a feedback/feedforward nonlinear controller for variable-speed wind turbines with doubly fed induction generators. By appropriately adjusting the rotor voltages and the blade pitch angle, the controller simultaneously enables: 1) control of the active power in both the maximum power tracking and power regulation modes; 2) seamless switching between the two modes; and 3) control of the reactive power so that a desirable power factor is maintained. Unlike many existing designs, the controller is developed based on original, nonlinear, electromechanically-coupled models of wind turbines, without attempting approximate linearization. Its development consists of three steps: 1) employ feedback linearization to exactly cancel some of the nonlinearities and perform arbitrary pole placement; 2) design a speed controller that makes the rotor angular velocity track a desired reference whenever possible; and 3) introduce a Lyapunov-like function and present a gradient-based approach for minimizing this function. The effectiveness of the controller is demonstrated through simulation of a wind turbine operating under several scenarios.

An Approximate Wind Turbine Control System Model for Wind Farm Power Control

Wind farm power control is key to reliable large-scale wind integration. The design of a sophisticated wind farm controller, however, is challenging partly because there is a lack of models that appropriately simplify the complex overall dynamics of a large number of wind turbine control systems (WTCSs). In this paper, using system identification approaches, we develop a simple approximate model that attempts to mimic the active and reactive power dynamics of two generic WTCS models under normal operating conditions: an analytical model described by nonlinear differential equations, and an empirical one by input-output measurement data. The approximate model contains two parts-one for active power and one for reactive-each of which is a third-order system that would have been linear if not for a static nonlinearity. For each generic model, we also provide an identification scheme that sequentially determines the approximate model parameters. Finally, we show via simulation that, despite its structural simplicity, the approximate model is accurate and versatile, capable of closely imitating several different analytical and empirical WTCS models from the literature and from real data. The results suggest that the approximate model may be used to facilitate research on wind farm power control.

A gossip algorithm for convex consensus optimization over networks

In many applications, nodes in a network desire not only a consensus, but an optimal one. To date, a family of subgradient algorithms have been proposed to solve this problem under general convexity assumptions. This technical note shows that, for the scalar case and by assuming a bit more, novel non-gradient-based algorithms with appealing features can be constructed. Specifically, we develop Pairwise Equalizing (PE) and Pairwise Bisectioning (PB), two gossip algorithms that solve unconstrained, separable, convex consensus optimization problems over undirected networks with time-varying topologies, where each local function is strictly convex, continuously differentiable, and has a minimizer. We show that PE and PB are easy to implement, bypass limitations of the subgradient algorithms, and produce switched, nonlinear, networked dynamical systems that admit a common Lyapunov function and asymptotically converge. Moreover, PE generalizes the well-known Pairwise Averaging and Randomized Gossip Algorithm, while PB relaxes a requirement of PE, allowing nodes to never share their local functions.

Distributed Asynchronous Algorithms for Solving Positive Definite Linear Equations over Networks—Part II: Wireless Networks

Abstract —In this Part II of the two-part paper, we study the interplay among wireless communications, distributed algorithms, and control in solving symmetric positive definite systems of linear equations over multi-hop wireless networks with fixed topologies. Building on the results from Part I, we develop and analyze Pairwise, Groupwise, Random Hopwise , and Controlled Hopwise Equalizing (PE, GE, RHE, and CHE), showing along the way how the broadcast nature of wireless transmissions may be fully utilized, how undesirable overlapping iterations may be avoided, and how iterations may be feedback controlled in a greedy, decentralized, Lyapunov-based fashion, leading to CHE. We show that CHE yields a networked dynamical system with state-dependent switching, provable exponential convergence, and quantifiable worst-case convergence rate. Finally, through extensive simulation on random geometric graphs, we show that GE, RHE, and CHE are dramatically more efficient and scalable than two existing, average-consensus-based schemes, with CHE having the best performance.

Control of distributed convex optimization

This paper addresses the problem of solving unconstrained, separable, convex optimization problems over networks and introduces a new approach to the problem: control of distributed convex optimization. We first develop Hopwise Equalizing (HE), a non-gradient-based, distributed asynchronous iterative algorithm that is asymptotically convergent and that is capable of solving the problem. Based on the framework provided by HE, we then develop Controlled Hopwise Equalizing (CHE), showing that a common Lyapunov function, constructed based on the first-order convexity condition, can be used to incorporate the notion of greedy, decentralized, feedback iteration control, whereby individual nodes use potential drops in the value of the Lyapunov function to control, on their own, when to initiate an iteration. Finally, via extensive simulation on wirelessly connected random geometric graphs, we show that CHE is significantly more bandwidth/energy efficient than several existing subgradient algorithms, requiring far less communications to solve a convex optimization problem.

Automatic Learning-based MANET Cross-Layer Parameter Configuration

Mobile ad hoc networks (MANETs) operate in highly dynamic environments with limited resources. Current approaches to network configuration are static and ad-hoc, and therefore frequently perform extremely poorly. We describe our approach to network configuration control that relies on automatically learning the relationships among configuration parameters and maintains near-optimal configurations adaptively, even during highly dynamic missions. We present a case study demonstrating the feasibility of the approach.

Model predictive and adaptive wind farm power control

This paper introduces a wind farm controller that enables the power output of a wind farm to accurately and smoothly track a desired reference from a power grid operator. Developed based on a model of wind turbine control systems we recently proposed, the wind farm controller consists of an outer control loop and an inner one. The outer loop contains a model predictive controller, which uses various forecasts and feedbacks to iteratively compute a set of desired power trajectories, so that the deterministic tracking accuracy of the wind farm power output on a receding horizon is optimized. In contrast, the inner loop contains an adaptive controller, which uses estimated wind speed characteristics to adaptively tune a set of proportional controller gains, so that the stochastic smoothness of the wind farm power output on a shorter timescale is optimized. The paper also provides a series of simulation studies that illustrate the salient features of the wind farm controller.

Multiple real-constant multiplication with improved cost model and greedy and optimal searches

This paper formulates and solves a multiple real-constant multiplication (MRCM) problem, where the goal is to find a multiplierless shift-add network that implements the multiplication of a signal by real constants, in a way which minimizes hardware cost subject to error constraints. Unlike our previous work, here we consider an improved hardware cost model, whereby instead of simply counting the number of adders needed, we count the number of bits required, which is more realistic. We also introduce two algorithms for solving the MRCM problem, namely: (i) a greedy algorithm without backtracking that heuristically traverses an exponentially growing search tree and rapidly produces a suboptimal solution; and (ii) an exact algorithm that exploits known cost upper bounds to determine whether and how to expand the search tree, leading to an optimal solution at the expense of longer execution time. Finally, we present a set of experimental results that compares the two algorithms with the Hcub algorithm.