Localized LQR Optimal Control

This paper introduces a receding horizon like control scheme for localizable distributed systems, in which the effect of each local disturbance is limited spatially and temporally. We characterize such systems by a set of linear equality constraints, and show that the resulting feasibility test can be solved in a localized and distributed way. We also show that the solution of the local feasibility tests can be used to synthesize a receding horizon like controller that achieves the desired closed loop response in a localized manner as well. Finally, we formulate the Localized LQR (LLQR) optimal control problem and derive an analytic solution for the optimal controller. Through a numerical example, we show that the LLQR optimal controller, with its constraints on locality, settling time, and communication delay, can achieve similar performance as an unconstrained H2 optimal controller, but can be designed and implemented in a localized and distributed way.Comment: Extended version for 2014 CDC submissio

A Matrix-Analytic Solution for Randomized Load Balancing Models with Phase-Type Service Times

In this paper, we provide a matrix-analytic solution for randomized load balancing models (also known as \emph{supermarket models}) with phase-type (PH) service times. Generalizing the service times to the phase-type distribution makes the analysis of the supermarket models more difficult and challenging than that of the exponential service time case which has been extensively discussed in the literature. We first describe the supermarket model as a system of differential vector equations, and provide a doubly exponential solution to the fixed point of the system of differential vector equations. Then we analyze the exponential convergence of the current location of the supermarket model to its fixed point. Finally, we present numerical examples to illustrate our approach and show its effectiveness in analyzing the randomized load balancing schemes with non-exponential service requirements.Comment: 24 page

Design issues of a reinforcement-based self-learning fuzzy controller for petrochemical process control

Fuzzy logic controllers have some often-cited advantages over conventional techniques such as PID control, including easier implementation, accommodation to natural language, and the ability to cover a wider range of operating conditions. One major obstacle that hinders the broader application of fuzzy logic controllers is the lack of a systematic way to develop and modify their rules; as a result the creation and modification of fuzzy rules often depends on trial and error or pure experimentation. One of the proposed approaches to address this issue is a self-learning fuzzy logic controller (SFLC) that uses reinforcement learning techniques to learn the desirability of states and to adjust the consequent part of its fuzzy control rules accordingly. Due to the different dynamics of the controlled processes, the performance of a self-learning fuzzy controller is highly contingent on its design. The design issue has not received sufficient attention. The issues related to the design of a SFLC for application to a petrochemical process are discussed, and its performance is compared with that of a PID and a self-tuning fuzzy logic controller

Cross-layer optimization in TCP/IP networks

TCP-AQM can be interpreted as distributed primal-dual algorithms to maximize aggregate utility over source rates. We show that an equilibrium of TCP/IP, if exists, maximizes aggregate utility over both source rates and routes, provided congestion prices are used as link costs. An equilibrium exists if and only if this utility maximization problem and its Lagrangian dual have no duality gap. In this case, TCP/IP incurs no penalty in not splitting traffic across multiple paths. Such an equilibrium, however, can be unstable. It can be stabilized by adding a static component to link cost, but at the expense of a reduced utility in equilibrium. If link capacities are optimally provisioned, however, pure static routing, which is necessarily stable, is sufficient to maximize utility. Moreover single-path routing again achieves the same utility as multipath routing at optimality

Joint vector magnetograph observations at BBSO, Huairou Station and Mees Solar Observatory

Joint vector magnetograph observations were carried out at Big Bear Solar Observatory (BBSO), Huairou Solar Observing Station (Huairou), and Mees Solar Observatory (MSO) in late September 1989. Comparisons of vector magnetograms obtained at the three stations show a high degree of consistency in the morphology of both longitudinal and transverse fields. Quantitative comparisons show the presence of noise, cross-talk between longitudinal field and transverse field, Faraday rotation and signal saturation effects in the magnetograms. We have tried to establish how the scatter in measurements from different instruments is apportioned between these sources of error