Self-stabilizing uncoupled dynamics

Dynamics in a distributed system are self-stabilizing if they are guaranteed to reach a stable state regardless of how the system is initialized. Game dynamics are uncoupled if each player's behavior is independent of the other players' preferences. Recognizing an equilibrium in this setting is a distributed computational task. Self-stabilizing uncoupled dynamics, then, have both resilience to arbitrary initial states and distribution of knowledge. We study these dynamics by analyzing their behavior in a bounded-recall synchronous environment. We determine, for every "size" of game, the minimum number of periods of play that stochastic (randomized) players must recall in order for uncoupled dynamics to be self-stabilizing. We also do this for the special case when the game is guaranteed to have unique best replies. For deterministic players, we demonstrate two self-stabilizing uncoupled protocols. One applies to all games and uses three steps of recall. The other uses two steps of recall and applies to games where each player has at least four available actions. For uncoupled deterministic players, we prove that a single step of recall is insufficient to achieve self-stabilization, regardless of the number of available actions

Segmental stabilizing exercises and low back pain: What is the evidence?

Study design: A systematic review of randomized controlled trials. Objectives: To evaluate the effectiveness of segmental stabilizing exercises for acute, subacute and chronic low back pain with regard to pain, recurrence of pain, disability and return to work. Methods: MEDLINE, EMBASE, CINAHL, Cochrane Controlled Trials Register, PEDro and article reference lists were searched from 1988 onward. Randomized controlled trials with segmental stabilizing exercises for adult low back pain patients were included. Four comparisons were foreseen: (1) effectiveness of segmental stabilizing exercises versus treatment by general practitioner (GP); (2) effectiveness of segmental stabilizing exercises versus other physiotherapy treatment; (3) effectiveness of segmental stabilizing exercises combined with other physiotherapy treatment versus treatment by GP and (4) effectiveness of segmental stabilizing exercises combined with other physiotherapy treatment versus other physiotherapy treatment. Results: Seven trials were included. For acute low back pain, segmental stabilizing exercises are equally effective in reducing short-term disability and pain and more effective in reducing long-term recurrence of low back pain than treatment by GP. For chronic low back pain, segmental stabilizing exercises are, in the short and long term, more effective than GP treatment and may be as effective as other physiotherapy treatments in reducing disability and pain. There is limited evidence that segmental stabilizing exercises additional to other physiotherapy treatment are equally effective for pain and more effective concerning disability than other physiotherapy treatments alone. There is no evidence concerning subacute low back pain. Conclusion: For low back pain, segmental stabilizing exercises are more effective than treatment by GP but they are not more effective than other physiotherapy interventions

Stabilizing data-link over non-FIFO channels with optimal fault-resilience

Self-stabilizing systems have the ability to converge to a correct behavior when started in any configuration. Most of the work done so far in the self-stabilization area assumed either communication via shared memory or via FIFO channels. This paper is the first to lay the bases for the design of self-stabilizing message passing algorithms over unreliable non-FIFO channels. We propose a fault-send-deliver optimal stabilizing data-link layer that emulates a reliable FIFO communication channel over unreliable capacity bounded non-FIFO channels

Stabilizing Randomly Switched Systems

This article is concerned with stability analysis and stabilization of randomly switched systems under a class of switching signals. The switching signal is modeled as a jump stochastic (not necessarily Markovian) process independent of the system state; it selects, at each instant of time, the active subsystem from a family of systems. Sufficient conditions for stochastic stability (almost sure, in the mean, and in probability) of the switched system are established when the subsystems do not possess control inputs, and not every subsystem is required to be stable. These conditions are employed to design stabilizing feedback controllers when the subsystems are affine in control. The analysis is carried out with the aid of multiple Lyapunov-like functions, and the analysis results together with universal formulae for feedback stabilization of nonlinear systems constitute our primary tools for control designComment: 22 pages. Submitte

A State-Space Approach to Parametrization of Stabilizing Controllers for Nonlinear Systems

A state-space approach to Youla-parametrization of stabilizing controllers for linear and nonlinear systems is suggested. The stabilizing controllers (or a class of stabilizing controllers for nonlinear systems) are characterized as (linear/nonlinear) fractional transformations of stable parameters. The main idea behind this approach is to decompose the output feedback stabilization problem into state feedback and state estimation problems. The parametrized output feedback controllers have separation structures. A separation principle follows from the construction. This machinery allows the parametrization of stabilizing controllers to be conducted directly in state space without using coprime-factorization