Feedback control of nonlinear stochastic systems for targeting a specified stationary probability density

In the present paper, an innovative procedure for designing the feedback control of multi-degree-of-freedom (MDOF) nonlinear stochastic systems to target a specified stationary probability density function (SPDF) is proposed based on the technique for obtaining the exact stationary solutions of the dissipated Hamiltonian systems. First, the control problem is formulated as a controlled, dissipated Hamiltonian system together with a target SPDF. Then the controlled forces are split into a conservative part and a dissipative part. The conservative control forces are designed to make the controlled system and the target SPDF have the same Hamiltonian structure (mainly the integrability and resonance). The dissipative control forces are determined so that the target SPDF is the exact stationary solution of the controlled system. Five cases, i.e., non-integrable Hamiltonian systems, integrable and non-resonant Hamiltonian systems, integrable and resonant Hamiltonian systems, partially integrable and non-resonant Hamiltonian systems, and partially integrable and resonant Hamiltonian systems, are treated respectively. A method for proving that the transient solution of the controlled system approaches the target SPDF as t→∞ is introduced. Finally, an example is given to illustrate the efficacy of the proposed design procedure.     

A new solution for a queueing model of a manufacturing cell with negative customers under a rotation rule

In this paper, we consider a queueing model extension for a manufacturing cell composed of a machining center and several parallel downstream production stations under a rotation rule. A queueing model is extended with the arrival processes of negative customers to capture failures of production stations, reorganization of works and disasters in the manufacturing cell. We present an exact solution for the steady-state probabilities of the proposed queueing model. The solution does not require the approximation of the infinite sum. In addition, it provides an alternative way to compute the rate matrix for the matrix-geometric method as well.     

A Faà di Bruno Hopf algebra for a group of Fliess operators with applications to feedback

A Faà di Bruno type Hopf algebra is developed for a group of integral operators known as Fliess operators, where operator composition is the group product. Such operators are normally written in terms of generating series over a noncommutative alphabet. Using a general series expansion for the antipode, an explicit formula for the generating series of the compositional inverse operator is derived. The result is applied to analytic nonlinear feedback systems to produce an explicit formula for the feedback product, that is, the generating series for the Fliess operator representation of the closed-loop system written in terms of the generating series of the Fliess operator component systems. This formula is employed to provide a proof that local convergence is preserved under feedback.     

"惯性交感"现象分析、控制与仿真

现代飞机设计变化,增大了喷气战斗机出现惯性交感的可能性,致使某些飞机在高滚转速率下完全失稳。这种现象的数学分析通常是相当困难的。为此,本文利用简化线性分析法研究了惯性交感的影响因素和灵敏度,并僵助计算机仿真手段确定了影响系统稳定性的参数和提供了通过附加航向及俯仰速率反馈进行人工稳定飞机的惯性交感控制系统。     

Dynamic programming for impulse controls

This paper describes the theory of feedback control in the class of inputs which allow delta-functions and their derivatives. It indicates a modification of dynamic programming techniques appropriate for such problems. Introduced are physically realizable bang-bang-type approximations of the “ideal” impulse-type solutions. These may also serve as “fast” feedback controls which solve the terminal control problem in arbitrary small time. Examples of damping high-order oscillations in finite time are presented.     

A constraint programming approach to cutset problems

We consider the problem of finding a cutset in a directed graph G=(V,E)$G=(V,E)$, i.e., a set of vertices that cuts all cycles in G  . Finding a cutset of minimum cardinality is NP-hard. There exist several approximate and exact algorithms, most of them using graph reduction techniques. In this paper, we propose a constraint programming approach to cutset problems and design a global constraint for computing cutsets. This cutset constraint is a global constraint over boolean variables associated to the vertices of a given graph and states that the subgraph restricted to the vertices having their boolean variable set to true is acyclic. We propose a filtering algorithm based on graph contraction operations and inference of simple boolean constraints, that has a linear time complexity in O(|E|+|V|)$O(|E|+|V|)$. We discuss search heuristics based on graph properties provided by the cutset constraint, and show the efficiency of the cutset constraint on benchmarks of the literature for pure minimum cutset problems, and on an application to log-based reconciliation problems where the global cutset constraint is mixed with other boolean constraints.     

A functional equations approach to nonlinear discrete-time feedback stabilization through pole-placement

The present work proposes a new approach to the nonlinear discrete-time feedback stabilization problem with pole-placement. The problem's formulation is realized through a system of nonlinear functional equations and a rather general set of necessary and sufficient conditions for solvability is derived. Using tools from functional equations theory, one can prove that the solution to the above system of nonlinear functional equations is locally analytic, and an easily programmable series solution method can be developed. Under a simultaneous implementation of a nonlinear coordinate transformation and a nonlinear discrete-time state feedback control law that are both computed through the solution of the system of nonlinear functional equations, the feedback stabilization with pole-placement design objective can be attained under rather general conditions. The key idea of the proposed single-step design approach is to bypass the intermediate step of transforming the original system into a linear controllable one with an external reference input associated with the classical exact feedback linearization approach. However, since the proposed method does not involve an external reference input, it cannot meet other control objectives such as trajectory tracking and model matching.     

一阶滞后对象的温度控制

本文主要介绍了利用μ XL中小型集散控制系统,对未知参数的一阶惯性滞后对象,实现温度控制,并得到理想的温度控制曲线。     

Predicting social cues during online discussions: Effects of evaluations and knowledge content

This study examined whether evaluations (agreements, disagreements), knowledge content (new ideas, justifications), or social cues (SCs) in recent messages affected a current message’s positive or negative SC during asynchronous, online discussions. Using statistical discourse analysis, we modeled 894 messages by 183 participants on 60 high school mathematics topics (typically eight people posted per topic) on a mathematics problem solving website not connected to any class or school. Results showed that recent agreements increased the likelihood of positive SC, whereas justifications reduced it. Disagreements increased the likelihood of negative SC, whereas new ideas reduced it. Meanwhile, recent positive or negative SCs did not affect the likelihood of a subsequent SC. Together, these results suggest that judicious use of positive SCs rather than negative SCs during disagreements can help students both construct knowledge and maintain social relationships.     

Multimodal feedback: an assessment of performance and mental workload

Multimodal interfaces offer great potential to humanize interactions with computers by employing a multitude of perceptual channels. This paper reports on a novel multimodal interface using auditory, haptic and visual feedback in a direct manipulation task to establish new recommendations for multimodal feedback, in particular uni-, bi- and trimodal feedback. A close examination of combinations of uni-, bi- and trimodal feedback is necessary to determine which enhances performance without increasing workload. Thirty-two participants were asked to complete a task consisting of a series of ‘drag-and-drops’ while the type of feedback was manipulated. Each participant was exposed to three unimodal feedback conditions, three bimodal feedback conditions and one trimodal feedback condition that used auditory, visual and haptic feedback alone, and in combination. Performance under the different conditions was assessed with measures of trial completion time, target highlight time and a self-reported workload assessment captured by the NASA Task Load Index (NASA-TLX). The findings suggest that certain types of bimodal feedback can enhance performance while lowering self-perceived mental demand.