Discussion on: "Multi-layer Switching Control using Generalized Sampled-data Hold Functions"

M. Verwoerd, O. Mason
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Abstract

In the paper under discussion, the authors consider the problem of designing switching controllers for plants that are subject to large levels of uncertainty or to abrupt changes in their dynamics. There has been a great deal of interest in this problem in the recent past [7,2], and the potential applications of switching controllers are numerous. For instance, one approach to the design of fault-tolerant systems [3,4] is to construct models and controllers for the various operating conditions corresponding to different system malfunctions. Once the correct plant has been identified, the associated controller is switched on. Of course, in order for this type of scheme to be practical, it is vitally important to be able to identify the correct plant as quickly and efficiently as possible, and tominimise any transient effects which may result from switching to incorrect controllers during the identification process. A major issue in the design of switching control schemes is that the system can switch to destabilising controllers before finally locking onto the correct one, which leads to very poor transient behaviour. We shall refer to such switches as destabilising switches throughout this discussion. The primary contribution of the paper is to describe a novel switching control scheme, which reduces the number of undesirable, destabilising switches that occur while identifying the correct plant. In fact, under a range of assumptions, which we shall discuss in detail below, the correct plant can be identified after a finite number of switches, at most one of which is destabilising. The authors also give an upper bound on the number of switches required in order to find the correct plant. The architecture underpinning the MLSC scheme consists of several layers or levels of controllers. In fact, given n plants, P1, . . . ,Pn, the proposed architecture consists of n 2 layers, each of which contains a number of controllers. The various control layers are constructed in such a way that if i denotes the layer number, C and C0 denote controllers, and P denotes a plant model, then:
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关于“基于广义采样数据保持函数的多层切换控制”的讨论
在讨论的论文中,作者考虑了设计具有大不确定性或其动力学突变的植物切换控制器的问题。在最近的过去,对这个问题有很大的兴趣[7,2],并且开关控制器的潜在应用是众多的。例如,设计容错系统的一种方法[3,4]是为不同的系统故障对应的各种运行条件构建模型和控制器。一旦确定了正确的工厂,就打开相关的控制器。当然,为了使这种类型的方案具有实用性,能够尽可能快速有效地识别正确的工厂,并最大限度地减少在识别过程中切换到错误控制器可能导致的任何瞬态影响是至关重要的。切换控制方案设计中的一个主要问题是,在最终锁定正确的控制器之前,系统可能会切换到不稳定控制器,这将导致非常糟糕的瞬态行为。在整个讨论中,我们将把这种开关称为不稳定开关。本文的主要贡献是描述了一种新的开关控制方案,它减少了在识别正确植物时发生的不希望的、不稳定的开关的数量。事实上,在一系列假设下(我们将在下面详细讨论),经过有限数量的开关后,可以确定正确的对象,其中最多有一个是不稳定的。作者还给出了找到正确植物所需开关数量的上限。支持MLSC方案的体系结构由若干层或控制器级别组成。事实上,给定n种植物,P1,…,所提出的体系结构由n 2层组成,每一层包含若干个控制器。各控制层的构造如下:i为层数,C和C0为控制器,P为植物模型,则:
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