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

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: