Emerging Applications of Control and Systems Theory by Roberto Tempo (deceased) Stephen Yurkovich & Pradeep Misra

Author:Roberto Tempo (deceased), Stephen Yurkovich & Pradeep Misra
Language: eng
Format: epub
Publisher: Springer International Publishing, Cham

13.2 General Problem Setting

We here propose a fairly general setting, which is represented by a block diagram depicted in Fig. 13.1. The system consists of two layers, the upper layer for global control and the lower layer for local control. They are connected each other by aggregation from bottom to up and distribution from up to bottom, where with size N.

Fig. 13.1Structure of total system

The upper and lower layer generalized plants are represented by and , respectively. The block diagonal property of means that the lower layer is a collection of independent subsystems. Each subsystem thus has an independent local controller , and hence we have the block diagonal property of .

The collections of inputs and outputs of the local controllers are denoted by and , respectively. Signals and are N-dimensional vectors which correspond to signals to link the upper layer, i.e., and . Signals and are the collections of input and output variables for representing the local objective, respectively. The element-wise representation of is given by , and the same notation is used for , , , , and . The upper layer is controlled by the global controller with input and output . Signals and are the aggregated signal from the lower layer and the reference signal to be sent out to the lower layer, respectively. Signals and are the input and output variables for representing the global objective, respectively.

Our main idea to achieve the two requirements (i) and (ii) mentioned above, or (i) stability of total system and (ii) global/local performance trade-off, is to introduce a set of model set named “Global/Local Shared Model Set,” which is defined by a standard LFT form as

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