Henrik Sandberg, July 2012
Henrik Sandberg will be visiting CDS on 30-31 July (Tue-Wed).
Synthesis of Models using Lossless Components and Some Related Design Trade-Offs
Speaker: Henrik Sandberg
Affiliation: Electrical Engineering, KTH
Date and time: Monday, 30 July 2012 - 11:00am
Location: 213 Annenberg
The area of network synthesis deals with how to implement mathematical models using a well-defined set of physical components. This area was thoroughly studied in the circuits community in the 1960-1970's, using components such as resistors, transformers, capacitors, inductors, and operational amplifiers. Today similar questions are being asked in synthetic biology and in mechanics, only now the given sets of physical components are very different. Typical questions of interest are to characterize what type of mathematical models can be implemented for given sets of components, and the minimal number of components required for a specific model.
In this talk, we address the problem of synthesizing some classes of active and passive mathematical models using only a small number of lossless physical components. The set of lossless components are relevant since they conserve energy and if we intend to implement anything on a microscopic level, for example a micro machine, we will need to respect this limitation. In our earlier work we have shown that linear models are passive if, and only if, they can be approximated to any desired degree of accuracy by a linear lossless system, over any fixed time horizon. Typically this requires a huge number of lossless components, however, which results in thermal noise as quantified by the fluctuation-dissipation theorem. Here we will see that by allowing the linear lossless components to be time-varying, not only can we avoid some thermal noise, but we can also synthesize some active components. Given the importance of active components such as operational amplifiers this is encouraging. The price for the decrease in implementation complexity is a need for an external power supply. We illustrate the control-theoretic relevance of these results by means of a few examples and design trade-offs.