A multiscale approach to the control of MIMO systems

The need for control systems that handle large numbers of inputs and outputs becomes increasingly important with the development of systems with large numbers of transducers for controlling distributed systems. For example, in the case of embedding transducers in materials for structural control, so-called “smart materials”, the development of control technology has lagged substantially behind that of the base materials, transducers and embedding techniques. Still, development of materials with ever-greater numbers of embedded elements continues, spurred by potential uses that require large arrays of sensors and actuators. No control technology suitable for such large arrays exists, however, and this presents a barrier to future applications. We report on work aimed at developing and demonstrating technology capable of controlling hundreds or thousands of sensors and actuators embedded in the base material. We have dubbed this the “KIKO control problem” (Kilo-Input/Kilo-Output). This paper focuses on a new multiscale/multirate theory of hierarchical design based on the wavelet transform. In the context of this theory, we develop efficient and highly scalable implementations of control systems using multiprocessor architectures