Uncertain systems: Adapting to circumstances

Many technologies rely on control systems whose components are connected by shared networks. In designing such systems it is essential to consider the limitations caused by high levels of communication, to ensure that the systems can operate appropriately within the given bandwidth. It is important to make use of quantization schemes (or ‘quantizers’) for the system operation that have sufficient precision and, at the same time, require low communication rates.

With this aim in mind, Tomohisa Hayakawa and Hideaki Ishii at Tokyo Institute of Technology and Koji Tsumura at the University of Tokyo have recently worked in collaboration to develop adaptive control frameworks, which aim to maintain the quantizer at as coarse a level as possible in the face of system uncertainties.

The quantizer that the researchers designed varies over time rather than remaining constant. At each instant in time its parameters are determined and adjusted in response to the update in the controller gain.

Furthermore, the control scheme has been extended to the case where the quantizer has a ‘deadzone’. This means that only a finite number of quantization levels is required for any compact set in the state space. Meanwhile the closed-loop system that is guaranteed, mathematically, to be ultimately bounded.

These results are expected to become the foundation for the development of future large-scale networked control systems.

• T. Hayakawa, H. Ishii, and K. Tsumura. Adaptive quantized control for linear uncertain discrete-time systems. Automatica 45(3), 692-700, 2009.
  (doi:10.1016/j.automatica.2008.07.005)
• T. Hayakawa, H. Ishii, and K. Tsumura. Adaptive quantized control for nonlinear uncertain systems. Sys. Contr. Lett. 58(9), 625-632, 2009.
  (doi:10.1016/j.sysconle.2008.12.007)

• Department of Mechanical and Environmental Informatics, Tokyo Institute of Technology
• Department of Computational Intelligence and Systems Science, Tokyo Institute of Technology
• Department of Information Physics and Computing, The University of Tokyo

Adaptive control scheme with a time-varying quantizer