RESEARCH

Randomized Algorithms for Systems and Control

The main objective of this research area is to study probabilistic and randomized methods for analysis and design of uncertain systems. This area is fairly recent, even though its roots lie in the robustness techniques for handling complex control systems developed in the 1980s. In contrast to these previous deterministic techniques, its main ingredient is the use of probabilistic concepts. One of the goals of this research endeavor is to provide a reapprochement between the classical stochastic and robust paradigms, combining worst-case bounds with probabilistic information, thus potentially reducing the conservatism inherent in the worst-case design. In this way, the control engineer gains additional insight that may help bridging the gap between theory and applications.

The algorithms derived in the probabilistic context are based on uncertainty randomization and are usually called randomized algorithms. For control systems analysis, these algorithms have low complexity and are associated with robustness bounds that are generally less conservative than the classical ones, obviously at the expense of a probabilistic risk of failure.

 

Al Karitsmi

Fabrizio beneath the statue of Muhammad ibn Mūsā al-Khwārizmī
(from whom the term algorithm), Urgench, Uzbekistan, August 2001

 

RACT Toolbox for MATLAB

The Randomized Algorithms Control Toolbox (RACT) is a Matlab toolbox for probabilistic analysis and synthesis of control systems affected by various uncertainty structures. Some of the RACT features are:

  • Handle a variety of uncertain objects: scalar, vector and matrix uncertainties, with different probability distributions
  • Easy and fast sampling for uncertain objects of almost any type
  • Randomized algorithms for probabilistic performance verification and probabilistic worst-case performance
  • Randomized algorithms for feasibility of uncertain LMIs using stochastic gradient, ellipsoid or cutting plane methods
  • Optimal design methods using the scenario approach

RACT is entirely based on Matlab. It can be freely downloaded from the web page:

http://ract.sourceforge.net

To install the toolbox, just unzip the downloaded version and update your path. In the current version, several bugs have been fixed, the part relative to control systems design has been improved, and new examples have been created. RACT is free, but as always, no guarantees! Working version of Matlab is 7.3, but it should definitely work under 6.5.

Thanks for trying RACT!

The RACT Project

RACT has been developed at IEIIT-CNR (Politecnico di Torino, Italy) and at the Institute for Control Science (Moscow, Russia), based on a bilateral international project funded by Consiglio Nazionale delle Ricerche (CNR) and Russian Academy of Sciences (RAS). Members of the project:

  • Andrey Tremba (Main Developer and Maintainer)
  • Giuseppe Calafiore
  • Fabrizio Dabbene
  • Elena Gryazina
  • Boris Polyak (Co-Principal Investigator)
  • Pavel Shcherbakov
  • Roberto Tempo (Co-Principal Investigator)

Recent research contracts

Under construction, see Recent projects

 

  
Politecnico di Torino CNR