Modelling of piecewise-linear multivariate functions

This research field is based on the theory of canonical representations developed in the last few years by Pedro Julián et al.

The main developments concern:

• numerical methods for the piecewise-linear approximation of nonlinear functions depending on an arbitrary finite number of variables. The following figure shows PWL approximations (in red) of four functions defined over 2D domains (in green): The following figure shows three PWL approximations of the same function with an incresing number of domain subdivisions. It is clearly visible how the approximation quality grows with the number of basis functions.
• approximation/identification of continuous dynamical systems depending on a arbitrary finite number of variables and parameters

Involved People:

• Marco Storace
• Mauro Parodi
• Daniele Linaro
• Tomaso Poggi
• Alberto Oliveri
• Federico Bizzarri

Major Publications:

• Storace M and Bizzarri F (2007), "Towards accurate PWL approximations of parameter-dependent nonlinear dynamical systems with equilibria and limit cycles", IEEE Transactions on Circuits and Systems I: Regular Papers., March, 2007. Vol. 54(3), pp. 620-631.

  [BibTeX]

• De Feo O and Storace M (2007), "Piecewise-linear identification of nonlinear dynamical systems in view of their circuit implementations", IEEE Transactions on Circuits and Systems I: Regular Papers., July, 2007. Vol. 54(7), pp. 1542-1554.

  [BibTeX]

• Storace M and De Feo O (2004), "Piecewise-linear approximation of nonlinear dynamical systems", IEEE Transactions on Circuits and Systems I: Regular Papers., Apr., 2004. Vol. 51(4), pp. 830-842.

  [BibTeX]

• M, Julián P and Parodi M (2002), "Synthesis of nonlinear multiport resistors: a PWL approach", IEEE Transactions on Circuits and Systems I: Fundamental Theory and Applications., Aug., 2002. Vol. 49(8), pp. 1138-1149.

  [BibTeX]

Funding:

• Italian Ministry of University and Research Grant - 2006-2008 (PRIN2006). Research network with the Universities of Genoa, Turin (Polytechnic), Rome "Tor Vergata". Title: "Approximation of networks of nonlinear dynamical systems (models of biologically plausible neurons) and implementation of parallel circuits for their emulation""
• Italian and Argentine Ministry for Foreign Affairs, in the framework of the bilateral agreement for scientific and technologic cooperation between Italy and Argentine 2004-2005 (Argentine coordinator: Prof. Pedro Julián, Universidad Nacional del Sur). Title: "Circuit implementations of piecewise-linear systems "