SICONOS is the European Project
IST2001-37172, funded by the Commission of the European Communities,
from
September 1, 2002, to August 31, 2006. It is a project of the
Information
Society Technologies programme, fifth framework programme (FP5). This
project's goal is the study of complementarity dynamical systems (a
class of
hybrid dynamical systems). It gathers scientists from various
communities
like Mechanics, Applied Mathematics, Systems and Control, and Numerical
Analysis.
The name Siconos comes from the title of the project: Modelling, Simulation and Control of Nonsmooth Dynamical Systems.
The purpose of this grant is to
develop algorithms and software for
the simulation and feedbackcontrol of dynamical systems which are
nonsmooth,
and more specifically so-called complementarity dynamical systems.
Nonsmoothness is usually introduced into the system either by some
nonsmooth
control action or by the presence of nonsmooth events at a macroscopic
level
(such as impacts or switchings). Nonsmooth models abound in many
engineering
systems such as sliding mode or hybrid control and rigid body mechanics
such
as rattle of automotive components and other mechanical freeplay, and
switching circuits in power electronics. We choose complementarity
systems as
the mathematical framework for studying nonsmooth nonlinear systems.
This
framework is large in terms of the range of potential applications, yet
specific enough to allow for deep investigation.
The research will tackle head on two
fundamental issues. Firstly
that smooth numerical methods fail on nonsmooth systems. Algorithms
need to
be developed that deal with hit crossings, impacts, complementarity
problems,
sliding and chatter in a robust and easily applicable way. Second, the
qualitative understanding of the dynamics including the design of
feedback
and robust control algorithms requires specific methods and cannot be
solved
with simple adaptations of known techniques for smooth linear or
nonlinear
dynamical systems.
The research teams comprise many of
the world experts in the theory
and applications of these disparate theories. Therefore, this grant
represents a unique opportunity to synthesise current knowledge in
order to
achieve the much needed goal of a general software for nonsmooth
dynamics.
The strategic aim of this project is
the development of novel algorithms and numerical routines for the
qualitative analysis, simulation and feedback control of nonsmooth
complementarity dynamical systems. The output of this project will be
an integrated numerical software package for the virtual prototyping of
systems with discontinuities and development of novel control
techniques for this class of dynamical systems. This will be achieved
through an in-depth investigation of the mathematical and engineering
open problems related to nonsmooth complementarity systems. Therefore,
this project is clearly focussed on the development over 4 years of a user-friendly,
versatile and computationally effective numerical tool for nonsmooth
systems, validated through its application to 3 key engineering
problems: power electronic converters, walking robots and automotive
systems.
The main requirements of the numerical software tool can be outlined as
follows
Efficient handling of
nonsmooth models.
Nonsmooth models need careful treatment as their phase space can
contain an intricate web of discontinuity boundaries which need to be
properly specified and dealt with. At the same time the formalism used
to describe the system of interest should be synthetic, easy to
implement and general enough to encompass a wide class of problems.
Under these conditions, the decision of the most effective analytical
framework was made to be that of complementarity systems. The
decision for this framework was made unanimously by all the
participating teams.
Ability to characterise
existence and stability of solutions.
In particular, methods
are required to investigate the existence of different types of
solutions (e.g. periodic solutions) and assess their stability. This is
particularly relevant to solve parametric continuation problems for
nonsmooth systems.
Fast computational engine for
time-integration and parametric continuation.
Numerical algorithms need to be derived in order to perform an accurate
time integration of complementarity systems incorporating their main
features (LCP or NCP solvers, treatment of finite accumulation of
events, collision detection, choice between event-driven and
time-stepping schemes, etc.). Efficient methods and algortithms for the
parametric continuations of solutions and identification of bifurcation
points are also needed.
Toolbox for the design and
validation of control strategies for nonsmooth systems.
The control of complementarity systems
(and other formalisms for nonsmooth systems) is a rapidly expanding
research direction. We envisage the development of novel control
techniques for nonsmooth complementarity systems (see below for further
details) and the development of numerical routines to perform their
validation.
Modular structure and user-friendly interface. The numerical software we plan to develop should be modular, easy to expand with additional routines (or toolboxes). In contrast to some of the existing software, it should be easy to use through an interactive, user-friendly graphical interface.