MATISSE is a free MATLAB toolbox for safety verification and reachable set
computation of large dimensional, constrained linear systems.
The main
functionalities of MATISSE are the following:
1  Given a constrained linear
systems, the toolbox computes a lower dimensional abstraction of the system,
and provides bounds for the precision of the approximation.

2  The computation of a bisimulation function between a constrained linear system and its projection.

3  The computation of the reachable sets of a constrained linear system using zonotope methods.

Download MATISSE
here!
Description:
Matisse is based on the framework of abstracting linear systems using
approximate bisimulation relations [1,2,3,4]. Contrary to the usual notions of
system equivalence and refinement based on language inclusion or exact
bisimulation relations, approximate bisimulation relations do not require the
behavior of a system and its abstraction to be exactly the same. Approximate
bisimulation relations aim in capturing the most significant characteristics
of a system dynamics and neglect less important ones. The degree of
approximation is given by the precision of the approximate bisimulation. This
precision notably provides a bound of the distance between the trajectories of a
system and of its abstraction.
Approximate bisimulation based abstraction is particularly useful for the
safety verification problem which consists in checking whether the
intersection of the reachable set of the system with an unsafe set is empty
or not. If we can check that the distance of the unsafe set to the reachable
set of the abstraction of the system is greater than the precision of the
approximate bisimulation then it follows that the original system is safe. The
more robustly safe a system, the more approximations are possible which
confirms the intuitive fact that the verification of robustly safe systems
should be easier.
In order to use MATISSE, you will need to install the following free MATLAB toolboxes:
Author: 
Antoine Girard,
Department of Electrical and Systems Engineering,
University of Pennsylvania. 

Collaborators: 
A. Agung Julius,
Department of Electrical and Systems Engineering,
University of Pennsylvania. 
George J. Pappas,
Department of Electrical and Systems Engineering,
University of Pennsylvania. 

References: 
1. Approximate Bisimulations Relations for Constrained Linear Systems. (pdf)
Antoine Girard and George J. Pappas, Automatica, 2005, accepted.

2. Approximation Metrics for Discrete and Continuous Systems. (pdf)
Antoine Girard and George J. Pappas, IEEE Transactions on Automatic Control, 2005, accepted.


About the painter (quoted from Nancy Doyle Fine Art): 


"Matisse began with still lifes and interiors which still contained some observation of nature in the drawing of objects, with some 'flattening' of forms and of the canvas surface. As he matured as an artist, the forms became more and more simplified, and the images became less concerned with 'correct' drawing. Eventually, his images appear to have been only cursorily drawn and painted  just the essential parts were distilled from the image. There was no use of linear perspective to indicate spatial depth in this new painting; on the contrary, Matisse used his curvilinear forms and bold decorative patterns to emphasize the flatness of the canvas surface. There was also no blending of colors  they were placed flatly against one another, avoiding the 'soft' look of blended color and the 'natural' look of this method of depicting three dimensions." 


Last update: 09/05/2005
