Set computations with subpavings in MATLAB: The SCS Toolbox

This paper presents a MATLAB Toolbox that allows to represent and manipulate subpavings, i.e. unions of non-overlapped boxes. The main property of subpavings is their ability to approximate compact sets in W1 with arbitrary precision. The functions provided in the SCS Toolbox allow to: create subpavings; calculate the union and the intersection between subpavings; evaluate the image of a subpaving by a function; evaluate the inverse image; visualize subpavings in R2. The algorithms for function evaluation (both image and inverse image), based on interval analysis tools, allow to deal with non-linear functions. The set of provided functions can be easily used to solve a wide spectrum of problems involving uncertainty that are studied in the automatic control literature. Two examples are presented, a parameter estimation problem where the measurements are uncertain and the simulation of a system from an uncertain initial state.