Data structures

% s is the polytope
s.dim=N % The dimension of the statespace

s.vertices={} % Lists the  vertices of the polytope
% are  vectors denominating the vertices of the state space polytope

s.facet{}.vertices={} % Specifying the facets as a function of the vertices
% denotes a facet and  are indices into the list of vertices,
% indicating the vertices  of facet 

s.facet{}.opposit= %A vertex opposit the facet
% #$j_{o}$ is a vertex opposit facet $j$ i.e. any vertex of s not in
% s.facet{}.

s.input % A substructure describing the polytopic input space for s
s.input.dim=m % The dimension of the input space

s.input.vertices={,ldots } % The vertices of the input space
%   are  vectors denoting the vertices of the input space

s.input.facet{}.vertices={}; % A facet of the input space
s.input.facet{}.opposit= % A vertex not in facet j

s.dynamics % Sub structure describing the dynamics acting on s
% Dynamics are on the form 

s.dynamics.A= % The autonomous dynamics
s.dynamics.B= % The input dynamics
s.dynamics.C= % The affine dynamics

%PAHS is a Piecewise-Affine Hybrid System

%A PAHS consists of a number of modes
pahs.mode{}= % The  mode of the PAHS

% Each mode has a number of substructures
mode.dynamics=dyn %Mode wide dynamics (not mandatory)
% Common dynamics shared between all polytopes of the mode

mode.input=input    %Mode wide input    (not mandatory)
% Common input shared between all polytopes of the mode

%Cell Array of locations
mode.loc{}= % is the  location of the  mode

%each location, $q_{i,j}$ (loc) is described as:
loc{}.s  % an affine system on a polytope
loc{}.bord=[]
% is an array of indices, one for each facet of loc.s,
% denoting neigboring locations to that facet.
% If empty there is no defined neighbor to the facet.

mode.trans{} % Cell array of transitions starting from this mode
% Each transitions is described by its destination and controllability
trans{}.dest=  %Destination mode  of the transition
trans{}.ctrb=   % Boolean describing the controllability of the transition, if true the transition is controllable.

pahs.samepart  %Boolean hint set to true if identical partitions is used in all modes

% de is the discrete equivalent
de.blockset= % The blockable set
%  is a vector of  facet indices

de.exits= % Possible exit facet vector
%  is a vector of  facet indices

de.exit{j}.testVec= % The test vector used for facet j

de.block.testVec= % Test vector used for the case of all facets blocked

% dgabs is a discrete game abstraction

dgabs.maxfacet= % this is the maximum number of facets of in any of the modes

mode.trans{} % Cell array of transitions starting from this mode
% Each transitions is described by its destination and controllability
trans{}.dest=  %Destination mode  of the transition
trans{}.ctrb=   % Boolean describing the controllability of the transition, if true the transition is controllable.

dgabs.mode{}= %is the abstraction of mode 

mode.da{}= % is the abstraction of location  in mode .
da{}.des{}=de % is a cell array of discrete equivalents of the location
da{}.numfacets= % is the number of facets of the location
da{}.bord=[] %bordering locations identical to the pahs definition
% is an array of indices, one for each facet of loc.s,
% denoting neigboring locations to that facet.
% If empty there is no defined neighbor to the facet.

da{}.trans{}=[] % is a cell array of arrays (one for each )
% The array contains indices $l_k$ specifying which locations in the destination mode of 
% can be reached by  from the discrete abstraction of .

%req is a requirement specification and  are polytopes.

%initial set
req.init{} % Cell array of initial set polytopes. Each cell contains a polytope
 init{}.poly= % Polytope describing an initial set
 init{}.modes=[] % An array of modes the polytope is valid in

%goal set
req.goal{} % Cell array of goal set polytopes. Each cell contains a polytope
 goal{}.poly= % Polytope describing a goal set
 goal{}.modes=[] % An array of modes the polytope is valid in

%avoid set
req.avoid{} % Cell array of avoid set polytopes. Each cell contains a polytope
 avoid{}.poly= % Polytope describing an avoid set
 avoid{}.modes=[] % An array of modes the polytope is valid in

%The specification on the dgabs is very similar to the requirements
%Here only the initial set specification is shown.

%Initial set
req.init{} % Cell array of inital sets
 init{}.loc= % An initial location
 init{}.modes=[] % An array of modes for the initial location
 %NB: Having more than one mode in the array mostly makes sense for problems where the
 %modes share a partition.