con_list6.m

由matlab开发的hybrid系统的描述语言

function [BC,Hi,Ki] = con_list6(Hi,Ki)
% Syntax
%
%    [BC,Hi,Ki] = con_list(Hi,Ki)
%
% Description
%	
%    Generate a list of conections among polyhedra
%    in (minimal representation) form
%    Hi{i} * x <= Ki(i),	1<=i<=N,
%
% where
%    x     - n x 1, state vector,
%    n     - number of states,
%    N     - total number of polyhedra,
%    Hi{i} - nb(i) x n, boundaries, 1<=nb(i)<=N-1,
%    Ki{i}	- nb(i) x 1, boundary shift, 1<=nb(i)<=N-1,
%    BC{i} - nb(i) x 1, conections between polyhedron 'i' and other polyhedra.
%            BC{i}(a)==j => polyhedron 'i' and polyhedron 'j' have common (n-1)
%            dimensional boundary. I don't count (n-2) and less dimensional
%            faces as conections !!!
%    PC{i} - nb(i) x 1, position of corresponding boundary in connected polyhedron
%            boundary list.
%
%
% (C) 2000 by M. Baotic, Zurich, 05/12/00
% Version 1.6
% contact [e-mail]
%
% Take care that the list of boundary conections is complete!
%
%     |  |
%   A |  | B
%  ____\/____    <--- ONE constraint on C can corespond to TWO neighbors
%
%      C
%  __________


EPSILON=1000*eps;


%%%%%%%%%%%%%%%%%%
% INITIALIZATION %
%%%%%%%%%%%%%%%%%%
N  = length(Hi);    % number of polyhedra
n  = size(Hi{1},2); % number of states
nb = zeros(N,1);    % number of boundaries trough all polyhedra
BC = {};            % boundary conections list


%%%%%%%%%%%%%%%
% CHECK SIZES %
%%%%%%%%%%%%%%%
if N<1,
   error('Number of polyhedra must be grater than zero!')
end
for i=1:N,
   [nb(i),aux2]=size(Hi{i});
   if aux2~=n,
      error('Number of states must be the same for all polyhedra!')
   end
   if nb(i)==0,
      error('Polyhedron must have at least one facet!')
   end
   %if nb(i)>N-1
   %   error('Polyhedron can not have more facets than neighbors!')
   %end
      
   [aux1,aux2]=size(Ki{i});
   if aux1~=nb(i) | aux2~=1
      error('Wrong size of vector Ki!')
   end
end

% more init
for i=1:N,
   BC{i}=zeros(nb(i),1);
end


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% NORMALIZE BOUNDARIES EQUATIONS %
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
for i=1:N
   % Use: Euclidean norm
   % better performance during later (possible)
   % checking of distance from a boundary
   norm = sqrt(sum((Hi{i}.*Hi{i})'));
   
   % Optional: Infinity norm
   % norm = max((abs(Hi{i}))');
   
   if min(norm) == 0,
      error('There is at least one badly defined polyhedron boundary!')
   end
   
   for j = 1:nb(i),
      Hi{i}(j,:) = Hi{i}(j,:) / norm(j);
      Ki{i}(j) = Ki{i}(j) / norm(j);
   end
   
end


%%%%%%%%%%%%%%%%%
% BUILD BC LIST %
%%%%%%%%%%%%%%%%%
for i=1:N,          % through all polyhedra
   for j=1:nb(i),   % through all boundaries
      
      found=0;
      
      for r=1:N,
         if r~=i,
            for s=1:nb(r),
               aux1 = sum(abs(Hi{i}(j,:)+Hi{r}(s,:)));
               aux2 = abs(Ki{i}(j)+Ki{r}(s));
               if (aux1 < EPSILON) & (aux2 < EPSILON),  % candidate (+/- tolerance)
                  %if AreNeighbors(i,j,r,s),
                  %   found=1;
                  %   BC{i}(j)=r;
                  %end
                  found=1;
                  BC{i}(j)=r;
                  break;
               end
            end
            if found==1,
               break;
            end
         end
      end
   end
end