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@logicalZonotope/encloseMany.m

@@ -1,17 +1,15 @@
-function [Zenclose,rotMatrixInv] = encloseMany(Z,direction)
+function [Zenclose] = encloseMany(Z)
 % encloseMany - function for the enclosure of many zonotopes
 %
 % Syntax:  
 %    [Zenclose,rotMatrixInv] = encloseMany(Z,direction)
 %
 % Inputs:
 %    Z - cell array of zonotopes to be enclosed
-%    direction - mean direction, in which the zonotopes to be enclosed are
-%    heading to
 %
 % Outputs:
-%    Zenclose - enclosing zonotope (which is an oriented rectangular hull)
-%    rotMatrix - rotation matrix of the oriented rectangular hull
+%    Zenclose - enclosing zonotope 
+%   
 %
 % Example: 
 %
@@ -21,46 +19,19 @@
 %
 % See also: dirPolytope
 
-% Author:       Matthias Althoff
-% Written:      15-January-2008
+% Author:       Amr Alanwar
+% Written:      21-August-2022
 % Last update:  ---
 % Last revision:---
 
 %------------- BEGIN CODE --------------
-
-%get dimension and original axis aligned orientation
-dim=length(direction);
-orient=eye(dim);
-
-%replace one of the axis aligned vectors
-newGen=direction/norm(direction);
-
-%retrieve most aligned generator from orient
-for iGen=1:length(orient(1,:))
-     h(iGen)=abs(newGen'*orient(:,iGen)/norm(orient(:,iGen)));
+resp= [];
+for i=1:length(Z)
+resp= [resp, evaluate(Z{i})];
 end
+Zenclose = logicalZonotope.enclosePoints(resp);
 
-[~,ind]=sort(h);
-pickedIndices=ind(1:(end-1));
 
-rotMatrix=[newGen,orient(:,pickedIndices)];
-
-%obtain and collect vertices
-Vsum=[];
-for i=1:length(Z)
-    Zred=reduce(Z{i},'parallelpiped');
-    Vnew=vertices(Zred);
-    Vsum=[Vsum,Vnew];
-end
 
-%rotate vertices
-rotMatrixInv=inv(rotMatrix);
-Vtrans=rotMatrixInv*Vsum;
-%compute enclosing interval
-Itrans=interval.enclosePoints(vertices(Vtrans));
-%generate zonotope
-Ztrans=zonotope(Itrans);
-%rotate zonotope back
-Zenclose=rotMatrix*Ztrans;
 
 %------------- END OF CODE --------------

@logicalZonotope/enclosePoints.asv

@@ -0,0 +1,90 @@
+function Z = enclosePoints(points,varargin)
+% enclosePoints - enclose a point cloud with a zonotope
+%
+% Syntax:  
+%    Z = enclosePoints(points)
+%
+% Inputs:
+%    points - matrix storing point cloud (dimension: [n,p] for p points)
+%
+% Outputs:
+%    Z - zonotope object
+%
+% Example: 
+%
+% References:
+% Other m-files required: none
+% Subfunctions: none
+% MAT-files required: none
+%
+% See also: interval, polytope
+
+% Author:        Amr Alanwar
+% Written:       11-Aug-2020
+% Last update:   ---
+% Last revision: ---
+
+%------------- BEGIN CODE --------------
+% [dim,numOfPoints] = size(points);
+% cen = [];
+% newpoints = [];
+% for i = 1:numOfPoints
+%     if zeros(dim,1) ==points(:,i)
+%         cen =zeros(dim,1);
+%     else
+%         newpoints= [newpoints points(:,i)];
+%     end
+% end
+% newpoints=unique(newpoints','rows')';
+% 
+% [row,cols] = size(newpoints);
+% for i = 1:cols
+%     gen{i} = newpoints(:,i);
+% end
+
+%points=unique(points','rows')';
+% cen =zeros(dim,1);
+% gen = {points};
+points=unique(points','rows')';
+[dim,numOfPoints] = size(points);
+cen = points(:,1);
+if numOfPoints > 1
+    containsZeroFlag=0;
+    newPoints = [];
+   for i =1:numOfPoints
+
+        if points(:,i) == zeros(dim,1)
+            containsZeroFlag =1;
+            saveI = i;
+            break;
+
+            els
+        end
+   end
+
+   if containsZeroFlag ==1
+       cen = points(:,saveI);
+       for i =1:numOfPoints
+           if i==saveI
+
+           else
+               gen{index} = xor(cen,points(:,i));
+               index = index +1;
+           end
+       end
+   else
+       index =1;
+       for i =2:numOfPoints
+           gen{index} = xor(cen,points(:,i));
+           index = index +1;
+       end
+   end
+    Z =logicalZonotope(cen,gen);
+else
+    Z =logicalZonotope(cen,{});
+end
+Z=unique(Z);
+
+end
+
+%------------- END OF CODE --------------

@logicalZonotope/enclosePoints.m

@@ -47,16 +47,35 @@
 % gen = {points};
 points=unique(points','rows')';
 [dim,numOfPoints] = size(points);
-
 cen = points(:,1);
-index =1;
-for i =2:numOfPoints
-    gen{index} = xor(cen,points(:,i));
-    index = index +1;
+if numOfPoints > 1
+    containsZeroFlag=0;
+    newPoints = [];
+    for i =1:numOfPoints
+        if points(:,i) == zeros(dim,1)
+            containsZeroFlag =1;
+        else
+            newPoints =[newPoints points(:,i)];
+        end
+    end
+
+    if containsZeroFlag ==1
+        cen = zeros(dim,1);
+        for i =1:numOfPoints-1
+            gen{i} =newPoints(:,i);
+        end
+    else
+        index =1;
+        for i =2:numOfPoints
+            gen{index} = xor(cen,points(:,i));
+            index = index +1;
+        end
+   end
+    Z =logicalZonotope(cen,gen);
+else
+    Z =logicalZonotope(cen,{});
 end
-
-
-Z =logicalZonotope(cen,gen);
+Z=unique(Z);
 
 end
 

@logicalZonotope/logicalZonotope.m

@@ -102,6 +102,7 @@
 methods (Static = true)
     %Z = generateRandom(varargin) % generate random zonotope
     Z = enclosePoints(points,varargin) % enclose point cloud with zonotope
+    Z = encloseMany(Zcell)
 end
 
 

@logicalZonotope/mtimes.asv → @logicalZonotope/mtSum.m

@@ -1,4 +1,4 @@
-function Z = mtimes(factor1,factor2)
+function Z = mtSum(factor1,factor2)
 % mtimes - Overloaded '*' operator for the multiplication of a matrix or an
 % interval matrix with a zonotope
 %
@@ -66,35 +66,42 @@
 [mrows,mcols]=size(matrix);
 
 
-% for k =1:mrows
-%     temp = 1;
-%     for ii =1:mcols
-%         temp=temp| (matrix(k,ii) & Z.c(ii) );
-%     end
-%     result.c(k,1) = temp;
-% end
-
+if ~isempty(Z.c)
+    for k =1:mrows
+        temp =0;
+        for ii =1:mcols
+            temp=or(temp,(matrix(k,ii) & Z.c(ii) ));
+            %temp=temp + matrix(k,ii) * Z.c(ii) ;
+        end
+        result.c(k,1) = temp;
+    end
+else
+    result.c ={};
+end
+%result.c=matrix * Z.c;
 
 if ~isempty(Z.G)
     for i =1:length(Z.G)
 
         [mrows,mcols]=size(matrix);
-        [grows,gcols]=size(Z.G);
+        [grows,gcols]=size(Z.G{i});
 
-        for j=1:gcols
+       % for j=1:gcols
 
             for k =1:mrows
-                temp = 1;
+                temp = 0;
                 for ii =1:grows
-                    temp=temp| (matrix(k,ii) & Z.G{i}(ii,j) );
+                   %temp=temp + matrix(k,ii) * Z.G{i}(ii,1) ;
+                    temp=or(temp,(matrix(k,ii) & Z.G{i}(ii,1) ));
                 end
-                result.G{i}(k,j) = temp;
+                result.G{i}(k,1) = temp;
             end
-
-        end
+           % result.G{i} = mod(result.G{i},2);
+       % end
     end
 
  Z = logicalZonotope(result.c,result.G);
+ Z = unique(Z);
 else
    Z = logicalZonotope(result.c,{}); 
 end

@logicalZonotope/mtimes.m

@@ -70,7 +70,8 @@
     for k =1:mrows
         temp =0;
         for ii =1:mcols
-            temp=temp| (matrix(k,ii) & Z.c(ii) );
+            %temp=or(temp,(matrix(k,ii) & Z.c(ii) ));
+            temp=temp + matrix(k,ii) * Z.c(ii) ;
         end
         result.c(k,1) = temp;
     end
@@ -90,15 +91,16 @@
             for k =1:mrows
                 temp = 0;
                 for ii =1:grows
-                    temp=temp| (matrix(k,ii) & Z.G{i}(ii,1) );
+                    temp=temp + matrix(k,ii) * Z.G{i}(ii,1) ;
+                    %temp=or(temp,(matrix(k,ii) & Z.G{i}(ii,1) ));
                 end
                 result.G{i}(k,1) = temp;
             end
-
+            result.G{i} = mod(result.G{i},2);
        % end
     end
 
- Z = logicalZonotope(result.c,result.G);
+ Z = logicalZonotope(mod(result.c,2),result.G);
  Z = unique(Z);
 else
    Z = logicalZonotope(result.c,{}); 

@logicalZonotope/reduce.m

@@ -32,21 +32,6 @@
 %    Zred=reduce(Z,'combastel',2);
 %    plot(Zred,[1,2],'b');
 %
-% References:
-%    [1] M. Althoff. "Reachability analysis and its application to the
-%        safety assessment of autonomous cars", 2010
-%    [2] A. Girard. "Reachability of uncertain linear systems using
-%        zonotopes". 2005
-%    [3] A. Kopetzki et al. "Methods for order reduction of zonotopes",
-%        CDC 2017
-%    [4] C. Combastel. "A state bounding observer based on zonotopes",
-%        ECC 2003
-%    [5] J. Scott et al. "Constrained zonotopes: A new tool for set-based
-%        estimation and fault detection", Automatica 2016
-%
-% Other m-files required: none
-% Subfunctions: see below
-% MAT-files required: none
 %
 % See also: none