addevalvariablecuts.m

求解线性矩阵不等式简单方便--与LMI工具箱相比

function pcut = addEvalVariableCuts(p)

temp = p.F_struc(1:p.K.f,:);
p.F_struc(1:p.K.f,:) = [];
pcut = p;
for i = 1:length(p.evalMap)
    y = p.evalVariables(i);
    x = p.evalMap{i}.variableIndex;
    xL = p.lb(x);
    xU = p.ub(x);

    % Generate a convex hull polytope
    switch p.evalMap{i}.fcn
        case 'exp'
            [Ax, Ay, b] = bound_exp(xL,xU);
        case {'sqrtm','sqrtm_internal'}
            [Ax, Ay, b] = bound_sqrtm(xL,xU);
        otherwise
            % sample function
            z = linspace(xL,xU,100);
            if isequal(p.evalMap{i}.fcn,'sdpfun')
                fz = feval(p.evalMap{i}.arg{2},z);
            else
                fz = feval(p.evalMap{i}.fcn,z);
            end
            % create 4 bounding planes
            % f(z) < k1*(x-XL) + f(xL)
            % f(z) > k2*(x-XL) + f(xL)
            % f(z) < k3*(x-XU) + f(xU)
            % f(z) > k4*(x-XU) + f(xU)
            k1 = max((fz(2:end)-fz(1))./(z(2:end)-xL))+1e-3;
            k2 = min((fz(2:end)-fz(1))./(z(2:end)-xL))-1e-3;
            k3 = min((fz(1:end-1)-fz(end))./(z(1:end-1)-xU))+1e-3;
            k4 = max((fz(1:end-1)-fz(end))./(z(1:end-1)-xU))-1e-3;
            Ax = [-k1;k2;-k3;k4];
            Ay = [1;-1;1;-1];
            b =  [k1*(-z(1)) + fz(1);-(k2*(-z(1)) + fz(1));k3*(-z(end)) + fz(end);-(k4*(-z(end)) + fz(end))];
            if 0
                hold on
                plot(z,fz)
                plot(z,fz(1) + k1*(z-z(1)))
                plot(z,fz(1) + k2*(z-z(1)))
                plot(z,fz(end) + k3*(z-z(end)))
                plot(z,fz(end) + k4*(z-z(end)))
            end
%                           Ax = zeros(0,1);
%                           Ay = zeros(0,1);
%                           b = zeros(0,1);
    end
    F_structemp = zeros(size(b,1),length(p.c)+1);
    F_structemp(:,1+y) = -Ay;
    F_structemp(:,1+x) = -Ax;
    F_structemp(:,1) = b;
    pcut.F_struc = [F_structemp; pcut.F_struc];
    pcut.K.l = pcut.K.l + length(b);
end
pcut.F_struc = [temp;pcut.F_struc];