robustify_eq_conic.m

求解线性矩阵不等式简单方便--与LMI工具箱相比

function F = robustify_eq_conic(F_xw,Zmodel,x,w)

if length(F_xw) == 0
    F = [];
    return;
else
    Ftemp = [];
    for i = 1:length(F_xw)
        Fi = sdpvar(F_xw(i));
        if degree(Fi(:),w) > 0
            [BilinearizeringConstraints,failure] = deriveBilinearizing(Fi,w,0);
            if failure
                error('Cannot get rid of nonlinear uncertainty in uncertain SDP')
            else
                Ftemp = Ftemp + BilinearizeringConstraints;
            end
        end
    end
    F = Ftemp;
    
    
    if any(Zmodel.K.q) | any(Zmodel.K.s)
        error('Only polytope uncertainty supported for uncertain equalities');
    else
        % FIX : Assumes all uncertainty in all constraints
        K = Zmodel.K;
        A = -Zmodel.F_struc((1+K.f):(K.f + K.l),2:end);
        b =  Zmodel.F_struc((1+K.f):(K.f + K.l),1);

        vertices = extreme(polytope(A,b))';
        if K.f > 0
            Aeq = -Zmodel.F_struc(1:K.f,2:end);
            beq =  Zmodel.F_struc(1:K.f,1);
            feasible = sum(abs(Aeq*vertices - repmat(beq,1,size(vertices,2))),1) < 1e-6;
            vertices = vertices(:,feasible);
            if isempty(feasible)
                error('The uncertainty space is infeasible.')
            end
        end
        
        for j = 1:length(F_xw)
            for i = 1:size(vertices,2)
                F = F + set(replace(F_xw(j),w,vertices(:,i)));
            end
        end
    end
    
end