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Improvement of the LMI method of [Scherer 2000] for multi-objective designs

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from Improvement of the LMI method of [Scherer 2000] for multi-objective designs by Emile Simon
This implements an improvement based on a new insight of the change of variables proposed in [S00].

Main.m 
close all
clear all
clc

[Pstruct,Pnormal,P,Obj0,Ts,n,m,p] = PlantS00;

%0th order Youla parameter, easily obtained with LMIs(Variables1) or a simple line search:
DQmix = -9.59;
ObjBestDQ = 119.4;%Corresponding multi-objective value.

QnewZ = ss([],[],[],DQmix,Ts);
globopt = 102.9799;%A priori known value for the global optimum, to draw the rate of convergence towards it (the smallest value found was 102.97996).
for i=1:25
    
    %FIR designs of [S00].
    t0 = clock;
    [QFIR,ObjBFir(i)] = FIR(Pstruct,i);
    tFIR(i)=etime(clock,t0);

    figure(1)
    plot(0:p:p*i,[ObjBestDQ ObjBFir],'bo')
    pause(0.001)
    
    figure(2)
    loglog(tFIR,ObjBFir/globopt-1,'bo')
    pause(0.001)
        
    
    %Proposed Growing Youla, with InnerLoop algorithm improving all four state-space matrices of the Youla parameter. The computations do not use the FIR results above.
    if(i<16)%Iterations for i>=10 are useless with this example, the multi-objective value is already at the globally optimal level and do not decrease further.
        t3 = clock;
        [QnewZ,QendZ,ObjBestZ(i)]=InnerLoop(Pstruct,AddPoleFIR(QnewZ),0.0001);
        tGrow = etime(clock,t3);
        if(i==1)
            tGrowT(i) = tGrow;
        else
            tGrowT(i) = tGrow + tGrowT(i-1);%The total computation time is acumulated, since we start from the controller obtained at the previous i
        end
        figure(1)
        hold on
        plot(0:p:p*i,[ObjBestDQ ObjBestZ],'g-s')
        pause(0.001)
        
        figure(2)
        hold on
        loglog(tGrowT,ObjBestZ/globopt-1,'g-s')
        pause(0.001)
    end
end

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