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Copy pathCMoN_Init.m
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CMoN_Init.m
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function [rho, c2] = CMoN_Init(sizes, mem, input)
nx=sizes.nx;
nu=sizes.nu;
nc=sizes.nc;
ncN=sizes.ncN;
N=sizes.N;
nbu=sizes.nbu;
nbu_idx=sizes.nbu_idx;
nbx=sizes.nbx;
nbx_idx=sizes.nbx_idx;
nz = nx+nu;
nw = (N+1)*nx+N*nu;
neq = (N+1)*nx;
nineq = 2*(N*nc+ncN+N*nbu+N*nbx);
H=[];
for i=0:N-1
H=blkdiag(H, [mem.Q(:,i*nx+1:(i+1)*nx), mem.S(:,i*nu+1:(i+1)*nu);
(mem.S(:,i*nu+1:(i+1)*nu))', mem.R(:,i*nu+1:(i+1)*nu)]);
end
H=blkdiag(H, mem.Q(:,N*nx+1:(N+1)*nx));
BT=zeros(nw,neq);
BT(1:nz,1:2*nx)=[eye(nx,nx), (mem.A(:,1:nx))'; zeros(nu,nx), (mem.B(:,1:nu))'];
for i=1:N-1
BT(i*nz+1:(i+1)*nz, i*nx+1:(i+2)*nx) = [-eye(nx,nx), (mem.A(:,i*nx+1:(i+1)*nx))'; zeros(nu,nx), (mem.B(:,i*nu+1:(i+1)*nu))'];
end
BT(N*nz+1:N*nz+nx, N*nx+1:(N+1)*nx) = -eye(nx,nx);
B=BT';
C=[];
Iu = zeros(nbu,nu);
for j=1:nbu
Iu(j,nbu_idx(j))=1;
end
Ix = zeros(nbx,nx);
for j=1:nbx
Ix(j,nbx_idx(j))=1;
end
for i=0:N-1
if i>0
C=blkdiag(C, [mem.Cgx(:,i*nx+1:(i+1)*nx), mem.Cgu(:,i*nu+1:(i+1)*nu);
-mem.Cgx(:,i*nx+1:(i+1)*nx) , -mem.Cgu(:,i*nu+1:(i+1)*nu);
zeros(nbu,nx), Iu;
zeros(nbu,nx), -Iu;
Ix, zeros(nbx,nu);
-Ix, zeros(nbx,nu)]);
else
C=blkdiag(C, [mem.Cgx(:,i*nx+1:(i+1)*nx), mem.Cgu(:,i*nu+1:(i+1)*nu);
-mem.Cgx(:,i*nx+1:(i+1)*nx) , -mem.Cgu(:,i*nu+1:(i+1)*nu);
zeros(nbu,nx), Iu;
zeros(nbu,nx), -Iu]);
end
end
C=blkdiag(C,[mem.CgN;-mem.CgN;
Ix;
-Ix]);
blk4 = [];
no_mu = zeros(1,N+1);
no_mu(1) = 2*nc+2*nbu;
for i=2:N
no_mu(i) = 2*(nc+nbu+nbx);
end
no_mu(N+1) = 2*(ncN+nbx);
dmu = mem.dmu(N*nu+N*nbx+1:end);
dmu_u = mem.dmu(1:N*nu);
dmu_x= mem.dmu(N*nu+1:N*nu+N*nbx);
% dmu = mem.mu_new;
% dmu_u = mem.mu_u_new;
% dmu_x = mem.mu_x_new;
for i=0:N-1
if i>0
mu_tmp = [max(dmu(i*nc+1:(i+1)*nc),0);min(dmu(i*nc+1:(i+1)*nc),0);
max(dmu_u(i*nbu+1:(i+1)*nbu),0);min(dmu_u(i*nbu+1:(i+1)*nbu),0);
max(dmu_x((i-1)*nbx+1:(i)*nbx),0);min(dmu_x((i-1)*nbx+1:(i)*nbx),0)];
blk4=[blk4; -mu_tmp.*C(sum(no_mu(1:i))+1:sum(no_mu(1:i+1)),:)];
else
mu_tmp = [max(dmu(i*nc+1:(i+1)*nc),0);min(dmu(i*nc+1:(i+1)*nc),0);
max(dmu_u(i*nbu+1:(i+1)*nbu),0);min(dmu_u(i*nbu+1:(i+1)*nbu),0)];
blk4=[blk4; -mu_tmp.*C(1:no_mu(1),:)];
end
end
mu_tmp = [max(dmu(N*nc+1:N*nc+ncN),0);min(dmu(N*nc+1:N*nc+ncN),0);
max(dmu_x((N-1)*nbx+1:N*nbx),0);min(dmu_x((N-1)*nbx+1:N*nbx),0)];
blk4=[blk4; -mu_tmp.*C(sum(no_mu(1:N))+1:sum(no_mu(1:N+1)),:)];
c=[];
tmp1=[];
tmp2=[];
for i=0:N-1
if i>0
c=[c;-mem.uc(i*nc+1:(i+1)*nc);
mem.lc(i*nc+1:(i+1)*nc)];
if nbu_idx>0
tmp1 = mem.ub_du(i*nu+1:(i+1)*nu);
tmp2 = mem.lb_du(i*nu+1:(i+1)*nu);
tmp1 = tmp1(nbu_idx);
tmp2 = tmp2(nbu_idx);
end
c=[c;-tmp1;
tmp2;
-mem.ub_dx((i-1)*nbx+1:i*nbx);
mem.lb_dx((i-1)*nbx+1:i*nbx)];
else
c=[c;-mem.uc(i*nc+1:(i+1)*nc);
mem.lc(i*nc+1:(i+1)*nc)];
if nbu_idx>0
tmp1 = mem.ub_du(i*nu+1:(i+1)*nu);
tmp2 = mem.lb_du(i*nu+1:(i+1)*nu);
tmp1 = tmp1(nbu_idx);
tmp2 = tmp2(nbu_idx);
end
c=[c;-tmp1;
tmp2;];
end
end
c=[c;-mem.uc(N*nc+1:end);
mem.lc(N*nc+1:end);
-mem.ub_dx((N-1)*nbx+1:N*nbx);
mem.lb_dx((N-1)*nbx+1:N*nbx)];
blk5 = -diag(c);
M=[H,C',BT;
blk4, blk5, zeros(nineq, neq);
B, zeros(neq,nineq), zeros(neq, neq)];
s = svd(M).^-1;
rho = max(s);
c2 = std(s) +1;
end