what is the difference between the two pieces of code？

[cillian bao]

The  mpc code can run well in optimizer ,but when i change the code into the optimize，it can't work, and the compute output is always 0.

optimizer:

yalmip('clear')

clear

k=1; % spring stiffness

m=10; % Masses

c=0.1; % Damping

t_0 = 0 ; % Start Time

t_f = 100; % Final Time

Ts = 0.5; % Time Step

t = t_0:Ts:t_f ; % Time Vector

Nt=length(t);

%% State-Space Model

A=[0 0 1 0;

0 0 0 1

-k/m k/m -c/m 0

k/m -k/m 0 -c/m];

B=[0 0;0 0;1/m 0;0 1/m];

C=[1 0 0 0;0 1 0 0];

tran=ss(A,B,C,0);

%% State-Space Model in discrete-time

trand = c2d(tran,Ts);

Am = trand.a;

Bm = trand.b;

Cm = trand.c;

Dm = trand.d;

nx = size(Am,1); % Number of states

nu = size(Bm,2); % Number of inputs

ny = size(Cm,1);

%% Construction of MPC matrices

R = 1e-3*eye(nu);

Q = eye(ny);

N = 10; % Prediction Horizon

%% Prediction variables

u = sdpvar(repmat(nu,1,N),repmat(1,1,N));

x = sdpvar(repmat(nx,1,N+1),repmat(1,1,N+1));

r = sdpvar(repmat(ny,1,N+1),repmat(1,1,N+1));

%% Optimization Problem

objective = 0;

constraints = [];

for k = 1:N

objective = objective + (C*x{k}-r{k})'*Q*(C*x{k}-r{k}) + u{k}'*R*u{k};

constraints = [constraints, x{k+1} == Am*x{k}+Bm*u{k}];

constraints = [constraints, -[5;5] <= u{k} <= [5;5],...

-[6;6;6;6] <= x{k+1} <= [6;6;6;6]];

end

objective = objective + (C*x{N+1}-r{N+1})'*(C*x{N+1}-r{N+1});

parameters_in = {x{1},[r{:}]};

solutions_out = {[u{:}], [x{:}]};

controller = optimizer(constraints, objective,[],parameters_in,solutions_out);

%% Buffer

uu = zeros(nu , Nt) ;

xx = zeros(size(Am , 1) , Nt) ;

%% Initial conditions

xx(:,1) = [0;0;0;0];

y(:,1) = Cm*xx(:,1);

%% Refrence trajectory

Rs(1 , :) =[ones(floor(Nt/4) , 1)' , 2*ones(floor(Nt/4) , 1)' , -ones(floor(Nt/4) , 1)' , zeros(floor(Nt/4+1) , 1)'] ;

Rs(2 , :) =-[ones(floor(Nt/4) , 1)' , 2*ones(floor(Nt/4) , 1)' , -ones(floor(Nt/4) , 1)' , zeros(floor(Nt/4+1) , 1)'] ;

%% Simulation Loop

for i = 1:Nt-N-1

future_r = Rs(: , i:i+N);

inputs = {xx(:,i),future_r};

[solutions,~] = controller{inputs};

U = solutions{1};

uu(:,i)=U(:,1);

xx(:,i+1) = Am*xx(:,i) + Bm*uu(:,i);

y(:,i+1) = Cm*xx(:,i+1);

end

optimize:

yalmip('clear')

clear

k=1; % spring stiffness

m=10; % Masses

c=0.1; % Damping

t_0 = 0 ; % Start Time

t_f = 100; % Final Time

Ts = 0.5; % Time Step

t = t_0:Ts:t_f ; % Time Vector

Nt=length(t);

%% State-Space Model

A=[0 0 1 0;

0 0 0 1

-k/m k/m -c/m 0

k/m -k/m 0 -c/m];

B=[0 0;0 0;1/m 0;0 1/m];

C=[1 0 0 0;0 1 0 0];

tran=ss(A,B,C,0);

%% State-Space Model in discrete-time

trand = c2d(tran,Ts);

Am = trand.a;

Bm = trand.b;

Cm = trand.c;

Dm = trand.d;

nx = size(Am,1); % Number of states

nu = size(Bm,2); % Number of inputs

ny = size(Cm,1);

%% Construction of MPC matrices

R = 1e-3*eye(nu);

Q = eye(ny);

N = 10; % Prediction Horizon

%% Buffer

uu = zeros(nu , Nt) ;

xx = zeros(size(Am , 1) , Nt) ;

%% Initial conditions

xx(:,1) = [0;0;0;0];

y(:,1) = Cm*xx(:,1);

%% Refrence trajectory

Rs(1 , :) =[ones(floor(Nt/4) , 1)' , 2*ones(floor(Nt/4) , 1)' , -ones(floor(Nt/4) , 1)' , zeros(floor(Nt/4+1) , 1)'] ;

Rs(2 , :) =-[ones(floor(Nt/4) , 1)' , 2*ones(floor(Nt/4) , 1)' , -ones(floor(Nt/4) , 1)' , zeros(floor(Nt/4+1) , 1)'] ;

%% Simulation Loop

for i = 1:Nt-N-1

future_r = Rs(: , i:i+N);

u = sdpvar(nu,N);

x = sdpvar(nx,N+1);

r = sdpvar(ny,N+1);

% 初始值迭代

x(:,1)=xx(:,i);

%% Optimization Problem

objective = 0;

constraints = [];

for k = 1:N

objective = objective + (C*x(:,k)-r(:,k))'*Q*(C*x(:,k)-r(:,k)) + u(:,k)'*R*u(:,k);

constraints = [constraints, x(:,k+1) == Am*x(:,k)+Bm*u(:,k)];

constraints = [constraints, -[5;5] <= u(:,k) <= [5;5],...

-[6;6;6;6] <= x(:,k)<= [6;6;6;6]];

end

objective = objective + (C*x(:,N+1)-r(:,N+1))'*(C*x(:,N+1)-r(:,N+1));

diagnostics=optimize(constraints, objective);

uu(:,i)=value(u(:,1));

xx(:,i+1) = Am*xx(:,i) + Bm*uu(:,i);

y(:,i+1) = Cm*xx(:,i+1);

end

[Johan Löfberg]

you are not using any reference

diagnostics=optimize([constraints,r==future_r], objective)