Explicit MPC of MIMO system using "solvemp"

[정준영]

Dear Prof. Löfberg,

I'm trying to make an Explicit MPC controller using YALMIP.

There are 8 states and 2 inputs. and,

There are 2 logical constraints so, I used the "implies" function for modeling this..

But, sometimes the solver is stopped, or when I using the "isinside" function, there is no solution in states' range.

I think, there is a mistake using logical constraints with 'implies".

Could you give me an advice??

I posted the code,

N = 2;

U = sdpvar(2,N,'full');

W = sdpvar(2,N,'full');

x = sdpvar(8,N+1,'full');

d = binvar(4,N,'full');

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

0 1 0 0 0 0 0 0;

0 0 0 0 1 0 0 0;

0 0 0 0 0 1 0 0;];

objective = 0;

constraints = [];

for k = 1:N

constraints = [constraints, implies(d(1,k), [(x(7,k)-x(5,k)+a1*x(6,k)) >= 0, ...

1000*(x(7,k)-x(5,k)+a1*x(6,k)) <= U(1,k) <= 10000*(x(7,k)-x(5,k)+a1*x(6,k))])];

constraints = [constraints, implies(d(2,k), [(x(7,k)-x(5,k)+a1*x(6,k)) <= 0, ...

10000*(x(7,k)-x(5,k)+a1*x(6,k)) <= U(1,k) <= 1000*(x(7,k)-x(5,k)+a1*x(6,k))])];

constraints = [constraints, d(1,k) + d(2,k) == 1];

constraints = [constraints, implies(d(3,k), [(x(8,k)-x(5,k)-a2*x(6,k)) >= 0, ...

1000*(x(8,k)-x(5,k)-a2*x(6,k)) <= U(2,k) <= 10000*(x(8,k)-x(5,k)-a2*x(6,k))])];

constraints = [constraints, implies(d(4,k), [(x(8,k)-x(5,k)-a2*x(6,k)) <= 0, ...

10000*(x(8,k)-x(5,k)-a2*x(6,k)) <= U(2,k) <= 1000*(x(8,k)-x(5,k)-a2*x(6,k))])];

constraints = [constraints, d(3,k) + d(4,k) == 1];

constraints = [constraints, x(:,k+1) == Ad*x(:,k) + Bd*U(:,k)];

constraints = [constraints, -25000 <= U(:,k) <= 25000];

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

constraints = [constraints, -5 <= x(:,k+1) <=5];

objective = objective + (C*x(:,k+1))'*diag([1e10 1e11 1e7 1e7])*(C*x(:,k+1));

end

sol = solvemp(constraints, objective, sdpsettings('verbose',1,'showprogress',1),x(:,1),U(:,1));

[Johan Löfberg]

I woukd have absolutely no hope of the mpMILP solver to work on a problem in R^8

[정준영]

Thank you for your response!

So, could you tell me why..? and would you recommend another solver for this problem, please?

2024년 9월 15일 일요일 오후 10시 11분 8초 UTC+9에 Johan Löfberg님이 작성:

[Johan Löfberg]

multiparametric LPs are extremely hard, and can perhaps be solved somewhat consistently in R^2 and R^3, and grows exponentially harder with growing dimension. mixed-ionteger multiparametric programming is much harder, so...

I am not aware of any other solver capable of mpMILPs

[정준영]

Thank you very much prof.

Your answer was very helpful for me.

2024년 9월 15일 일요일 오후 10시 54분 42초 UTC+9에 Johan Löfberg님이 작성: