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  It is known that modern CPUs have both Performance cores (P-cores) and efficiency cores (E-cores), different types of CPU cores that have different purposes and are designed for different tasks. P-cores typically have higher clock speeds and designed for high-performance tasks, while E-cores operate at lower clock speeds and focus on energy-efficient processing. In MATLAB, maxNumCompThreads returns the current maximum number of computational threads. Currently, the maximum number of computational threads is equal to the number of physical cores on your machine. How MATLAB makes the distinction between P-Cores and E-Cores ? NOTE:- Matlabsolutions.com  provide latest  MatLab Homework Help, MatLab Assignment Help  ,  Finance Assignment Help  for students, engineers and researchers in Multiple Branches like ECE, EEE, CSE, Mechanical, Civil with 100% output.Matlab Code for B.E, B.Tech,M.E,M.Tech, Ph.D. Scholars with 100% privacy guaranteed. Get MATLAB projects...

discrete time optimization with non-linear constraints

 Hello,

I have an optimization problem to solve with non-linear constraints. It is a control theory based discrete time model (which i feel fules out using fmincon) over a time horizon say N seconds.

I found a few old posts similar to this, but none I felt had clear answers.

I am going nuts trying to find a way to implement it in matlab. Which Matlab tool would be best suited in this case?

Thanks,

italic EDIT: the system is continuous, but we analyse it in a discrete time domain. Thus, variables have discrete values. There are n_v entities and each of the entity has each parameter described below:

variables: p,v,u; size(p)=size(v)=size(u)=(1,N) vectors

Obj. fn: minimize sum(u(1,:))

ANSWER:

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I tried to create an example. Hope this helps.

xLast = []; % Last place computeall was called
myf = []; % Use for objective at xLast
myc = []; % Use for nonlinear inequality constraint
myceq = []; % Use for nonlinear equality constraint
N = 10;
x0 = rand(1,2+2*N);
fun = @objfun; % the objective function, nested below
cfun = @constr; % the constraint function, nested below
options = optimoptions('fmincon');
lb = zeros(1,2+2*N);
ub = ones(1,2+2*N);
% Call fmincon
[x,f,eflag,outpt] = fmincon(fun,x0,[],[],[],[],lb,ub,cfun,options);
function y = objfun(x)
if ~isequal(x,xLast) % Check if computation is necessary
[myf,myc,myceq] = myDiscreteTimeModel(x);
xLast = x;
end
% Now compute objective function
y = myf;
end
function [c,ceq] = constr(x)
if ~isequal(x,xLast) % Check if computation is necessary
[myf,myc,myceq] = myDiscreteTimeModel(x);
xLast = x;
end
% Now compute constraint functions
c = myc; % In this case, the computation is trivial
ceq = myceq;
end
function [f,c,ceq] = myDiscreteTimeModel(x)
p = zeros(1,N);
v = p;
u = p;
Ts = 0.01;
p_max = 100;
p_init = 10;
vel_init = 1;
% initial conditions:
p(1)=p_init;
v(1)=vel_init;
p1 = x(1);
p2 = x(2);
v1 = x(3:3+N-1);
v2 = x(3+N:end);
for n = 1:N
t = N*Ts;
% non linear equalities:
s_star= v1(n) * (v1(n)-v2(n));
% where v1 and v2 are parameters of entities 1 and 2 respectively at nth instant.
% * this is the non-linear equality/constraint.
%s_star2 = v1(n) * (v1(n)-v1(n-1));
% Note: we use either s_star or s_star2 in our code
% linear equalities:
p(n+1)= p(n)+ v(n)*t + 0.5*u(n)*t^2;
v(n+1)= v(n)+ u(n)*t;
u(n+1)= (s_star / (p1-p2))^2 ; % p1 and p2 correspond to entity 1 and 2's p parameter
end
% end conditions:
ceq = v(N);
c = p(N)-p_max;
f = sum(u(:));
end
end

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