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,:)) constraints:- Upper and lower bounds like: p_min<= p(1,:)<= p_max v_min<= v(1,:)<= v_max u_min<= u(1,:)<= u_max linear equalities: p(n+1)=p(n)+ v(n)t + 0.5u(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 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 initial conditions: p(1)=p_init; v(1)=vel_init; end conditions: p(N)<= p_max; v(N)=0; I can give more information if required.
Neeta Dsouza answered .
2025-11-20
function [x,f,eflag,outpt] = myModelParamsSolver
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