# how to apply bounds restriction in PSO

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chaker ben salem on 10 Mar 2022
Answered: Walter Roberson on 11 Mar 2022
Hello,
i need more clarification about the different ways to ensure that the end results in PSO are still in bounds
in pso, bound controls should be applied on velocity, however doing so still gives me value out of bound in the particle position
because in pso the new position in iteration i, X(i)= X(i-1) + Velocity , that means the position could still receive a value out of bounds when we add the value of previous position.
my question is how to i fix this without changing the fundamentals of PSO.
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chaker ben salem on 10 Mar 2022
No,am using a simple self made pso to better understand how it work

Walter Roberson on 11 Mar 2022
If you were using particleswarm() and if each position element was paired with a velocity element, then the way it would be handled would be to create a matrix of linear constraints
for k = 1:N
A(k, k) = 1;
A(k, k+N) = 1
b(k) = position_upper_bound(k);
A(k+N, k) = -1;
A(k+N, k+N) = -1;
b(k+N) = -position_lower_bound(k);
end
and then it would just be a normal linear constraints check.