Discretization of position and velocity

Hey all,

I need to discretize the states x (x(1) is position, x(2) is velocity) in a function called dicretize.

function s = discretize(x, par)
    
    if 0 < x(1) < 2*pi
        x(1) = x(1);
    else
        x(1) = mod(x(1), 2*pi);
    end
    s(1) = discretize(x(1), 1,par.pos_states)
    
    

Answer 1

[Ameer Hamza]

First, the condition

if 0 < x(1) < 2*pi

is not doing what it seem it does. The correct it

if 0 < x(1) && x(1) < 2*pi

Beside, why do you use the if block when you are using mod function which will automatically wrap all values in the interval [0,2*pi]. Check the following code

function s = discretize_state(x, par)
    % TODO: Discretize state. Note: s(1) should be
    % TODO: position, s(2) velocity.
    x(1) = mod(x(1), 2*pi);
    s(1) = round(x(1)/(2*pi)*(par.pos_states-1) + 1);
end

[Ameer Hamza]

There can be several way to wrap the values in this interval. What type of warping do you want? For example

y = mod(x, 2*pi)-pi; % but it will map 0 to -pi but all values will be in range [-pi,pi]

or

y = rem(x, pi); % but it will map all positive values to [0,pi] and all negative to [-pi,0]

Can you give example of how the numbers will be mapped.

[Ameer Hamza]

Try this:

y = mod(x+pi, 2*pi)-pi;

[GCats]

Mm unfortunately it doesn't appear to be working, but perhaps it's because of the s(n) fucntion, which for this case has to be different. The values of x(1) will not exceed the range [−π, π], but they must be kept to this range just in case. The resulting state must be mapped also in the range [1, 31].

[Ameer Hamza]

So in this case you want to map -pi to 1 and pi to 31?

[Ameer Hamza]

Giulio, try this

x(2) = mod(x(2)+pi, 2*pi);

The second line should be correct.

[Ameer Hamza]

The first one map -pi -> 0 and pi -> 2*pi and it will wrap the values according to interval [-pi, pi]. The second one map all the values in the range [-pi pi], but to use that, you will need to change

round((x(1)/(2*pi)+0.5)*(par.pos_states-1) + 1);