how can i bound rate of changes (dx/dt) in fmincon optimization?

I need a inequality constraint for (dx/dt<c) in my optimization with fmincon.

i tried many methods,but didnt work.

is there anyone can help me?

Answer 1

[Walter Roberson]

Use the non-linear constraint parameter and have it return (dx/dt - c) . Though if you want a strict inequality rather than <= c then you might need to be a bit careful with the boundary.

[Ali Barari]

when i use this function for nonlinear contraint

nonlcon=@(u)[(u(t+dt)-u(t))/dt-0.26,0];

it says "Array indices must be positive integers or logical values."

[Walter Roberson]

What will be passed to the function is the current values of the trial variables that are being optimized over. In a dx/dt system, I would expect those to be named x in your code. The vector will be the same length as the number of variables. You are attempting to index that vector at (t+dt) and I rather doubt that t+dt and t just happen to be positive integers suitable for indexing.

None of the minimizers have any idea of "time", just of what the trial values are of the variables being minimized with respect to (one of which is potentially interpreted as time in your function.) For example you could conceivably have a system with two states, t and x, and

obj = @(tx) u(tx(1)).^2 + w(tx(2)).^2;
nonlcon = @(tx) deal( (u(tx(1)+dt) - u(tx(1)))/dt - 0.26, [])

for some function u(t) and some function w(x)

Though I would suggest instad of (u(tx(1)+dt) - u(tx(1)))/dt that you have an explicit derivative function, du(tx(1)).

[Ali Barari]

All i want is to reduce frequency of my solution (x),because i get resuts with high frequency that a real actuator cannot follow.

[Walter Roberson]

Create a non-linear inequality that knows the derivative of the function. It is better not to try to estimate it.

fmincon naturally tries to find the zeros of the gradient of the function: when there are no constraints then the minima of a continuous function always satisfies the condition that the gradient is 0 (however, the gradient can also be all zero at maxima or at saddle points.) Therefore unless you have constraints, dx/dt<c will normally be satisfied for positive c.

If you do have constraints then fmincon is still going to be looking for a dx/dt that is as close to zero as feasible, under the constraints

It is therefore not obvious that testing the derivative will do a lot for you, unless c is negative

Answer 2

[Matt J]

See

https://www.mathworks.com/matlabcentral/answers/490758-limit-on-the-change-rate-of-the-variable-in-fmincon-function#answer_401223