Optimize two inputs into a system of ODES

Hi, I'm having trouble finding the right function to optimize the time history of two torques inputted into a system of ODES.

I'm trying to find the input history of 2 torques, to move two link system from a given starting position to a given finish position in the shortest time possib;e.

I have a range of possible values for each of the two torques that they can be at each time. T1 (-300,300) T2 (-250,150)

The two torques are then inputted into a system of ODEs describing the links angular accelerations, velocities and postions.

I first thought of using ODE45 and fmincon. But it seemed fmincon is used to find the optimal input values, not optimizing the inputs once the function is running.

Any suggestions of MATLAB functions to use or general help would be much appreaciated!

Thank You!

[Star Strider]

‘... fmincon is used to find the optimal input values ...’

It is used to optimise the parameters of the system in order to get the desired result, not the input.

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[Jcross]

Thanks for your reply, do the parameters have to be constant or can fmincon find the optimal value at each time within a given range.

[Star Strider]

My pleasure!

The parameters themselves should not change unless the optimisation function changes them. The optimisation routines iterate until they arrive at a set of parameters that results in the value of the objective function being a minimum.

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[Jcross]

Thanks again,

I've tried to write up the equations to make it clearer what I'm trying to do.

I have the intial conditions and want to solve the above ODE to reach a given in the minimum time possible.

The two torques T1 & T2 can have any values at any time as long as they are always within their given ranges: T1 (-300,300) T2 (-250,150)

So the parameters are free to change with time, is fmincon able to find the applied T1 & T2 over time to reach the final position in minimum time.

[Star Strider]

This would appear to be an optimal control problem, and likely an extremely difficult one at that. It would be necessary to use the Robust Control or Model Reference Control Toolbox functions to work with it. (I have neither of them, and have not worked with optimal control problems in decades.)