# Question:Optimal control ODE or DAE formulation

## Question:Optimal control ODE or DAE formulation

Maple 12

Further tags : implicit form, Matlab codegen for GPOPS purposes

Hi there,

I would like to introduce my self and ask you for an advice.

I have a four linked robot that i would really like to control by the meaning of the optimal control theory. The arm has 4 actuators (giving torques U) in corrispondence of 4 rotational joints. P parameters describe the system.

I got ht edynamic system with the Lagrangian method and now I have 4 2nd order differential equations and 2 constraint equations PHI. So the system is

f(x, xdot, xdotdot, u, P)=0

PHI=0

If i downorder the system I will have

f(x, xdot, u, P)=0

PHI=0

With 8 state variables. If i collect the state vars terms and the two reaction forces (i.e. the lagrangian multipliers) i got a mass matrix and a residual matrix. So the system becomes

M(x, xdot, P)= RES(x, P, U)

Writing the system in an explicit form is impossible (at least symbolically) but i'd really love to get an explicit solution because i want to export the system and compile a GPOPS Matlab script in order to solve the problem numerically. I solved the problem numerically (dsolve is able to do that!).

Is there a way in which i can solve the optimal control problem of any implicit ODE or DAE system numerically with Maple? Or, is there a way in which i may obtain a straightforward explicit form of this complicated system?