1- is it necessary to discretize the state space model which is a non-linear model (robot) if I want execute a direct shooting search policy or direct collection policy?
2- is there is a good reference book which is talking about the search policy especially shooting method and direct collection policies in the field of the optimal control?
3- which model I must use in shooting method (the reduced state space model or the normal state state model)?
well, it depends on the solutions you want to obtain. If you want to get numerical solutions, Yes- you'd better discrete it. However, if you want to solve it, in that direction, to get a general solution, it is not that necessary. Actually, it needs more work when you discrete it, using either finite element or finite difference methods as far as I know. Hope it will help. Good luck.
Also discretisation of non-linear models is not an easy task. Usually you are confined to rather simple discretisation schemes and they can introduce numerical instability (or excesive amount of work)
thanks for your answer for both of you but which is best method to desensitizes a non-linear differential equations? please if you have any refereance or book please send to me
I think that these reference can helpe
H.G. Bock& SK.J. Plitt[1984]“A multiple shooting algorithm for direct solution of optimal control problems,” in: Proceedings 9th IFAC World Congress Budapest, Pergamon Press, 1984,pp,243-247
M. Diehl, H.G. Bock, J.P. Schlder, R. Findeisen Z. Nagy,& F. Allgwer [2002] “Real-time optimization and nonlinear model predictive control of processes governed by differential algebraic equations,” Journal of Process Control. 12, (4) 577–585.
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