Nonlinear-Control-Homework 4 Accessibility of the N-Trailer System Solved

In some special coordinates, the kinematic model of the N-trailer system is described by

 

We computed dimH2 = n−2 so that H2 = span{ω1,ω2,··· ,ωn−2}. The two first basis vectors were computed as well as

ω1 = −x3dx1 + dx2

and

ω2 = −x4dx1 + dx3

1.     Compute the            ]              [              H···2 in the form of row vectors∗   ]

                                                                                                                        0          0    .     Write the corre-

sponding 1-forms ω3 and ωn−2.

2.   Check whether ˙ω1 ∈ H2

3.   Check whether ˙ω2 ∈ H2

4.   Check whether ˙ωn−2 ∈ H2

5.   Write a basis for H3