Both Mick and Jack have commented on the added loading on the cantilevered rafters or truss top chord. I think this needs needs a closer look before you get started.

If you think there is ever a possibility of roofing all or part of the pergola at some later date (Many people decide to add laser lite or something similar) you could be adding large wind loading into the equation. Best to plan for this possibility from the outset.

You don't mention how wide your eaves are. There is a big difference in how much load can be added if the eaves are 450mm compared to 900mm. Truss spacing will similarly have a large influence.

My suggestion is to have a talk to one of the truss manufacturers about what they recommend to support the additional loading. My guess is that they may have been called in from time to time to rectify the results of over loading.

Probably worth having a close look at the trusses and having some specific measurements and details to hand when you speak to the truss people.