Hello everyone :)
I have a problem that I really can’t figure out about marginal stability. It is as follow:
Consider a group of n agents (can be whatever: spacecraft, ship, robots) decentralised (without a leader). Each agent follow the next agent, so agent 1 follows agent 2, agent 2 follows agent 3, … and agent n follows agent 1, according to the following law
dot_xi = ui
ui = A xi
The matrix A is of size 2n x 2n, and has two conjugate poles on the imaginary axis, which make my system marginally stable. So it means that if there is ant disturbances, those poles go either to LHP or to RHP, and I want neither.
The question is simple:
If there are disturbances, do you know any method that could make my poles “stay” on the imaginary axis, or make them move along the imaginary axis ?
I’m really struggling, and honestly any help is more than welcome !
Thanks in advance
Hi Antoine Ansart,
For a 2nd-order system x" = A·x,
If you have the full knowledge about the disturbance (d), then you just need to fully cancel out the disturbance.
If the disturbance is unknown and you make a priori assumption that it is bounded, then adding a control action "− K·sign(x)", such that K > max{d}, should be able to 'keep' the system relatively marginally stable.
Hi Antoine,
I suggest you to see links and attached files on topic.
Self-stabilization as multiagent systems property - DOIs
https://doi.org/10.1145/545056.545144
Complex system - Wikipedia
https://en.wikipedia.org/wiki/Complex_system
Best regards
Hi @Yew-Chung Chak
Yes, I think it can work using the sign, but my system is a first-order one.
Indeed idk the disturbance at all, so i need to set some bounds. I will try also to see how my eigenvalues are moving, maybe I could find something with this
Mohamed-Mourad Lafifi
thanks for your document. It doesn't reply totally to my question but I spot some little informations that I maybe use :)
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