I mean to separate the PID controller for different operating points of a complex nonlinear system. Is this possible, and will this be viewed as a multi-agent system?
If I understand you correctly, you want to use the controller for one single control variable and one single controlled variable. You then want to replace the PID-Controllers parameters according to the operating point.
Bad news: no, not a multi-agent system (probably, depends on who is doing the marketing I guess)
Good news: yes, it is possible. You might want to go searching for the term "gain-scheduling"
gain scheduling is a term that allow us to change PID control parameters in different operational condition. but you should know the optimum PID parameter in every condition. you should do some experiment before you give the algorithm.
i think you might want to read about "optimal control", after know the basic about gain-scheduling.
Yes, it is possible; for example, I invite you to check “Cooperative adaptive control for synchronization of second order systems with unknown nonlinearities”.
In this paper authors used PD controller, please see (15) how the term “r” has been defined and the control input as (29).