Dither signal optimization for multi-agent extremum seeking control

In this paper we formulate and solve the problem of multi-agent extremum seeking with dither signals optimization. The solution is a distributed perturbation-based extremum-seeking controller with an additional objective of minimizing overall dither signals disturbances for the whole system. In particular, the proposed method dynamically calculates dither signals for individual subsystems to minimize the dither-induced variations in the total input and output of the process. The overall scheme consists of a dither signal optimizer coupled with a least-squares gradient estimator and a distributed synchronization-based process optimizer. Simulation results for an oil production system with multiple gas-lifted wells demonstrate that the proposed controller is capable of optimizing the production process, while minimizing, on the fast time scale, dither-induced variations both in the total input (total gas injection rate) and in the total output (total oil production rate) of the production system.