Dither signals optimization in constrained multi-agent extremum seeking control

Abstract

Abstract In this paper we consider the problem of optimization of a multi-agent system with constraints through perturbations-based extremum seeking control. We demonstrate that for such systems, effects of dither signals applied to individual agents can sum up to significant perturbations in the outputs at the overall system level despite the fact that individual dither signals can be small. These perturbations are especially detrimental in constrained outputs. To resolve this challenge, we propose a method of dither signals optimization: while maintaining persistent perturbations of individual agents, dither signals are coordinated between the agents to minimize their summed effect in constrained outputs. This problem is formulated as a computationally feasible mathematical programming problem that can be solved numerically at each time step. Combined with a constrained steady-state optimizer and a least squares-based gradient estimator, this method provides better performance than a similar perturbation-based extremum seeking scheme without dither optimization. This is demonstrated with an example on oil production optimization from a system of multiple gas-lifted wells with a total water processing constraint.