Dither signal optimization for multi-agent extremum seeking control

Abstract

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.

Nondisturbing Extremum Seeking Control for Multiagent Industrial Systems

“…For large systems with many ESC loops, the combined effects and consequences of the introduced dither signals may be substantial, even if all dither amplitudes are small. For instance, for a multi-agent system comprised of many parallel subsystems, the amplitude of the dither-induced fluctuation in the overall output of the system may be as large as the absolute sum of the fluctuation amplitudes of all individual subsystems [31]. Therefore, it can be challenging to choose suitable dither signals that are sufficiently large to ensure proper tracking of changes in the optimum of each individual subsystem, and, at the same time, are small enough to avoid losses and damages due to overly large fluctuations in the overall system output.…”

“…However, that result does not guarantee cancellation of dither-induced fluctuations. The challenge of designing dither signals to cancel fluctuations both in the total input and total output of a multi-agent system, while at the same time ensuring that each subsystem is sufficiently excited, was first treated in [31]. The solution presented in that paper calculates dither signals by solving a non-convex, yet computationally feasible optimization problem.…”

“…The proposed algorithm implicitly coordinates both amplitudes and phases of individual dither signals to achieve minimization of ditherinduced fluctuations both in the total input and output. This approach was then successfully applied to the case of a network of subsystems sharing a common constraint [32], with practical benefits demonstrated for the case of constrained ESC optimization for an oil production system.…”

“…Considerations to avoid rapid changes in dither signals, and to maintain a constant excitation level in each subsystem's input, make a complete cancellation in total output infeasible. In contrast to the method proposed in [31], [32], we propose an algorithm for direct calculation of the dither signals, which is much lighter than the computationally heavy method proposed in these references. Furthermore, the dither signal optimizer of [31], [32] considers only sinusoidal dither signals, while the new proposed method holds for a larger class of dither signals.…”

“…In contrast to the method proposed in [31], [32], we propose an algorithm for direct calculation of the dither signals, which is much lighter than the computationally heavy method proposed in these references. Furthermore, the dither signal optimizer of [31], [32] considers only sinusoidal dither signals, while the new proposed method holds for a larger class of dither signals. Finally, the paper presents a solvability analysis for the problem of cancelling dither-induced fluctuations in the total output and a complete stability proof for each extremum seeking loop consisting of a subsystem, an extremum seeking controller, and the dither signal generated by the proposed algorithm.…”