Distributed Newton-Seeking for Resource Allocation

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Schultz, Matt
Distributed Optimization , Resource Allocation , Consensus , Extremum Seeking Control
Real-time optimization (RTO) is a category of closed-loop process control techniques that is focused on the improvement of process performance. To develop effective strategies, models of the systems are usually required. To circumvent this issue, model-free techniques such as Extremum-seeking control (ESC) have been developed that can accomplish the RTO task in the absence of any knowledge of the process dynamics and of the objective function. Using this optimization methodology, this thesis develops an approach to solve resource allocation problems in a fully distributed fashion where the separable cost function is unknown with dynamics in discrete time. To accomplish this, we utilize a distributed extremum-seeking scheme that estimates the cost function’s gradient and Hessian to implement Newton step dynamics. It is shown that the extremum-seeking approach yields asymptotic convergence of the primal and dual problem to a neighbourhood of the optimal values. We propose two strategies to solve finite resource allocation problems. The first strategy tackles the globally convex cost function case. It requires a simultaneous solution of the primal problem and its associated dual problem. The second strategy utilizes a more general approach with an pseudo-Hessian for the solution of local saddle point problems. It allows a full separation of the primal and dual dynamics. Two simulation case studies are performed for each strategy. The first case is a small-scale 3-agent problem highlighting the differences between the strategies. The second is a 25-agent problem that mimics more realistic scenarios. Finally, a stability analysis is conducted to characterize the transient performance of the two strategies.
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