Distributed Feedback-Feedforward Algorithms for Time-Varying Resource Allocation

TL;DR

This paper introduces distributed feedback-feedforward algorithms for time-varying resource allocation problems, ensuring feasibility and convergence even with changing constraints and initial infeasibility.

Contribution

It proposes a novel initialization-free, projection-based method with fixed-time convergence for distributed time-varying resource allocation, handling local feasibility constraints effectively.

Findings

Guarantees entry into feasible set within fixed time

Ensures convergence to optimal trajectory

Effective in power system applications

Abstract

This paper studies distributed Time-Varying Resource Allocation (TVRA) where the local cost functions, global equality constraints, and Local Feasibility Constraints (LFCs) vary with time. Algorithms that mimic the structure of feedback-feedforward control systems are proposed. Feedback and feedforward laws are generated using local estimates from a distributed estimator, while a distributed controller enforces the stationarity condition within a fixed time and updates the candidate solution accordingly. To handle the LFCs, feedback laws based on projection and feedforward laws that switch between different modes are introduced as an initialization-free alternative to the barrier-based methods used in most related works. Our projection-based method guarantees that, for any infeasible initial value, the state trajectory enters the locally feasible set within a fixed time and remains within it thereafter, and that the set is forward invariant if the initial value is locally feasible. Convergence analyses are conducted under mild assumptions. For cases without LFCs, the proposed algorithm converges to the optimal trajectory within a fixed time. For cases with LFCs, the proposed algorithm is globally asymptotically stable at the optimal trajectory while exhibiting fixed-time convergence between consecutive switching instants. Numerical examples and a power system application verify their effectiveness.