Distributed Feedback-Feedforward Algorithms for Time-Varying Resource Allocation

TL;DR

The paper tackles distributed time-varying resource allocation (TVRA) in networks where costs, global equalities, and local feasibility constraints evolve over time. It introduces fully distributed feedback-feedforward algorithms that separate estimation (local coordination) from control (primal-dual updates), employing a projection-based, initialization-free mechanism to handle LFCs and a state-dependent switching scheme to coordinate feedforward actions. The main theoretical results establish fixed-time convergence without LFCs and global asymptotic stability with fixed-time convergence between switches when LFCs are present, along with non-Zeno switching and forward invariance of the locally feasible set. Case studies, including numerical examples and a UK power-system dynamic-regulation application, validate rapid convergence and practical feasibility, demonstrating the approach’s potential for real-time, distributed energy and resource management.

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.

Figures (7)

• Figure 1: Topology of the communication network.
• Figure 2: Evolution of (a) local estimates; (b) decision variable; (c) error with respect to the stationarity condition; (d) dual variable; and (e) violation of the global equality constraint for Numerical Example 1.
• Figure 3: Evolution of (a) local estimates; (b) decision variable; (c) error with respect to the stationarity condition; (d) dual variable; and (e) violation of the global equality constraint for Numerical Example 2.
• Figure 4: Non-Zenoness of switching and its negligible effects on global equality constraint satisfaction.
• Figure 5: Schematic overview of distributed TVRA for DR.

Theorems & Definitions (22)

• Definition 1
• Definition 2
• Definition 3
• Definition 4
• Definition 5
• Lemma 1 \citation{8322314}
• proof
• Remark 1
• Remark 2
• Lemma 1 \citation{8322314}