Balancing time-varying demand-supply in distribution networks: An internal model approach

Abstract

The problem of load balancing in a distribution network under unknown timevarying demand and supply is studied. A set of distributed controllers which regulate the amount of flow through the edges is designed to guarantee convergence of the solution to the steady state solution. The results are then extended to a class of nonlinear systems and compared with existing results. Incremental passivity and internal model are the main analytical tools. * C. De Persis is with ITM,

Output agreement in networks with unmatched disturbances and algebraic constraints

“…This is particularly relevant in applications involving demand and supply balancing, including power as well as hydraulic networks; see e.g. [4], [6].…”

Dynamic Pricing Control for Constrained Distribution Networks With Storage

“…For the feedback controller design, we extend now the control objective and require in additions that the feedback controller achieves a balancing of the inventory levels of (1). Network balancing is widely accepted as control objective in storage networks, as it promises to make best use of the available storage, [8], [14]. 4 Please note that the solution to (18) could equivalently be expressed aṡ ζ w (t) = −L † (ζ w (t))Bω(t), where L † (ζ w (t)) is the generalized inverse of the weighted Laplacian matrix (17).…”

“…, λ m ] T ∈ R m the flow along the lines, and P w an external in-/outflow of the inventories, i.e., the supply or demand. This basic model (or its discrete time version) is studied in [5], [9], [7], [8], [14] and is a relevant model for supply chains ( [18]) or data networks ( [19]). The objective of this paper is to design distribution control laws for the flows λ, that achieve two objectives: (i) balancing of the storage levels, i.e., lim t→∞ |x i (t) − x j (t)| = 0 for all i, j ∈ {1, .…”

“…Furthermore, the phenomena of output agreement and clustering are mathematically related to optimal network flow problems [13]. The connection between output agreement and network flow control has been further studied from an internal model control perspective in [14], [15], [16]. Considering demands and supplies that are generated by an external dynamical system (exo-system), distributed dynamic controllers were proposed that ensure an exact routing as well as a balancing of the inventory levels.…”

Disturbance decoupling problem for multi-agent systems: A graph topological approach

“…Another example of dynamical networks in which one seeks for disturbance rejection is balancing demand-supply in distribution networks; see e.g. [6,7]. In this framework, storage variables correspond to vertices, flow inputs corresponding to edges, disturbances amount for inflows and outflows at certain vertices, and the objective is to achieve load balancing, that is convergence of storage variables to the same value by regulating the flow inputs.…”