We treat the emerging power systems with direct current (DC) MicroGrids, characterized with high penetration of power electronic converters. We rely on the power electronics to propose a decentralized solution for autonomous learning of and adaptation to the operating conditions of the DC Mirogrids; the goal is to eliminate the need to rely on an external communication system for such purpose. The solution works within the primary droop control loops and uses only local bus voltage measurements. Each controller is able to estimate (i) the generation capacities of power sources, (ii) the load demands, and (iii) the conductances of the distribution lines. To define a well-conditioned estimation problem, we employ decentralized strategy where the primary droop controllers temporarily switch between operating points in a coordinated manner, following amplitude-modulated training sequences. We study the use of the estimator in a decentralized solution of the Optimal Economic Dispatch problem. The evaluations confirm the usefulness of the proposed solution for autonomous MicroGrid operation.The proposed solution is illustrated in Fig. 1. We consider a generic DC MG model with multiple buses, described in Sections III and IV. We assume that the MG does not have access to reliable external communication resources. The physical state of DC MGs is characterized by the steady state bus voltages. We introduce a parameter vector θ that collects all system variables whose values are determined by exogenous influences; this includes the generation capacities of the DERs, the load demands and the distribution network topology, i.e., the conductance matrix, see Section IV-A. Using the power balance equation, we represent the bus voltages thorough a non-linear and implicit model, parametrized by θ, see Section III-B. Evidently, θ varies with time; to respond to its variations on different time scales, the DC MG is governed by a hierarchical control system, comprising primary and upper control layer. The primary control is decentralized: several controllers regulate the bus voltages, using only local feedbacks without exchanging any information with peer controllers. They are very fast and capable of responding to high frequency variations in θ. Popular primary controller in DC MGs is the Voltage Source Converter (VSC) with voltage droop control, which is reminiscent to the widespread frequency droop control in AC systems, but defined over the DC voltage; it is therefore standard practice to refer to it simply as droop controller [2], [3]. The upper control layer, on the other hand, responds to less frequent changes in θ that affect the global behavior of the system; examples include changes of the load/generation profile, faults, attacks, etc. Its main role is to adapt the system to the new conditions by computing updated optimal control references for the primary controllers; all upper layer control applications require full/partial knowledge of θ to determine the control references that adequately reflect the new conditions [15]...