This paper introduces a new approach to estimation and control problems called "BDAC," for Big Data Approximating Control. It includes a training process and an estimation & control process. The training process creates and maintains an online training set of representative trajectories, updating them for adaptation to changing processes or sustained unmeasured disturbances. Trajectories are acquired by online monitoring, usually with some automated testing to speed up the process. Training and adaptation can occur in manual mode, test mode, and under closed loop control by BDAC or other controls. BDAC does not use models or state space representation, bypassing the usual "silos" of model identification, state estimation, and control. BDAC solves estimation and control problems by approximate pattern matching directly on the training set. It should benefit from rapid progress in "Big Data" techniques such as nearest neighbor search and clustering. A new data clustering technique and its specialization for real time filtering in causal systems is also introduced: "Real Time Exponential Cluster Filtering" (RTECF). BDAC is centered on solutions or approximate solutions to the "BDAC approximation problem," which includes multivariable overdetermined or underdetermined control problems. A linear approach based on orthogonalization is given, as well as a nonlinear approach based on nearest neighbor interpolation. Even the linear method captures nonlinearity in individual training set trajectories, and the "kernel trick" is demonstrated for directly addressing nonlinearity with the linear controller. Simulation results in supplementary materials demonstrate combined feedforward and feedback control, dealing with setpoint and load changes, nonlinearities, dead times, integrating processes, adaptation, noise, unmeasured disturbances, co-linearity in measurements, estimating missing sensor values, and control while some controller outputs remain in manual or test modes. The well-known quadruple tank simulation shows control of a process switching between nonminimum phase behavior and minimum phase behavior. Integral action and adaptation approaches to avoid offset from setpoints due to changing processes or unmeasured disturbances are demonstrated. Comparisons of parts of the overall process are drawn to K-means clustering, Kalman filtering, linear optimal control/LQG, multivariable predictive control (MPC), and missing data replacement based on Kalman filtering, PCA or autoassociative neural networks. (C) 2017 Elsevier Ltd. All rights reserved.