An adaptive recurrent neural-network controller using a stabilization matrix and predictive inputs to solve a tracking problem under disturbances

Abstract

This is the accepted version of the paper.This version of the publication may differ from the final published version. Permanent repository link AbstractWe present a recurrent neural-network (RNN) controller designed to solve the tracking problem for control systems. We demonstrate that a major difficulty in training any RNN is the problem of exploding gradients, and we propose a solution to this in the case of tracking problems, by introducing a stabilization matrix and by using carefully constrained context units. This solution allows us to achieve consistently lower training errors, and hence allows us to more easily introduce adaptive capabilities. The resulting RNN is one that has been trained off-line to be rapidly adaptive to changing plant conditions and changing tracking targets.The case study we use is a renewable-energy generator application; that of producing an efficient controller for a three-phase grid-connected converter. The controller we produce can cope with random variation of system parameters and fluctuating grid voltages. It produces tracking control with almost instantaneous response to changing reference states, and virtually zero oscil-$ This work was supported in part by the U.S. National Science Foundation under Grant EECS 1059265/1102159, the Mary K. Finley Missouri Endowment, and the Missouri S&T Intelligent Systems Center.Email addresses: michael.fairbank@virgin.net (Michael Fairbank), sli@eng.ua.edu (Shuhui Li), xfu@crimson.ua.edu (Xingang Fu), E.Alonso@city.ac.uk (Eduardo Alonso), dwunsch@mst.edu (Donald Wunsch) Preprint submitted to Neural Networks September 23, 2013 lation. This compares very favorably to the classical proportional integrator (PI) controllers, which we show produce a much slower response and settling time. In addition, the RNN we propose exhibits better learning stability and convergence properties, and can exhibit faster adaptation, than is achievable with adaptive critic designs.

Actor–Critic-Based Optimal Tracking for Partially Unknown Nonlinear Discrete-Time Systems

“…where u d is given by (4) and u * e is given by (9). Remark 2: The feedback part of the control input (9) is designed to stabilize the tracking error dynamics.…”

“…One can refer to [9], [45], and [46] for an exact gradient descent algorithm with improved convergence guarantees.…”

“…Several techniques have been proposed to approximate the HJB solution. Included are reinforcement learning (RL) [1]- [8] and backpropagation through time [9]. RL techniques have been successfully applied to find the solution to the HJB equation online in real time for unknown or partially unknown continuous-time (CT) systems [10]- [12] and discrete-time (DT) systems [13]- [17].…”

H2/H∞ control for grid-feeding converter considering system uncertainty

“…The control strategy of a GFC is crucial to maintain the power quality and the security of the GFC system (Fairbank, Li, Fu, Alonso, & Wunsch, 2014). Both subsystems of a GFC may exhibit certain degrees of uncertainty and volatility.…”

“…In Fairbank et al (2014), Fu, Li, and Jaithwa (2015), Li et al (2014), recurrent neural networks (RNNs), as an intelligence control method, have been used to control GFC systems in which the RNN is trained by the back propagation through time (BPTT) algorithm. However, the training process is complex.…”