Neurocontrol of nonlinear dynamical systems with Kalman filter trained recurrent networks

Abstract

Although the potential of the powerful mapping and representational capabilities of recurrent network architectures is generally recognized by the neural network research community, recurrent neural networks have not been widely used for the control of nonlinear dynamical systems, possibly due to the relative ineffectiveness of simple gradient descent training algorithms. Developments in the use of parameter-based extended Kalman filter algorithms for training recurrent networks may provide a mechanism by which these architectures will prove to be of practical value. This paper presents a decoupled extended Kalman filter (DEKF) algorithm for training of recurrent networks with special emphasis on application to control problems. We demonstrate in simulation the application of the DEKF algorithm to a series of example control problems ranging from the well-known cart-pole and bioreactor benchmark problems to an automotive subsystem, engine idle speed control. These simulations suggest that recurrent controller networks trained by Kalman filter methods can combine the traditional features of state-space controllers and observers in a homogeneous architecture for nonlinear dynamical systems, while simultaneously exhibiting less sensitivity than do purely feedforward controller networks to changes in plant parameters and measurement noise.

Deep learning in neural networks: An overview

“…LSTM generalized well though, requiring only the 30 shortest exemplars (n ≤ 10) of the CSL a n b n c n to correctly predict the possible continuations of sequence prefixes for n up to 1000 and more. A combination of a decoupled extended Kalman filter (Kalman, 1960;Williams, 1992b;Puskorius and Feldkamp, 1994;Feldkamp et al, 1998;Haykin, 2001;Feldkamp et al, 2003) and an LSTM RNN (Pérez-Ortiz et al, 2003) learned to deal correctly with values of n up to 10 million and more. That is, after training the network was able to read sequences of 30,000,000 symbols and more, one symbol at a time, and finally detect the subtle differences between legal strings such as a 10,000,000 b 10,000,000 c 10,000,000 and very similar but illegal strings such as a 10,000,000 b 9,999,999 c 10,000,000 .…”

A Self Organizing Recurrent Neural Network

“…The final sequence numbers of subsystems for approximating COD were 1, 28, 9, 6, 18, 7, 21, 13, 23. The final sequence numbers of subsystems for approximating NH 3 -N were 13,21,18,24,5,8. Different quality parameter are needed to active different subsystems.…”

“…The classical fully recurrent network [6,7] is composed of a single layer of fully interconnected neurons. several such recurrent layers are combined to obtain a richer architecture [8]. Other cases of recurrent networks are the external feedback representations [9], the higher-order recurrent neural networks [10], and the block-structured recurrent neural networks [11].…”

A recursive algorithm based on the extended Kalman filter for the training of feedforward neural models

“…such that the initial output values of the hidden neurons are in the linear part of the tanh. We propose to initialize the weights with small random values, a choice which is also made in most EKF approaches (in [4], [11] and [12] for example).…”