Design of Globally Robust Control for Biologically-Inspired Noisy Recurrent Neural Networks

Design of Globally Robust Control for Biologically-Inspired Noisy Recurrent Neural Networks

Ziqian Liu (State University of New York Maritime College, USA)
DOI: 10.4018/978-1-60960-018-1.ch006
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This chapter presents a theoretical design of how a global robust control is achieved in a class of noisy recurrent neural networks which is a promising method for modeling the behavior of biological motor-sensor systems. The approach is developed by using differential minimax game, inverse optimality, Lyapunov technique, and the Hamilton-Jacobi-Isaacs equation. In order to implement the theory of differential games into neural networks, we consider the vector of external inputs as a player and the vector of internal noises (or disturbances or modeling errors) as an opposing player. The proposed design achieves global inverse optimality with respect to some meaningful cost functional, global disturbance attenuation, as well as global asymptotic stability provided no disturbance. Finally, numerical examples are used to demonstrate the effectiveness of the proposed design.
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Problem Formulation

Consider the class of recurrent neural networks described by the following differential equations

(1) where xRn is the state of recurrent neural network, uRm is the input, usually mn, ARn×n is a matrix that represents the neuron self-inhibitions, S(x) = [s(x1), …, s(xn)]TRn is a vector function and its component s(xi) is a sigmoidal function that models the nonlinear input-output activations of the neurons, W1Rn×n, W2Rn×m are weight matrices. Model (1) encompasses a large class of neural networks, such as the popular Hopfield neural networks, the paradigm of cellular neural networks, and many other recurrent neural network models frequently used in the literature.

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