Existence and learning of oscillations in recurrent neural networks

Townley, Stuart; Ilchmann, Achim; Weiss, Martin; Mcclements, W.; Ruiz, A.; Owens, D.H.; Prätzel-Wolters, D.

doi:10.1109/72.822523

Cited by 112 publications

(47 citation statements)

References 21 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In many applications, the properties of periodic solutions are of great interest, which have been successfully applied in, for example, learning theory [21] since effective learning usually requires repetition. In addition, an equilibrium point can be viewed as a special periodic solution of neural networks with arbitrary period.…”

Section: Introductionmentioning

confidence: 99%

A delay-dependent LMI approach to dynamics analysis of discrete-time recurrent neural networks with time-varying delays

2007

View full text Add to dashboard Cite

In this Letter, the analysis problem for the existence and stability of periodic solutions is investigated for a class of general discrete-time recurrent neural networks with time-varying delays. For the neural networks under study, a generalized activation function is considered, and the traditional assumptions on the boundedness, monotony and differentiability of the activation functions are removed. By employing the latest free-weighting matrix method, an appropriate Lyapunov-Krasovskii functional is constructed and several sufficient conditions are established to ensure the existence, uniqueness, and globally exponential stability of the periodic solution for the addressed neural network. The conditions are dependent on both the lower bound and upper bound of the time-varying time delays. Furthermore, the conditions are expressed in terms of the linear matrix inequalities (LMIs), which can be checked numerically using the effective LMI toolbox in MATLAB. Two simulation examples are given to show the effectiveness and less conservatism of the proposed criteria.

show abstract

Section: Introductionmentioning

confidence: 99%

A delay-dependent LMI approach to dynamics analysis of discrete-time recurrent neural networks with time-varying delays

2007

View full text Add to dashboard Cite

show abstract

“…With (Z) R c 3 .Since satisfies the persistency of excitation condition Lemma 3.6 in [11] it also follows Corollary 2.3 in [12] that the system given by (18) is equally exponentially stable. Now, using the fact that lim t→∞ = 0, it follows from normal perturbation results [13, p.134] that for the transition matrix ψ (.,.)…”

Section: V(z) =mentioning

confidence: 84%

Existence and Learning of Teaching Network for CRNN

Sahu¹,

Kumar²

2011

IJCA

View full text Add to dashboard Cite

Existence and Learning of Teaching Network for Complex Recurrent Neural Network (CRNN) has been discussed in this piece of research. Issues related to the quaternionic neural network have been taken into consideration. In this paper by considering the special class of CRNN for which existence of attractive periodic solution in teaching network has been obtained and theoretical results has been proved, limit cycle, existence and uniqueness have also been discussed. This work has very much significant for several real world applications.

show abstract

“…Recurrent Neural Networks (RNN) offer a similar approach to CPG-networks where instead of coupled oscillators, coupled neurons (e.g., Leaky integrator neurons) generate rhythmic patterns [29,30]. However, the unnecessary complexity of the neuron-model makes this tool less applicable for motion generation in robotic applications where tractability of the learning is of particular interest.…”

Section: Related Workmentioning

confidence: 99%

Adaptive Natural Oscillator to exploit natural dynamics for energy efficiency

Khoramshahi

Nasiri

Shushtari

et al. 2017

Robotics and Autonomous Systems

View full text Add to dashboard Cite

We present a novel adaptive oscillator, called Adaptive Natural Oscillator (ANO), to exploit the natural dynamics of a given robotic system. This tool is built upon the Adaptive Frequency Oscillator (AFO), and it can be used as a pattern generator in robotic applications such as locomotion systems. In contrast to AFO, that adapts to the frequency of an external signal, ANO adapts the frequency of reference trajectory to the natural dynamics of the given system. In this work, we prove that, in linear systems, ANO converges to the system's natural frequency. Furthermore, we show that this tool exploits the natural dynamics for energy efficiency through minimization of actuator effort. This property makes ANO an appealing tool for energy consumption reduction in cyclic tasks; especially in legged systems. We also extend the proposed adaptation mechanism to high dimensional and general cases; such as n-DOF manipulators. In addition, by investigating a hopper leg in simulation, we show the efficacy of ANO in face of dynamical discontinuities; such as those inherent in legged locomotion. Furthermore, we apply ANO to a simulated compliant robotic manipulator performing a periodic task where the energy consumption is drastically reduced. Finally, the experimental results on a 1-DOF compliant joint show that our adaptive oscillator, despite all practical uncertainties and deviations from theoretical models, exploits the natural dynamics and reduces the energy consumption.

show abstract

Existence and learning of oscillations in recurrent neural networks

Cited by 112 publications

References 21 publications

A delay-dependent LMI approach to dynamics analysis of discrete-time recurrent neural networks with time-varying delays

A delay-dependent LMI approach to dynamics analysis of discrete-time recurrent neural networks with time-varying delays

Existence and Learning of Teaching Network for CRNN

Adaptive Natural Oscillator to exploit natural dynamics for energy efficiency

Contact Info

Product

Resources

About