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Yayın Equilibrium and stability analysis of delayed neural networks under parameter uncertainties(Elsevier Science Inc, 2012-02-15) Faydasıçok, Özlem; Arik, SabriThis paper proposes new results for the existence, uniqueness and global asymptotic stability of the equilibrium point for neural networks with multiple time delays under parameter uncertainties. By using Lyapunov stability theorem and applying homeomorphism mapping theorem, new delay-independent stability criteria are obtained. The obtained results are in terms of network parameters of the neural system only and therefore they can be easily checked. We also present some illustrative numerical examples to demonstrate that our result are new and improve corresponding results derived in the previous literature.Yayın A new robust stability criterion for dynamical neural networks with multiple time delays(Elsevier Science BV, 2013-01-01) Faydasıçok, Özlem; Arik, SabriThis paper investigates the problem of the existence, uniqueness and global asymptotic stability of the equilibrium point for the class of neural networks with multiple time delays and parameter uncertainties. Under the assumption that the activation functions are globally Lipschitz continuous, we derive a new criterion for the robust stability of a class of delayed neural networks by utilizing the Lyapunov stability theorems and the Homomorphic mapping theorem. Different from those previously published conditions in the recent literature, the robust stability result presented in this paper not only establishes a time-independent relationship between the network parameters of the neural network, but also takes into account the number the neurons of the designed neural system. Some illustrative numerical examples are also given to make a detailed comparison between our result and the previously published corresponding results. This comparison proves that our result is new and can be considered an alternative condition to those of the previously reported robust stability results.Yayın New criteria for the existence of stable equilibrium points in nonsymmetric cellular neural networks(IEEE, 2003) Özcan, Neyir; Arık, Sabri; Tavşanoğlu, Ahmet VedatA new criteria for the existence of stable equilibrium points in nonsymmetric cellular neural networks (CNN) was presented. It was shown that the results obtained can be used to derive some complete stability conditions for some special classes of CNNs such as positive cell-linking CNNs, opposite-sign CNNs and dominant-template CNNs. The model of the CNN whose dynamical behavior was described by the state equations was discussed.Yayın Further analysis of stability of uncertain neural networks with multiple time delays(Springer International Publishing AG, 2014-01-27) Arik, SabriThis paper studies the robust stability of uncertain neural networks with multiple time delays with respect to the class of nondecreasing activation functions. By using the Lyapunov functional and homeomorphism mapping theorems, we derive a new delay-independent sufficient condition the existence, uniqueness, and global asymptotic stability of the equilibrium point for delayed neural networks with uncertain network parameters. The condition obtained for the robust stability establishes a matrix-norm relationship between the network parameters of the neural system, and therefore it can easily be verified. We also present some constructive numerical examples to compare the proposed result with results in the previously published corresponding literature. These comparative examples show that our new condition can be considered as an alternative result to the previous corresponding literature results as it defines a new set of network parameters ensuring the robust stability of delayed neural networks.Yayın End-effector trajectory control in a two-link flexible manipulator through reference joint angle values modification by neural networks(Sage Publications, 2006-02) Öke, Gülay; İstefanopulos, YorgoThe basic difficulty in the control of flexible link manipulators stems from the fact that the link deflections cannot be controlled directly. Since the number of control inputs, applied by the actuators, is less than the total number of variables to be controlled, control approaches aiming at the suppression of deflections and vibrations are generally insufficient. Another possible approach is to determine new joint trajectories to minimize the error of the end-effector in the operational space. In this paper, a neural network is designed to compute incremental changes for the reference values of the joint angles to achieve successful tip tracking in the operational space. Tip position errors in the x- and y-directions are utihzed as inputs to the neural network. The cost function, which is minimized in training the neural network, is also chosen as the sum of squares of the tip position error in both directions. Joint angle control is provided by a PD controller. Simulations are carried out to evaluate the performance of the neural-network-based trajectory tracking method, and the results are depicted in both joint and operational spaces.Yayın Robust stability analysis of a class of neural networks with discrete time delays(Pergamon-Elsevier Science Ltd, 2012-05) Faydasıçok, Özlem; Arik, SabriThis paper studies the existence, uniqueness and global asymptotic stability of the equilibrium point for the class of neural networks with discrete constant time delays under parameter uncertainties. The class of the neural network considered in this paper employs the activation functions which are assumed to be continuous and slope-bounded but not required to be bounded or differentiable. We conduct a stability analysis by exploiting the stability theory of Lyapunov functionals and the theory of Homomorphic mapping to derive some easily verifiable sufficient conditions for existence, uniqueness and global asymptotic stability of the equilibrium point. The conditions obtained mainly establish some time-independent relationships between the network parameters of the neural network. We make a detailed comparison between our results and the previously published corresponding results. This comparison proves that our results are new and improve and generalize the results derived in the past literature. We also give some illustrative numerical examples to show the effectiveness and applicability of our proposed stability results.Yayın New global robust stability condition for uncertain neural networks with time delays(Elsevier Science BV, 2014-10-22) Özcan, Neyir; Arik, SabriIn this paper, we investigate the robust stability problem for the class of delayed neural networks under parameter uncertainties and with respect to nondecreasing activation functions. Firstly, some new upper bound values for the elements of the intervalized connection matrices are obtained. Then, a new sufficient condition for the existence, uniqueness and global asymptotic stability of the equilibrium point for this class of neural networks is derived by constructing an appropriate Lyapunov-Krasovskii functional and employing homeomorphism mapping theorem. The obtained result establishes a new relationship between the network parameters of the neural system and it is independent of the delay parameters. A comparative numerical example is also given to show the effectiveness, advantages and less conservatism of the proposed result.Yayın An improved robust stability result for uncertain neural networks with multiple time delays(Pergamon-Elsevier Science Ltd, 2014-06) Arik, SabriThis paper proposes a new alternative sufficient condition for the existence, uniqueness and global asymptotic stability of the equilibrium point for the class of delayed neural networks under the parameter uncertainties of the neural system. The existence and uniqueness of the equilibrium point is proved by using the Homomorphic mapping theorem. The asymptotic stability of the equilibrium point is established by employing the Lyapunov stability theorems. The obtained robust stability condition establishes a new relationship between the network parameters of the system. We compare our stability result with the previous corresponding robust stability results derived in the past literature. Some comparative numerical examples together with some simulation results are also given to show the applicability and advantages of our result.
