Toward non-conservative stability conditions for equilibrium points of genetic networks with SUM regulatory functions

An important problem in systems biology consists of establishing whether an equilibrium point of a genetic regulatory network is stable. This paper investigates this problem for genetic networks with SUMregulatory functions. It is shown that a sufficient condition for global asymptotical stability of an equilibrium point of these networks can be derived in terms of convex optimizations with LMI constraints by exploiting polynomial Lyapunov functions and SOS techniques. This condition is interesting because does not introduce approximations of the nonlinearities present in the genetic regulatory network, and the conservatism can be decreased by increasing the degree of the involved polynomials. ©2009 IEEE.published_or_final_versionThe Joint 48th IEEE Conference on Decision and Control and the 28th Chinese Control Conference (CDC/CCC 2009), Shanghai, China, 16-18 December 2009. In Proceedings of the IEEE Conference on Decision and Control, 2009, p. 5631-563

An LMI approach to global asymptotic stability of the delayed Cohen-Grossberg neural network via nonsmooth analysis

In this paper, a linear matrix inequality (LMI) to global asymptotic stability of the delayed Cohen-Grossberg neural network is investigated by means of nonsmooth analysis. Several new sufficient conditions are presented to ascertain the uniqueness of the equilibrium point and the global asymptotic stability of the neural network. It is noted that the results herein require neither the smoothness of the behaved function, or the activation function nor the boundedness of the activation function. In addition, from theoretical analysis, it is found that the condition for ensuring the global asymptotic stability of the neural network also implies the uniqueness of equilibrium. The obtained results improve many earlier ones and are easy to apply. Some simulation results are shown to substantiate the theoretical results

Deriving sufficient conditions for global asymptotic stability of delayed neural networks via nonsmooth analysis

In this paper, we obtain new sufficient conditions ensuring existence, uniqueness, and global asymptotic stability (GAS) of the equilibrium point for a general class of delayed neural networks (DNNs) via nonsmooth analysis, which makes full use of the Lipschitz property of functions defining DNNs. Based on this new tool of nonsmooth analysis, we first obtain a couple of general results concerning the existence and uniqueness of the equilibrium point. Then those results are applied to show that existence assumptions on the equilibrium point in some existing sufficient conditions ensuring GAS are actually unnecessary; and some strong assumptions such as the boundedness of activation functions in some other existing sufficient conditions can be actually dropped. Finally, we derive some new sufficient conditions which are easy to check. Comparison with some related existing results is conducted and advantages are illustrated with examples. Throughout our paper, spectral properties of the matrix (A + A/sup /spl tau//) play an important role, which is a distinguished feature from previous studies. Here, A and A/sup /spl tau// are, respectively, the feedback and the delayed feedback matrix defining the neural network under consideration

Deriving sufficient conditions for global asymptotic stability of delayed neural networks via nonsmooth analysis II

Following our recent approach of nonsmooth analysis, we report a new set of sufficient conditions and its implications for the global asymptotic stability of delayed cellular neural networks (DCNN). The new conditions not only unify a string of previous stability results, but also yield strict improvement over them by allowing the symmetric part of the feedback matrix positive definite, hence enlarging the application domain of DCNNs. Advantages of the new results over existing ones are illustrated with examples. We also compare our results with those related results obtained via LMI approach

Supervised fault tolerant control architecture for nonlinear systems

Scope: The growing complexity of physical plants and control missions inevitably leads to increasing occurrence, diversity and severity of faults. Availability, defined as the probability that a system or equipment will operate satisfactory and effectively at any point of time, becomes a factor of increasing importance. Fault Tolerant Control (FTC) is a field of research that aims to increase availability and reduce the risk of safety hazards and other undesirable consequences by specifically designing control algorithms capable of maintaining stability and/or performance despite the occurrence of faults. This report presents a novel FTC solution based on a hierarchical architecture in which an adaptive critic controller is overseen by a supervisor managing a dynamic model bank of fault solutions.Findings and Conclusions: The presented work has demonstrated that the implementation of a synergistic combination of a reconfigurable controller and a fault diagnosis and controller malfunction detection supervisor based on three distinct quality indexes generates an efficient and reliable FTC architecture. The application of adaptive critic designs as reconfigurable controllers is shown to give the hierarchical algorithm the degree of flexibility required to deal with both abrupt and incipient unknown changes in the plant dynamics due to faults. The proposed supervisor system is used to accelerate the convergence of the method by loading new initial conditions to the controller when the plant is affected by a known abrupt fault. Moreover, the developed fault diagnosis decision logic is capable of recognizing new fault scenarios and assimilating them online to the dynamic model bank, along with parameters for the corresponding controller. The introduction of the weight quality index has made possible to distinguish between faults in the plant and controller malfunctions caused by online training divergence or local minima convergence. In order to achieve application-specific key FTC specifications, a methodology for initializing and tuning twelve distinct parameters of the quality indexes was also developed. Finally, a series of key steps that form the basis for the fault development information extraction module capable of providing the probability of occurrence of future faults to the user, are also included in this report