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1.
This paper proposes a fuzzy neural network (FNN) based on wavelet support vector regression (WSVR) approach for system identification, in which an annealing robust learning algorithm (ARLA) is adopted to adjust the parameters of the WSVR-based FNN (WSVR-FNN). In the WSVR-FNN, first, the WSVR method with a wavelet kernel function is used to determine the number of fuzzy rules and the initial parameters of FNN. After initialization, the adjustment for the parameters of FNNs is performed by the ARLA. Combining the self-learning ability of neural networks, the compact support of wavelet functions, the adaptive ability of fuzzy logic, and the robust learning capability of ARLA, the proposed FNN has the superiority among the several existed FNNs. To demonstrate the performance of the WSVR-FNN, two nonlinear dynamic plants and a chaotic system taken from the extant literature are considered to illustrate the system identification. From the simulation results, it shows that the proposed WSVR-FNN has the superiority over several presented FNNs even the number of training parameters is considerably small.  相似文献   

2.
This paper considers a class of nonlinear fractional-order multi-agent systems (FOMASs) with time-varying delay and unknown dynamics, and a new robust adaptive control technique is proposed for cooperative control. The unknown nonlinearities of the systems are online approximated by the introduced recurrent general type-2 fuzzy neural network (RGT2FNN). The unknown nonlinear functions are estimated, simultaneously with the control process. In other words, at each sample time the parameters of the proposed RGT2FNNs are updated and then the control signals are generated. In addition to the unknown dynamics, the orders of the fractional systems are also supposed to be unknown. The biogeography-based optimization algorithm (BBO) is extended to estimate the unknown parameters of RGT2FNN and fractional-orders. A LMI based compensator is introduced to guarantee the robustness of the proposed control system. The excellent performance and effectiveness of the suggested method is verified by several simulation examples and it is compared with the other methods. It is confirmed that the introduced cooperative controller results in a desirable performance in the presence of time-varying delay, unknown dynamics, and unknown fractional-orders.  相似文献   

3.
In this paper, a discrete hybrid three-species food chain system is proposed, where commercial harvesting on top predator is considered. Two time delays are introduced to represent gestation delay for prey and predator population, respectively. In absence of time delay, sufficient conditions associated with economic interest and step size are derived to show system undergoes flip bifurcation. In presence of double time delays, existence of Neimark–Sacker bifurcation and local stability switch are discussed due to variations of time delays. Furthermore, by utilizing new normal form of delayed discrete hybrid system and center manifold theorem, direction and stability of Neimark–Sacker bifurcation are studied. Numerical simulations are performed not only to validate theoretical analysis, but also exhibit cascades of period-doubling bifurcation, chaotic behavior and stable closed invariant curve.  相似文献   

4.
In this paper, we consider the problem of Hopf bifurcation control for a complex network model with time delays. We know that for the system without control, as the positive gain parameter of the system passes a critical point, Hopf bifurcation occurs. To control the Hopf bifurcation, a time-delayed feedback controller is proposed to delay the onset of an inherent bifurcation when such bifurcation is undesired. Furthermore, we can also change the stability and direction of bifurcating periodic solutions by choosing appropriate control parameters. Numerical simulation results confirm that the new feedback controller using time delay is efficient in controlling Hopf bifurcation.  相似文献   

5.
In this paper, a delayed feedback controller with the delay-dependent coefficient is introduced into a multiple delay phytoplankton-zooplankton system. For uncontrolled system, choosing delays as the bifurcation parameters, we prove that Hopf bifurcation can occur when the delays change and cross some values. Then, the delays are still chosen as the bifurcation parameters to research the dynamic behaviors of the controlled system. Under this control mechanism, the onset of Hopf bifurcation can be delayed by selecting the appropriate control parameters and the stability domain can be extended as feedback gain (the decay rate) decreases (increases), and the influence of the decay rate cannot be ignored. Furthermore, using the crossing curve methods, the stable changes of equilibrium in two delay plane can be obtained. Some numerical simulations are given to verify the correctness and validity of the delayed feedback controller in the bifurcation control.  相似文献   

6.
In this paper, a hybrid triple delayed prey predator bioeconomic system with prey refuge and Lévy jumps is established, where both maturation delay for prey and predator population and gestation delay for predator population are considered. For deterministic system, positivity and uniform permanence of solution are discussed. Local stability of deterministic system around interior equilibrium is investigated due to variations of triple time delays. For stochastic system without time delay, sufficient conditions for stochastically ultimate boundedness and stochastic permanence are discussed. Existence of stochastic Hopf bifurcation and stochastic stability are investigated. For stochastic system with triple time delays, existence and uniqueness of global positive solution are studied. Finally, combined dynamic effects of triple time delays and Lévy jumps on the hybrid stochastic system are discussed by constructing appropriate Lyapunov functions. Numerical simulations are supported to illustrate theoretical analysis.  相似文献   

7.
A differential-algebraic model system which considers a prey-predator system with stage structure for prey and harvest effort on predator is proposed. By using the differential-algebraic system theory and bifurcation theory, the dynamic behaviors of the proposed model system with and without discrete time delay are investigated. Local stability analysis of the model system without discrete time delay reveals that there is a phenomenon of singularity induced bifurcation due to variation of the economic interest of harvesting, and a state feedback controller is designed to stabilize the proposed model system at the interior equilibrium; on the other hand, the local stability of the model system with discrete time delay is also studied. The theoretical analysis shows that the discrete time delay has a destabilizing effect in the model of population dynamics, and a phenomenon of Hopf bifurcation occurs as the discrete time delay increases through a certain threshold. Numerical simulations are carried out to show the consistency with theoretical analysis.  相似文献   

8.
In this paper, a delayed fractional eco-epidemiological model with incommensurate orders is proposed, and a control strategy of this model is discussed. Firstly, for the system with no controller, the stability and Hopf bifurcation with respect to time delay are investigated. Secondly, under the influence of the controller, the stability and Hopf bifurcation of the system is discussed, and it is indicated that the stability of the system can be changed by increasing the feedback control delay. In particular, a separate study is carried out on the bifurcation with respect to the extended feedback delay, and the bifurcation point is calculated. At last, to support the theoretical results, some numerical simulations are depicted.  相似文献   

9.
Communication delays in networked control systems (NCSs) has been shown to have non-uniform distribution and multifractal nature. This paper proposes a delay distribution based stability analysis and synthesis approach for NCSs with non-uniform distribution characteristics of network communication delays. A stochastic control model related with the characteristics of communication networks is established to describe the NCSs. Then, delay distribution-dependent NCS stability criteria are derived in the form of linear matrix inequalities (LMIs). Also, the maximum allowable upper delay bound and controller feedback gain can be obtained simultaneously from the developed approach by solving a constrained convex optimization problem. Numerical examples showed that the results derived from the proposed method are less conservativeness than those derived from the existing methods.  相似文献   

10.
Based on the generalized probability-interval-decomposition approach, the delay-dependent stability analysis for a class of T-S fuzzy systems with stochastic delays is investigated. The information of the probability distribution of stochastic delay is fully exploited and a series of sufficient stability criteria are obtained. A rigorous mathematical proof is provided that the conservatism of the proposed stability criteria can be reduced progressively by increasing the number of the probability interval. Based on this, a novel hierarchy of LMI conditions is established. It is rigorously proved that with the same decomposition of probability interval, the conservatism of the proposed stability criteria is less than the one obtained by time-varying delay decomposition approach. The computation burden of the proposed method is analyzed and compared with one of the time-varying delay decomposition approach. Finally, a numerical example is given to illustrate the validness and effectiveness of the proposed approach.  相似文献   

11.
This paper investigates the problem for stability of neutral-type dynamical neural networks involving delay parameters. Different form the previously reported results, the states of the neurons involve multiple delays and time derivative of states of neurons include discrete time delays. The stability of such neural systems has not been given much attention in the past literature due to the difficulty of finding Lyapunov functionals which are suitable for stability analysis of this type of neural networks. This paper constructs a generalized Lyapunov functional by introducing new terms into the well-known Lyapunov functional that enables us to conduct a theoretical investigation into stability analysis of delayed neutral-type neural systems. Based on this modified novel Lyapunov functional, sufficient criteria are derived, which guarantee the existence, uniqueness and global asymptotic stability of the equilibrium point of the neutral-type neural networks with multiple delays in the states and discrete delays in the time derivative of the states. The applicability of the proposed stability conditions rely on testing two basic matrix properties. The constraints impose on the system matrices are determined by using nonsingular M-matrix condition, and the constraints imposed on the coefficients of the time derivative of the delayed state variables are derived by exploiting the vector-matrix norms. We also note that the obtained stability conditions have no involvement with the delay parameters and expressed in terms of nonlinear Lipschitz activation functions. We present a constructive numerical example for this class of neural networks to give a systematic procedure for determining the imposed conditions on the whole system parameters of the delayed neutral-type neural systems.  相似文献   

12.
In this paper, the problem of stability analysis for linear systems with time-varying delays is considered. By the consideration of new augmented Lyapunov functionals, improved delay-dependent stability criteria for asymptotic stability of the system are proposed for two cases of conditions on time-varying delays with the framework of linear matrix inequalities (LMIs), which can be solved easily by various efficient convex optimization algorithms. The enhancement of the feasible region of the proposed criteria is shown via three numerical examples by the comparison of maximum delay bounds.  相似文献   

13.
This paper investigates the problem of global exponential stability for neutral systems with interval time varying delays and nonlinear perturbations. It is assumed that the state delay belongs to a given interval, which means that both the lower and upper bounds of the time-varying delay are available. The uncertainties under consideration are norm-bounded. Based on the Lyapunov–Krasovskii stability theory, delay-partitioning technique and lower bounds lemma, less conservative delay-dependent exponential stability criteria are derived in terms of linear matrix inequalities (LMIs) with fewer decision variables than the existing ones. Numerical examples are given to show the effectiveness of the proposed method.  相似文献   

14.
Bifurcation theory is commonly used to study the dynamical behavior of ecosystems. It involves the analysis of points in the parameter space where the stability of the system changes qualitatively. The type of bifurcation that associates equilibria with periodic solution is called Hopf bifurcation. In this paper, a life energy system dynamic model of two components with multiple delays is presented. It is shown that the interaction parameters of the delayed ecosystem play a fundamental role in classifying the rich dynamics and bifurcation phenomena. Regarding the combined interaction parameter as a bifurcation parameter, the bifurcation values in the parameter plane are displayed. The direction of the Hopf bifurcation and the stability of the bifurcating periodic solutions are determined by applying the normal form theory and the center manifold theorem. Moreover, the amplitudes of oscillations always increase as the interaction parameters increase, while the robustness of periods occurs as the interaction parameters vary. From an ecological point of view, the existence of Hopf bifurcation expresses periodic oscillatory behavior of the life energy system.  相似文献   

15.
《Journal of The Franklin Institute》2022,359(17):10017-10037
This paper investigates the positivity and stability of discrete-time coupled homogeneous systems with time-varying delays. First, an explicit criterion is given for the positivity of discrete-time coupled homogeneous delay systems. Then, by using the properties of homogeneous functions, a sufficient condition is presented for ensuring the stability of the considered systems. Moreover, the obtained result is applied to study the stability of positive singular systems with time-varying delay. It should be noted that it is the first time that the stability result is given for discrete-time coupled homogeneous positive systems with time-varying delays. Two numerical examples are presented to demonstrate the effectiveness of the derived results.  相似文献   

16.
In this paper, an eco-epidemiological model with time delay is considered. The asymptotical stability of the three equilibria, the existence of stability switches about both the disease-free planar equilibrium and the positive equilibrium are investigated. It is found that Hopf bifurcation occurs when the delay τ passes through a critical value. Some explicit formulae determining the stability and the direction of the Hopf bifurcation periodic solutions bifurcating from Hopf bifurcations at the positive equilibrium are obtained by using the normal form theory and center manifold theory. Some numerical simulations for justifying the theoretical analysis are also provided. Finally, biological explanations and main conclusions are given.  相似文献   

17.
In this study, an approach to identify and control stable, unstable and integrating systems with unknown delays, framed on the generalized Pattern Search Method is presented. The proposed method inherits the global convergence properties of the generalized Pattern Search Method, allowing us to make a stability analysis of the proposed approach and delay identification capabilities. The proposed approach identifies the delay and guarantees closed-loop stability, which could be a difficult task since in unstable and integrating cases, open-loop experiments are not feasible. Simulation examples show the usefulness of the proposed strategy proving that the scheme is capable of identifying the delay and stabilizing the system even with long delay.  相似文献   

18.
In this paper, we study the local stability and bifurcation of a delay-coupled genetic regulatory networks consisting of two modes with the hub structure. By analyzing the equilibrium equation, the number of the positive equilibria is discussed in both the cases that there are inhibition coupling and activation coupling in the networks. It is revealed that multiple equilibria could exist in the developed genetic networks and the number of the equilibria could be distinct under the two cases of delayed-coupling. For the equilibrium, the conditions of the coupling-delay-independent stability and the saddle-node bifurcation are derived with respect to the biochemical parameters. The coupling-delay-dependent stability and the Hopf bifurcation criteria on the biological parameters and the coupling delay are also given. Moreover, the complexity of the algorithm used in this paper is analyzed. The numerical simulations are made to certify the obtained results. The multistability of the developed genetic regulatory networks is displayed. The different effects of the coupling delay on the stability of the genetic networks under different biochemical parameters are shown.  相似文献   

19.
This paper proposes novel conditions based on linear matrix inequalities (LMI) for stability analysis of arbitrarily-fast time-varying delays systems. The time-varying delay interval is divided into smaller pieces in order to obtain an equivalent switched model with multiple time-varying delays of smaller interval, which differently from other existing approaches, the maximum switching frequency is not required for stability analysis. Thus, by the use of augmented Lyapunov-Krasovskii functionals and the Finsler’s lemma, together with some relationships among state variables intentionally defined, the inherent conservatism can be progressively reduced by refining more and more the delay partition. The superiority of the proposed method is illustrated through two benchmark examples.  相似文献   

20.
This paper is concerned with the stability analysis of discrete-time linear systems with time-varying delays. The novelty of this paper lies in that a novel Lyapunov–Krasovskii functional that updates periodically along with the time is proposed to reduce the conservatism and eventually be able to achieve the non-conservativeness in stability analysis. It can be proved that the stability of a discrete-time linear delay system is equivalent to the existence of a periodic Lyapunov–Krasovskii functional. Two necessary and sufficient stability conditions in terms of linear matrix inequalities are proposed in this paper. Furthermore, the novel periodic Lyapunov–Krasovskii functional is employed to solve the ?2-gain performance analysis problem when exogenous disturbance is considered. The effectiveness of the proposed results is illustrated by several numerical examples.  相似文献   

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