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Neural networks suffer from the natural intra- and inter-cellular noise perturbations and environmental fluctuations. Such noises will undoubtedly affect the dynamics of the neural networks both quantitatively and qualitatively. In this paper, we study the effects of noise perturbations on the stability and periodicity of delayed recurrent neural networks. We first derive the mean-square stability conditions for stochastic delayed recurrent neural networks without and with parametric uncertainties, respectively. After that, we study the stochastic periodicity (stability) with disturbance attenuation of delayed recurrent neural networks. The analysis are all based on the Lyapunov-Krasovskii functional approach, and the conditions are all expressed in terms of linear matrix inequalities, which can be easily solved by using the effective convex optimization techniques. Several numerical examples are also given to demonstrate the correctness and effectiveness of the theoretical results. [ABSTRACT FROM AUTHOR]

In this paper, the consensus problem of second-order multi-agent systems with exogenous disturbances is investigated. Firstly, by using the input-to-state stability of the systems, we show that the global exponential stability of the estimate error system will lead to the asymptotical consensus of the second-order multi-agent systems with exogenous disturbances. Secondly, by utilizing the dynamic gain technique, a disturbance observer is proposed to estimate the disturbance generated by nonlinear exosystem. Based on this disturbance observer, a consensus protocol is presented for the second-order multi-agent systems. Finally, two examples are provided to show the effectiveness of the proposed results. [ABSTRACT FROM PUBLISHER]

This paper analyses a dynamic model of Cournot–Stackelberg which involves a feedback regulation system based on the costs of production. The manufacturer makes decisions based on costs of production and wholesale prices as the leader of the market, while the retailers make decisions according to order amount. The decision-making process of the system is divided into two stages in order to carry out the research more clearly and the doubling period bifurcation will occur with speed of adjusting decision-making increase. It is proved that the stability of the model can be considered separately into two decision-making processes, the cross-effects of the two decision-making stages are analyzed. The manufacturer's decision-making has a decisive influence on the stability of the whole system when the manufacturer is a marketing leader and the parameters also have a significant effect on the stability of the system. Finally, the paper proposes a chaos control method based on adaptive method, which is inspired by decision-making methods. The result of the paper has great significance to the Cournot–Stackelberg game with variable costs and master-slave status. [ABSTRACT FROM AUTHOR]

In this paper, we explore the possibility of designing a continuous controller for a class of nonaffine system to achieve asymptotically tracking results with robustness to system uncertainties, unvanishing disturbances, and unknown control effectiveness. A robust integral of the sign of the error design is formulated to search a robust control for the nonaffine dynamics, while a time-varying gain of Nussbaum-type-function (NTF) is augmented to estimate the unknown direction and magnitude for control effectiveness. A second-order filter is employed to proceed the design when the NTF gain is involved without using any unmeasurable signals. Rigorous analysis shows that the proposed controller can asymptotically stabilizes the closed-loop system and the output tracking error. Simulation results on a Duffing–Holmes chaotic system demonstrate the effectiveness of the proposed approach. [ABSTRACT FROM PUBLISHER]

The paper focuses on the dynamic pricing game of the duopoly air conditioner market with disturbance in demand and analyzes the influence of disturbance on the dynamic game system. Considering the demand for products, such as air conditioner, varies with different seasons, we assume three cases based on the condition of disturbance, including growth market (Case 1), declining market (Case 2) and completely random market (Case 3). By analyzing these three cases and making comparison among them, the paper shows that the growth market is more sensitive to the changing parameters such as the adjustment variable and the competitive factor than the declining market. It is more difficult to keep the system stable in a growth market. Although the demand is completely random, the dynamic system can reach a stable state, on condition that the adjustment variable is small enough. The results also indicate that the bullwhip effect between the order quantity and the actual demand is weakened gradually along with the price adjustment. [ABSTRACT FROM AUTHOR]

Abstract In this paper, one robust identification method is proposed for the discrete-time linear systems with unknown time-varying disturbance. The disturbance is considered as a time-varying parameter for tracking estimation. A robust recursive least squares method is proposed using a forgetting factor. Moreover a new forgetting scheme to update the covariance matrix is developed to improve the stable convergence property of the time-invariant model parameters and the tracking performance of time-varying disturbance. The convergence performance of parameter estimation is analyzed with a proof. Two examples with different types of time-varying disturbance are shown to illustrate the effectiveness and advantage of the proposed method. [ABSTRACT FROM AUTHOR]

As well as technological forces, real-life belt and conveyor systems are loaded by disturbing effects that have a mostly random character. To analyze importance of their influence on belt and conveyor system behavior, a computational model was set up in which the disturbances were represented by the discretization and round-off errors occurring during the solving of the governing equations, which is a new and original idea. The simulations that were carried out show that the disturbances can spawn hidden and co-existing attractors and transitions between vibrations of different periods or between regular and chaotic motions and reverse bifurcations. The main contribution of the paper is a new and original way to modeling of the systems' inaccuracies and disturbances having frequently a random character by means of numerical inaccuracies caused by round-off errors and set tolerances of the solution methods for solving the equations of motion. The computational simulations give evidence that these factors have the same effect as inaccuracies and uncertainties of real machines on their behavior. The simulation showed that these factors can lead to qualitatively different system behavior, like the transitions between the regular and chaotic regimes. The physical validity of all operating regimes was proved by the theorem of the time change of the kinetic energy. The main goal of the presented article is to point out that small deviations from the rated state can cause qualitatively different behavior of the machine systems. • Introduction of a belt and conveyor impact system. • The idea of representing the disturbances by round off and discretization errors occurring during the simulations. • Finding that small disturbances can induce motions of different character of the system running at the same operating conditions. [ABSTRACT FROM AUTHOR]

The active disturbance rejection control (ADRC) is now considered as a powerful control strategy in dealing with large uncertainty covering unknown dynamics, external disturbance, and unknown part in coefficient of the control. However, all theoretical works up to present are limited to deterministic uncertainty. In this technical note, we generalize the ADRC to uncertain nonlinear systems subject to external bounded stochastic disturbance described by an uncertain stochastic differential equation driven by white noise. We first design an extended state observer (ESO) that is used to estimate both state, and total disturbance which includes the internal uncertain nonlinear part and the external uncertain stochastic disturbance. It is shown that the resulting closed-loop system is practically stable in the mean-square topology. The numerical experiments are carried out to illustrate effectiveness of the proposed approach. [ABSTRACT FROM AUTHOR]

We address the problem of synthesizing provably correct controllers for linear systems with reach-avoid specifications. Discrete abstraction-based controller synthesis techniques have been developed for linear and nonlinear systems with various types of specifications. However, these methods typically suffer from the state space explosion problem. Our solution decomposes the overall synthesis problem into two smaller, and more tractable problems: one synthesis problem for an open-loop controller, which can produce a reference trajectory, and a second for synthesizing a tracking controller, which can enforce the other trajectories to follow the reference trajectory. As a key building-block result, we show that, once a tracking controller is fixed, the reachable states from an initial neighborhood, subject to any disturbance, can be overapproximated by a sequence of ellipsoids, with shapes that are independent of the open-loop controller. Hence, the open-loop controller can be synthesized independently to meet the reach-avoid specification for an initial neighborhood. Moreover, we are able to reduce the problem of synthesizing open-loop controllers to satisfiability problems over quantifier-free linear real arithmetic. The number of linear constraints in the satisfiability problem is linear to the number of hyperplanes as the surfaces of the polytopic obstacles and goal sets. The overall synthesis algorithm, computes a tracking controller, and then iteratively covers the entire initial set to find open-loop controllers for initial neighborhoods. The algorithm is sound and, for a class of robust systems, is also complete. We implement this synthesis algorithm in a tool RealSyn ver 2.0 and use it on several benchmarks with up to 20 dimensions. Experiment results are very promising: RealSyn ver 2.0 can find controllers for most of the benchmarks in seconds. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, the tracking control and generalized projective synchronization of a class of hyperchaotic system with unknown parameter and disturbance are investigated. Based on the LaSalle’s invariant set theorem, a robust adaptive controller is contrived to acquire tracking control and generalized projective synchronization and parameter identification simultaneously. It is proved theoretically that the proposed scheme can allow us to drive the hyperchaotic system to any desired reference signals, including hyperchaotic signals, chaotic signals, periodic orbits or fixed value by the given scaling factor. The presented simulation results further demonstrate that the proposed method is effective and robust. [Copyright &y& Elsevier]

Practical time-varying formation tracking problems for second-order nonlinear multiagent systems with multiple leaders are investigated using adaptive neural networks (NNs), where the time-varying formation tracking error caused by time-varying external disturbances can be arbitrarily small. Different from the previous work, there exists a predefined time-varying formation formed by the states of the followers and the formation tracks the convex combination of the states of the leaders with unknown control inputs. Besides, the dynamics of each agent has both matched/mismatched heterogeneous nonlinearities and disturbances simultaneously. First, a practical time-varying formation tracking protocol using adaptive NNs is proposed, which is constructed using only local neighboring information. The proposed control protocol can process not only the matched/mismatched heterogeneous nonlinearities and disturbances, but also the unknown control inputs of the leaders. Second, an algorithm with three steps is introduced to design the practical formation tracking protocol, where the parameters of the protocol are determined, and the practical time-varying formation tracking feasibility condition is given. Third, the stability of the closed-loop multiagent system is proven by using the Lyapunov theory. Finally, a simulation example is showed to illustrate the effectiveness of the obtained theoretical results. [ABSTRACT FROM AUTHOR]

In this note, we investigate the stabilization of switched systems with nonlinear impulse effects and disturbances. Based on the estimate on transition matrices and Gronwall inequality, feedback laws are designed to achieve the exponential stability of the closed-loop system with arbitrary switching frequency. [ABSTRACT FROM AUTHOR]

This note proposes a robust nonlinear observer for systems with Lipschitz nonlinearity. The proposed nonlinear observer, whose linear part adopts the linear LTR observer design technique, has two important advantages over previous designs. First, the new observer does not impose the small-Lipschitz-constant condition on the system nonlinearity, nor other structural conditions on the system dynamics as in the existing observer designs. Second, it is robust in the sense that its state estimation error decays to almost zero even in the face of large external disturbances. [ABSTRACT FROM AUTHOR]

In this note, we propose new receding horizon H∞, control (RHHC) schemes for linear input-constrained discrete time-invariant systems with disturbances. The proposed control schemes are based on the dynamic game problem of a finite-horizon cost function with a fixed finite terminal weighting matrix and a one-horizon cost function with time- varying finite terminal weighting matrices, respectively. We show that the resulting RHHCs guarantee closed-loop stability in the absence of disturbances and H∞, norm bound for 2-norm bounded disturbances. We also show that the proposed schemes can easily be implemented via linear matrix inequality optimization. We illustrate the effectiveness of the proposed schemes through simulations. [ABSTRACT FROM AUTHOR]