Global Robust Stability Research Articles

Decoupling control based on terminal sliding mode and wavelet network for the speed and tension system of reversible cold strip rolling mill

To weaken the nonlinear coupling influences among the variables in the speed and tension system of reversible cold strip rolling mill, a novel dynamic decoupling control strategy is proposed based on nonsingular fast terminal sliding mode (NFTSM) and wavelet neural network (WNN). First, nonlinear disturbance observers are developed to counteract the mismatched uncertainties, and then input/output dynamic decoupling and linearisation for the speed and tension nonlinear coupling system are realised by utilising the inverse system theory. Second, nonsingular fast terminal sliding mode controller (NFTSMC) for each pseudo linear subsystem is presented based on backstepping and two-power reaching law, so as to improve the global convergence speed and robust stability of the system. Third, adaptive WNNs are used to approximate the uncertain items of the system, so as to improve the control precision of the speed and tension of reversible cold strip rolling mill. Theoretical analyses show that the NFTSMs satisfy reachability condition, the system error variables can converge to equilibrium point in finite time, and the resulting closed-loop system is globally asymptotically stable. Finally, simulation research is carried out on the speed and tension system of a 1422 mm reversible cold strip rolling mill by using the actual data, and results show the superiority of the proposed control strategy in comparison with the strategies of cascade PI, linear sliding mode control and internal model control.

Global Optimal Output Regulation of Partially Linear Systems via Robust Adaptive Dynamic Programming

A non-model-based robust adaptive dynamic programming (RADP) approach is developed to solve the global optimal output regulation problem (GOORP) of partially linear systems with nonlinear dynamic uncertainties. By converting the output regulation problem into a global robust optimal stabilization problem, a robust optimal controller is designed by means of the RADP for the transformed system. Nonlinear small-gain theory is applied to conclude the global asymptotic stability for the closed-loop system and thus solves the original GOORP. Simulation results illustrate the effectiveness of the proposed methodology.

Global solutions of quasilinear systems of Klein–Gordon equations in 3D

We prove small data global existence and scattering for quasilinear systems of Klein-Gordon equations with different speeds, in dimension three. As an application, we obtain a robust global stability result for the Euler-Maxwell equations for electrons.

A family of multi-path congestion control algorithms with global stability and delay robustness

The goal of traffic management is to efficiently allocate network resources via adjustment of source transmission rates and routes selection. Mathematically, it aims to solve a traditional utility maximization problem in a fair and distributed manner. In this paper, we first develop a generalized multi-path utility maximization problem which features a weighted average of the classical Kelly’s formulation and the Voice’s model. Next, we design from this broader framework a family of multi-path dual congestion control algorithms whose equilibrium point can both achieve a desired bandwidth utilization and preserve a notion of fairness among competing users. Global stability can be guaranteed for the proposed schemes in the absence of delays by use of a totally novel Lyapunov function. Moreover, when heterogeneous propagation delays are taken into account, we establish decentralized and scalable sufficient conditions for robust global stability by constructing a reasonable Lyapunov–Krasovskii functional candidate. These conditions give estimates for the maximum admissible delays that the controller can tolerate without losing stability. Finally, we verify the results through simulation.

New results of stability analysis for a class of neutral-type neural network with mixed time delays

In this paper, by using Lyapunov–Krasovskii functionals involving triple terms, we investigate the global exponential robust stability for uncertain neutral-type neutral networks with discrete and distributed delays. Several stability criteria are derived for the delayed neural networks in terms of LMIs. Some numerical examples are given to illustrate the applicability of the obtained results by using LMI control toolbox in MATLAB.

Robust stability of stochastic fuzzy impulsive recurrent neural networks with\ time-varying delays

In this paper, global robust stability of stochastic impulsive recurrent neural networks with time-varyingdelays which are represented by the Takagi-Sugeno (T-S) fuzzy models is considered. A novel Linear Matrix Inequality (LMI)-based stability criterion is obtained by using Lyapunov functional theory to guarantee the asymptotic stability of uncertain fuzzy stochastic impulsive recurrent neural networks with time-varyingdelays. The results are related to the size of delay and impulses.Finally, numerical examples and simulations are given to demonstrate the correctness of the theoretical results.

Global robust asymptotic stability of variable-time impulsive BAM neural networks

In this paper, the global robust asymptotic stability of the equilibrium point for a more general class of bidirectional associative memory (BAM) neural networks with variable time of impulses is addressed. Unlike most existing studies, the case of non-fix time impulses is focused on in the present study. By means of B-equivalence method, which was introduced in Akhmet (2003, 2005, 2009, 2010), Akhmet and Perestyuk (1990) and Akhmet and Turan (2009), we reduce these networks to a fix time impulsive neural networks system. Sufficient conditions ensuring the existence, uniqueness and global robust asymptotic stability of the equilibrium point are obtained by employing an appropriate Lyapunov function and linear matrix inequality (LMI). Finally, we give one illustrative example to show the effectiveness of the theoretical results.

Robust Global Stabilization of Spacecraft Rendezvous System via Gain Scheduling

The problem of robust global stabilization of a spacecraft circular orbit rendezvous system with input saturation and input-additive uncertainties is studied in this paper. The relative models with saturation nonlinearity are established based on Clohessey-Wiltshire equation. Considering the advantages of the recently developed parametric Lyapunov equation-based low gain feedback design method and an existing high gain scheduling technique, a new robust gain scheduling controller is proposed to solve the robust global stabilization problem. To apply the proposed gain scheduling approaches, only a scalar nonlinear equation is required to be solved. Different from the controller design, simulations have been carried out directly on the nonlinear model of the spacecraft rendezvous operation instead of a linearized one. The effectiveness of the proposed approach is shown.

Further results on robust stability of bidirectional associative memory neural networks with norm-bounded uncertainties

Abstract In this paper, we have a further study about global robust stability of dynamical bidirectional associative memory (BAM) neural networks with norm-bounded uncertainties. By introducing four new upper bound norms for the interconnection matrices of the neural networks and constructing a suitable Lyapunov functional, several new criteria on global robust stability are established. The obtained results can be easily verified as they can be expressed in terms of the network parameters only. In comparison with the results reported in the literature, the proposed approach leads to results with less restrictive conditions. Two numerical examples are also worked through to illustrate our results.

Robust containment tracking of uncertain linear multi-agent systems: a non-smooth control approach

This paper addresses the distributed robust containment tracking problem of networked systems with uncertain linear dynamics and multiple controlled leaders. The uncertainty class considered in this paper satisfies some matched conditions. To achieve containment tracking in such a multi-agent system, some distributed controllers consisting of using relative state-based continuous feedback and a non-smooth manoeuvre are developed. By transforming the containment tracking problem into the global robust stabilisation problem of interconnected systems, it is shown that the states of followers will asymptotically converge to a convex hull formed by those of the leaders if the control parameters in the proposed controllers are appropriately selected. It is clearly pointed out that the involved control parameters can be successfully found for solving the containment tracking problem if each follower can be directly or indirectly influenced by at least one leader, and the nominal dynamics of followers are stabilisable. The important issue of how fast containment can be achieved is also addressed. Finally, some numerical simulations are given for illustration.

New Criteria for Global Robust Stability of Delayed Neural Networks With Norm-Bounded Uncertainties

In this paper, we study the global asymptotic robust stability of delayed neural networks with norm-bounded uncertainties. By employing the Lyapunov stability theory and homeomorphic mapping theorem, we derive some new types of sufficient conditions ensuring the existence, uniqueness, and global asymptotic stability of the equilibrium point for the class of neural networks with discrete time delays under parameter uncertainties and with respect to continuous and slope-bounded activation functions. An important aspect of our results is their low computational complexity, as the reported results can be verified by checking some properties of symmetric matrices associated with the uncertainty sets of the network parameters. The obtained results are shown to be generalizations of some of the previously published corresponding results. Some comparative numerical examples are also constructed to compare our results with some closely related existing literature results.

New global robust stability condition for uncertain neural networks with time delays

In 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.

Improved robust stability criteria for bidirectional associative memory neural networks under parameter uncertainties

This paper deals with the global robust stability problem of dynamical bidirectional associative memory neural networks with multiple time delays under parameter uncertainties. Using some new upper bound norms for the interconnection matrices of the neural networks and constructing suitable Lyapunov functional, we derive novel conditions for the global robust asymptotic stability of equilibrium point. The obtained results can be easily verified as they can be expressed in terms of the network parameters only. It is shown that the established stability condition generalizes some existing ones, and it can be considered to an alternative result to some other corresponding results derived in previous literature. We also provide two comparative numerical examples to illustrate the advantages of our result over the previously published corresponding robust stability results.

Global robust stability of complex-valued recurrent neural networks with time-delays and uncertainties

This paper focuses on the existence, uniqueness and global robust stability of equilibrium point for complex-valued recurrent neural networks with multiple time-delays and under parameter uncertainties with respect to two activation functions. Two sufficient conditions for robust stability of the considered neural networks are presented and established in two new time-independent relationships between the network parameters of the neural system. Finally, three illustrative examples are given to demonstrate the theoretical results.

Speed tracking control of surface‐mounted permanent‐magnet synchronous motor with unknown exosystem

SummaryThe surface‐mounted permanent‐magnet synchronous motor is a two‐input, two‐output nonlinear system. The multi‐input, multi‐output nature of the system has posed some specific challenges to various control methods. Recently, the robust output regulation problem of the system subject to a known neutrally stable exosystem was studied. The problem came down to a global robust stabilization problem of an augmented system composed of the original plant and an internal model. In this paper, we will further study the robust output regulation problem of the system subject to an unknown neutrally stable exosystem. Like in the case where the exosystem is known, the current problem can be solved by globally stabilizing an augmented system. But unlike in the case where the exosystem is known, the augmented system takes a much more complicated form because of uncertainty in the exosystem than the case where the exosystem is known. In particular, the dynamic uncertainty in the current augmented system contains linearly parameterized uncertainty, and hence is not input‐to‐state stable. By utilizing some dynamic coordinate transformation technique, and combining some robust control and adaptive control techniques, we will solve the problem via a recursive approach. Copyright © 2014 John Wiley & Sons, Ltd.

Dynamical Nonlinear Neural Networks with Perturbations Modeling and Global Robust Stability Analysis

paper is devoted to studying both the global and local stability of dynamical neural networks. In particular, it has focused on nonlinear neural networks with perturbation. Properties relating to asymptotic and exponential stability and instability have been detailed. This paper also looks at the robustness of neural networks to perturbations and examines if the related properties have been preserved. Circumstances for global and local exponential stability of nonlinear neural network dynamics have been studied. We mentioned that the local exponential stability of any equilibrium point of dynamical neural networks is equivalent to the stability of the linearized system around that equilibrium point. From this, some well-known and new sufficient conditions for local exponential stability of neural networks have been obtained. The Lyapunov's procedure has been used to analyze the stability property of nonlinear dynamical systems and many outcomes have been combined and generalized. A kind of Lyapunov's stability of the stable points of Hopfield neural network (HNN) have been proven, which means that if the initial state of the network is close enough to a stable point, then the network state will remain in a small neighborhood of the stable point. These stability results indicate the convergence of the memory process of HNN. The theoretical results are illustrated through a few problem cases for a nonlinear dynamical system with perturbation behavior. Keywordserturbed nonlinear systems, Hopfield neural network,

Global Exponential Robust Stability of High-Order Hopfield Neural Networks with S-Type Distributed Time Delays

By employing differential inequality technique and Lyapunov functional method, some criteria of global exponential robust stability for the high-order neural networks with S-type distributed time delays are established, which are easy to be verified with a wider adaptive scope.

Global Exponential Robust Stability of Static Interval Neural Networks with Time Delay in the Leakage Term

The stability of a class of static interval neural networks with time delay in the leakage term is investigated. By using the method ofM-matrix and the technique of delay differential inequality, we obtain some sufficient conditions ensuring the global exponential robust stability of the networks. The results in this paper extend the corresponding conclusions without leakage delay. An example is given to illustrate the effectiveness of the obtained results.

Robust Stability Analysis of Neutral-Type Hybrid Bidirectional Associative Memory Neural Networks with Time-Varying Delays

The global asymptotic robust stability of equilibrium is considered for neutral-type hybrid bidirectional associative memory neural networks with time-varying delays and parameters uncertainties. The results we obtained in this paper are delay-derivative-dependent and establish various relationships between the network parameters only. Therefore, the results of this paper are applicable to a larger class of neural networks and can be easily verified when compared with the previously reported literature results. Two numerical examples are illustrated to verify our results.

Global robust stabilisation of a class of uncertain switched nonlinear systems with dwell time specifications

This paper is concerned with the global robust stabilisation problem for a class of uncertain switched nonlinear systems in lower triangular form under any switching signal with dwell time specifications. The switched systems under consideration allow the uncertainties to appear in the system. We first design two classes of controllers containing a tuning gain. One designed by backstepping is related to a global convergence with respect to a compact set and the other with gain-scaling factor characters a local asymptotic stable toward the origin. A controller selection mechanism is then introduced to determine which class of controller is employed based on the compact set. The gain tuning mechanism related to the dwell time is then proposed to tune online the controller gain. It is shown that under our proposed control strategy, the global robust stability of the closed-loop switched system is achieved with the dwell time specifications. Finally, simulation results are presented to demonstrate the effectiveness of the proposed approach.