Aid Of Lyapunov Functions Research Articles

Distributed fusion filtering for cyber-physical systems under Round-Robin protocol: a mixed H 2/H ∞ framework

ABSTRACT In this paper, the distributed mixed fusion filter design problem is investigated for a class of cyber-physical systems subject to non-ideal measurements under Round-Robin protocol. To save the limited communication resources, the Round-Robin protocol is employed to schedule the data transmissions from the sensors to the remote filters. The measurement is imperfect by taking into account the noises, the random saturations, nonlinearity perturbations and packet dropouts. The objective of this study is to propose a desired fusion filtering method that ensures the prescribed performance constraints on both the local and fusion filtering error dynamics. With the aid of Lyapunov function and stochastic analysis technique, a sufficient condition is established to guarantee the mixed / performance index for the local filtering error systems, and then the filter parameter matrices are derived by resorting to the solutions to some matrix inequalities. Subsequently, on the basis of the obtained local state estimates, the proper fusion parameters are acquired by solving a convex optimisation problem. Finally, a numerical example is provided to demonstrate the effectiveness of the designed fusion filter.

Traveling wave solutions of a class of multi-species non-cooperative reaction–diffusion systems *

In this paper we establish a sharp existence result on weak traveling wave solutions for a general class of multi-species reaction–diffusion systems. Moreover, the minimal speed of the traveling waves is explicitly determined. Such a weak traveling wave solution connects the predator-free equilibrium point E 0 at but needs not to connect the coexistence equilibrium at . We apply this result to three important non-cooperative systems: the classical diffusive SIS system for the spread of infectious disease, a predator–prey system with age structure and a generalised Lotka–Volterra predator–prey system of one predator species feeding on n prey species, and prove with the aid of Lyapunov functions and the LaSalle invariance principle that their weak traveling wave solutions are actually traveling wave solutions that connect at . For the SIS system and the generalised Lotka–Volterra predator–prey system, we develop additional techniques to establish the boundedness of their weak traveling wave solutions before applying the LaSalle’s invariance principle.

Attitude dynamics and control of high-mass-ratio fixed-trim moving mass reentry vehicle

This paper concerns the attitude dynamics and control synthesis of fixed-trim moving mass reentry vehicle (MMRV) suffering from stochastic uncertainties. In order to enhance the roll maneuverability, a new high-mass-ratio configuration is proposed and analyzed. The attitude dynamic analysis presents that the steady-state angle of attack and the interference on yaw channel increase with the mass ratio of moving mass to the whole aircraft as well as the distance between the moving mass mass centre and the vehicle body mass centre. Also, the roll control authority and roll maneuverability are proved to be enhanced when the mass ratio is higher. Considering the practical multi-source disturbances caused by aerodynamic parameter perturbation and stochastic disturbances, the parameter adaptive law and extended state observers (ESOs) are introduced into the control scheme and developed through backstepping design procedure. Meanwhile, an auxiliary system is introduced to compensate for the control saturation caused by the limitation on the moving mass deflection angle. With the aid of Lyapunov function and Ito differential rule, the adaptive backstepping ADRC controller is designed with a guarantee of uniformly ultimate boundness (UUB) of the closed-loop tracking error in mean square. Simulation results are presented to demonstrate the validity and superiority of the proposed configuration and controller.

A novel fuzzy control with filter-based event-triggered mechanism for nonlinear uncertain stochastic systems suffered input hysteresis

In this paper, an adaptive fuzzy tracking control with filter-based event-triggered mechanism for stochastic nonlinear uncertain system suffered input hysteresis is presented. Considering stochastic disturbances and input hysteresis, Fuzzy Logic Systems (FLSs) are adopted to handle such issues. A time-varying vector contained weight vector and approximation error is established. Then, a class of smooth function is introduced to develop the adaptive control laws. It is aiming to avoid the chattering issue. Further, to achieve the desired tracking performance, this paper considers the discontinuous control input caused by the event-triggered control strategy. And the filter-based event-triggered strategy is presented. With the aid of Lyapunov function and Backstepping technique, the fuzzy event-triggered tracking control method is established for the considered system. It is testified that all signals are bounded under the action of the proposed method. Finally, the theoretical results are verified by the presented simulation examples.

Adaptive neural network asymptotic tracking control for nonstrict feedback stochastic nonlinear systems

The adaptive neural network asymptotic tracking control issue of nonstrict feedback stochastic nonlinear systems is studied in our article by adopting backstepping algorithm. Compared with the existing research, the hypothesis about unknown virtual control coefficients (UVCC) is overcome in the control design. By using the bound estimation scheme and some smooth functions, associating with approximation-based neural network, the asymptotic tracking controller is recursively constructed. With the aid of Lyapunov function and beneficial inequalities, the asymptotic convergence character and stability with stochastic disturbance and unknown UVCC can be ensured. Finally, the theoretical finding is verified via a simulation example.

Survival and ergodicity of a stochastic Holling-III predator\u2013prey model with Markovian switching in an impulsive polluted environment

Based on the effects of white noise and colored noise, we propose a stochastic Holling-III predator–prey model in an impulsive polluted environment. Firstly, we prove an existence and uniqueness theorem of the presented model. Secondly, we establish sufficient criteria of extinction, nonpersistence in mean, and weak persistence in mean for both prey and predator species. Thirdly, with the aid of Lyapunov functions, we prove that this system is ergodic and has a unique stationary distribution under certain conditions. Finally, we verify the theoretical results by performing some numerical simulations.

Neurodynamic Approximation-Based Quantized Control With Improved Transient Performances for Microelectromechanical System Gyroscopes: Theory and Experimental Results

This article investigates a neurodynamic quantized control problem with improved transient performances for microelectromechanical system (MEMS) gyroscopes subject to lumped disturbances induced by parameter uncertainties, dynamic coupling, and external disturbances. First, a modified prescribed performance control mechanism based on a hyperbolic cosecant performance function is proposed to specify the transient behavior of tracking errors with an arbitrarily small overshoot. Then, to eliminate the lumped disturbances with a better identification property, a novel echo state network approximator that uses the estimation error to learn neural weights is designed with the aid of a minimal learning parameter technique, which not only can exclude the poor transient behaviors occurring extensively in the existing neural control with a large adaptive gain, but also dramatically reduce the number of parameters to be updated online. Furthermore, contrasting to the available tracking results assuming a continuous control updating, a hysteresis quantizer is introduced to provide discrete values of control signals, supporting the use of digital devices in MEMS gyroscope implementations to realize a closed-loop error stabilization. Finally, ultimately uniformly bounded stability of closed-loop system is proved with the aid of Lyapunov function and nonsmooth analysis technique, while not only simulations but also experimental results are performed to validate the effectiveness of the proposed scheme.

Boundedness analysis of stochastic pantograph differential systems

This paper investigates the exponential ultimate boundedness for stochastic pantograph differential systems. With the aid of Lyapunov functions and algebraic inequality techniques, some pth moment exponential ultimate boundedness conditions are derived for the addressed systems.

Antiperiodic solutions to delayed inertial quaternion‐valued neural networks

This manuscript mainly deals with quaternion‐valued neural networks (QVNNs) with delays and inertial term. Using Wirtinger inequality and coincidence degree theory, a new sufficient criterion to ensure the existence of antiperiodic solution of involved quaternion‐valued neural networks is derived. With the aid of Lyapunov function, we discuss the exponential stability of antiperiodic solutions to quaternion‐valued neural networks. Numerical simulations are presented to illustrate the established theoretical findings.

ROBUST FIXED-TIME CONSENSUS PROTOCOLS FOR MULTI-AGENT SYSTEMS WITH NONLINEAR STATE MEASUREMENTS

This paper solves the robust fixed-time consensus problem for multi-agent systems with nonlinear state measurements. Sufficient conditions are established for the proposed protocol to reach fixed-time consensus under time-varying undirected and fixed directed topology with the aid of Lyapunov functions. It is proved that the finite settling time of the presented protocol for robust consensus is uniformly bounded for any initial condition, which makes it possible for people to design and estimate the convergence time off-line. Numerical simulations are preformed to show the effectiveness of our proposed protocol.

Global Stabilization of Fractional-Order Memristor-Based Neural Networks With Time Delay.

This paper addresses the global stabilization of fractional-order memristor-based neural networks (FMNNs) with time delay. The voltage threshold type memristor model is considered, and the FMNNs are represented by fractional-order differential equations with discontinuous right-hand sides. Then, the problem is addressed based on fractional-order differential inclusions and set-valued maps, together with the aid of Lyapunov functions and the comparison principle. Two types of control laws (delayed state feedback control and coupling state feedback control) are designed. Accordingly, two types of stabilization criteria [algebraic form and linear matrix inequality (LMI) form] are established. There are two groups of adjustable parameters included in the delayed state feedback control, which can be selected flexibly to achieve the desired global asymptotic stabilization or global Mittag-Leffler stabilization. Since the existing LMI-based stability analysis techniques for fractional-order systems are not applicable to delayed fractional-order nonlinear systems, a fractional-order differential inequality is established to overcome this difficulty. Based on the coupling state feedback control, some LMI stabilization criteria are developed for the first time with the help of the newly established fractional-order differential inequality. The obtained LMI results provide new insights into the research of delayed fractional-order nonlinear systems. Finally, three numerical examples are presented to illustrate the effectiveness of the proposed theoretical results.

A Novel Leader-following Consensus of Multi-agent Systems with Smart Leader

This article studies the leader-following consensus problem for mixed-order multi-agent systems with a leader. Different from the traditional leader which is independent of all the other agents, the leader, called smart leader, can obtain and utilize the feedback information from its neighbors at some disconnected time intervals. A new distributed consensus control protocol based on intermittent control is developed for leader-following consensus with a smart leader. Moreover, the smart leader can adjust the control protocol based on the feedback information from its neighbors. With the aid of Lyapunov function, some sufficient conditions are derived for leader-following consensus of multi-agent systems with mixed-order dynamics under fixed directed topology. In addition, the similar results are obtained under switching directed topology. Finally, simulation results are provided to verify the correctness and effectiveness of theoretical results.

Expansivity and Cone-fields in Metric Spaces

Due to the results of Lewowicz and Tolosa expansivity can be characterized with the aid of Lyapunov function. In this paper we study a similar problem for uniform expansivity and show that it can be described using generalized cone-fields on metric spaces. We say that a function $$f:X\rightarrow X$$ is uniformly expansive on a set $$\varLambda \subset X$$ if there exist $$\varepsilon >0$$ and $$\alpha \in (0,1)$$ such that for any two orbits $$\hbox {x}:\{-N,\ldots ,N\} \rightarrow \varLambda $$ , $$\hbox {v}:\{-N,\ldots ,N\} \rightarrow X$$ of $$f$$ we have $$\begin{aligned} \sup _{-N\le n\le N}d(\hbox {x}_n,\hbox {v}_n) \le \varepsilon \implies d(\hbox {x}_0,\hbox {v}_0) \le \alpha \sup _{-N\le n\le N}d(\hbox {x}_n,\hbox {v}_n). \end{aligned}$$ It occurs that a function is uniformly expansive iff there exists a generalized cone-field on $$X$$ such that $$f$$ is cone-hyperbolic.

Distributed Cooperative Current-Sharing Control of Parallel Chargers Using Feedback Linearization

We propose a distributed current-sharing scheme to address the output current imbalance problem for the parallel chargers in the energy storage type light rail vehicle system. By treating the parallel chargers as a group of agents with output information sharing through communication network, the current-sharing control problem is recast as the consensus tracking problem of multiagents. To facilitate the design, input-output feedback linearization is first applied to transform the nonidentical nonlinear charging system model into the first-order integrator. Then, a general saturation function is introduced to design the cooperative current-sharing control law which can guarantee the boundedness of the proposed control. The cooperative stability of the closed-loop system under fixed and dynamic communication topologies is rigorously proved with the aid of Lyapunov function and LaSalle invariant principle. Simulation using a multicharging test system further illustrates that the output currents of parallel chargers are balanced using the proposed control.

A new class of finite-time nonlinear consensus protocols for multi-agent systems

This paper is devoted to investigating the finite-time consensus problem for a multi-agent system in networks with undirected topology. A new class of global continuous time-invariant consensus protocols is constructed for each single-integrator agent dynamics with the aid of Lyapunov functions. In particular, it is shown that the settling time of the proposed new class of finite-time consensus protocols is upper bounded for arbitrary initial conditions. This makes it possible for network consensus problems that the convergence time is designed and estimated offline for a given undirected information flow and a group volume of agents. Finally, a numerical simulation example is presented as a proof of concept.

Lyapunov functions in stability of nonlinear systems on time scales

Uniform stability and uniform asymptotic stability of nonlinear finite-dimensional systems on arbitrary time scales are studied. Sufficient as well as necessary conditions of stability are given with the aid of Lyapunov functions. They extend known stability criteria for continuous-time and discrete-time systems. The Massera lemma, needed to construct a Lyapunov function for uniformly asymptotically stable systems, is extended to time scales. The role played by the graininess function associated to the time scale is discussed. Some peculiarities that appear for time scales with an unbounded graininess function are exhibited.

Stability and Controllability in Non-autonomous Time-discrete Dynamical Systems

In this paper stability and attractivity in non-autonomous time-discrete dynamical systems is investigated with the aid of Lyapunov functions. The results are applied to the problem of stabilization of controlled systems by feedback controls. In the final section of the paper we give sufficient conditions for norm-bounded null-controllability of linear systems.

Suppression of structural vibrations of an air-inflated membrane dam by its internal pressure

The suppression of vibrations in air-inflated membrane dams is considered. The vibrations are assumed to result from disturbances that include unsteady water flow and wind pressure. A mathematical model describing the vibratory motion in the air-inflated membrane and developed in J. C. Hsieh, Free Vibrations of Inflatable Dams, Ph.D. Dissertation, Virginia Polytechnic and State University (1988), is employed for devising a strategy for vibration suppression. The governing equations of motion are discretized to include a finite number of vibrational modes. The proposed suppression strategy is developed with the aid of Lyapunov functions. It has been shown that the suppression of vibrations can be accomplished by properly varying the internal pressure. In other words, the pressure by itself is capable of suppressing the vibrations in the membrane. Possible generalization of the proposed suppression scheme to other systems of relevance is discussed.