Periodic Time-varying Parameters Research Articles

Stabilization of Periodic Piecewise Time-Varying Systems With Time-Varying Delay Under Multiple Cyber Attacks: An Augmented Lyapunov Functional Approach.

This article investigates the asymptotic stabilization of periodic piecewise time-varying systems with time-varying delay under various cyber attacks, particularly deception and DoS attacks. The addressed system is reformed into a number of time-varying subsystems based on the time interval for each period. Following that, a state-feedback controller with periodic time-varying gain parameters is developed to solve the stabilization problem. The control design depicts the possibility of the aforementioned cyber attacks with two mutually exclusive stochastic Bernoulli distributed parameters. Then, an augmented Lyapunov-Krasovskii functional with periodically varying matrices is used to determine the conditions for designing the proposed controller that ensures the mean-square asymptotic stability of the addressed system. The results of numerical examples support the conclusion that the proposed method is effective and superior, regardless of the cyber attacks involved.

Distributed Filtering With Dynamic Event-Triggered Communication for Networked Periodic Systems

This article deals with the problem of distributed filtering of periodic systems over sensor networks under event-triggered communications, based on a piecewise impulsive method. The continuous-time periodic system is approximated by several linear time-invariant subsystems through a piecewise constant method. The sensor network deployed to the periodic system is taken into account for the actual needs of monitoring or estimation. A dynamic event-triggering mechanism is designed to reduce the unnecessary data transmission over the wireless network from the sensor to the filter as well as between each filter. Distributed peak-to-peak filters with periodic time-varying parameters are designed under the event-triggering mechanism to estimate the networked continuous-time periodic systems with the bounded and local differentiable disturbance. Then, a periodic piecewise filtering error system is modeled as an impulsive periodic piecewise system, for which sufficient conditions of a guaranteed peak-to-peak performance are proposed. The gains of the filters are obtained by the method of convex linearization. The validity of the proposed results is demonstrated by a pendulum tracking system.

A new adaptive iterative learning control of finite-time hybrid function projective synchronization for unknown time-varying chaotic systems

A new adaptive iterative learning control (AILC) scheme is proposed to solve the finite-time hybrid function projective synchronization (HFPS) problem of chaotic systems with unknown periodic time-varying parameters. Fourier series expansion (FSE) is introduced to deal with the problem of uncertain time-varying parameters. The bound of the expanded remaining items is unknown. A typical convergent series is used to deal with the unknown bound in the design process of the controller. The adaptive iterative learning synchronization controller and parameter update laws are designed. Two different chaotic systems are synchronized asymptotically according to different proportional functions on a finite time interval by Lyapunov stability analysis. The simulation example proves the feasibility and effectiveness of the proposed method.

Periodic stationarity conditions for mixture periodic INGARCH models

<abstract><p>This paper proposes strict periodic stationarity and periodic ergodicity conditions for a finite mixture integer-valued GARCH model with $ S $-periodic time-varying parameters that depend on the state of an independent and periodically distributed regime sequence. In this model, the past conditional mean values depend on the past of the regime variable in the same order, so the model is characterized by path-regime dependence. We also propose sufficient conditions for periodic stationarity when the conditional means are nonlinear of past observations. The results are applied to various discrete conditional distributions.</p></abstract>

A Novel Scheme of Nonfragile Controller Design for Periodic Piecewise LTV Systems

In this article, a novel nonfragile controller design scheme is developed for a class of periodic piecewise systems with linear time-varying subsystems. Two types of norm-bounded controller perturbations, including additive and multiplicative ones, are considered and partially characterized by periodic piecewise time-varying parameters. Using a new matrix polynomial lemma, the problems of nonfragile controller synthesis for periodic piecewise time-varying systems (PPTVSs) are made amenable to convex optimization based on the favorable property of a class of matrix polynomials. Depending on selectable divisions of subintervals, sufficient conditions of the stability and nonfragile controller design are proposed for PPTVSs. Case studies based on a multi-input multi-output PPTVS and a mass-spring-damper system show that the proposed control schemes can effectively guarantee the close-loop stability and accelerate the convergence under controller perturbations, with more flexible periodic time-varying controller gains than those obtained by the existing methods.

Globally repetitive learning consensus control of unknown nonlinear multi-agent systems with uncertain time-varying parameters

This paper studies the globally repetitive learning leader-following consensus for a class of unknown nonlinear multi-agent systems with uncertain periodic time-varying parameters. Neural networks are used as the feed-forward compensators to model some unknown nonlinear system functions. According to the different distributions of agents in the network topology, and by learning periodic uncertainties, a new hybrid repetitive learning control protocol is presented based on Lyapunov theory. Meanwhile, the proposed learning control protocol can guarantee that all the followers can track the leader asymptotically. Moreover, the boundedness of all the signals is ensured. Finally, three simulation examples are provided to verify the effectiveness of the proposed scheme.

A multimode perturbation method for frequency response analysis of nonlinearly vibrational beams with periodic parameters

A multimode perturbation method for frequency response analysis of nonlinearly vibrational beams with periodic distribution parameters is proposed. The partial differential equation with spatial varying parameters for nonlinear vibration of beams with periodic parameters under harmonic excitations is derived. The procedure of the multimode perturbation method includes three main steps: first, the nonlinear partial differential equation is transformed into linear partial differential equations with varying parameters by applying perturbation method; second, the linear partial differential equations are transformed into ordinary differential equations with multimode coupling by applying Galerkin method, where multiple vibration modes of the beams are used and the equations are suitable to nonlinear vibration of periodic structures with high parameter-varying wave in wide frequency band; third, the ordinary differential equations are solved by applying harmonic balance method to obtain vibration response of the nonlinear periodic beam, which is used for characteristics analysis of frequency response and spatial mode. Furthermore, the stability problem of nonlinear harmonic vibration as multidegree-of-freedom system with periodic time-varying parameters is solved by applying direct eigenvalue analysis approach. The proposed method can incorporate multiple vibration modes into response analysis of nonlinear periodic structures and consider mode-coupling effects due to structural nonlinearity and parametric periodicity. Finally, a nonlinear beam with periodic supports under harmonic excitations is studied. Numerical results on frequency response of the beam are given to illustrate an application of the proposed method, new frequency response characteristics, and influences of periodic parameters on structural response. The results have potential application to nonlinear structural vibration control and support damage detection of nonlinear structures with periodic supports.

On the theory of periodic multivariate INAR processes

In this paper a multivariate integer-valued autoregressive model of order one with periodic time-varying parameters, and driven by a periodic innovations sequence of independent random vectors is introduced and studied in detail. Emphasis is placed on models with periodic multivariate negative binomial innovations. Basic probabilistic and statistical properties of the novel model are discussed. Aiming to reduce computational burden arising from the use of the conditional maximum likelihood method, a composite likelihood-based approach is adopted. The performance of such method is compared with that of some traditional competitors, namely moment estimators and conditional maximum likelihood estimators. Forecasting is also addressed. Furthermore, an application to a real data set concerning the monthly number of fires in three counties in Portugal is presented.

Parametrically excited stability of a periodically stiffened beam under axial periodic excitation

The parametrically excited stability of a periodically stiffened beam under general periodic axial excitation is studied and the effect of periodic stiffeners on the beam stability is considered for the first time. The partial differential equation of motion of the beam with periodic stiffeners under axial excitation is given. The Galerkin method is used to convert the partial differential equation into ordinary differential equations with periodic time-varying parameters. The direct eigenvalue analysis method based on the Fourier expansion and generalized eigenvalue analysis is applied to solve the parametrically excited stability problem of the stiffened beam. A simply supported beam with periodic stiffeners under periodic axial excitation is considered for numerical investigation. The parametrically excited stability of the stiffened beam and the effects of stiffeners and excitation on the stability are illustrated by numerical results on unstable regions.

New distributed adaptive protocols for uncertain nonlinear leader-follower multi-agent systems via a repetitive learning control approach

In this paper, the distributed consensus problem of leader-follower multi-agent systems with unknown time-varying coupling gains and parameter uncertainties are investigated, and the fully distributed protocols with the adaptive updating laws of periodic time-varying parameters are designed by using a repetitive learning control approach. By virtue of algebraic graph theory, Barbalat’s lemma and an appropriate Lyapunov-Krasovskii functional, it is shown that each follower agent can asymptotically track the leader even though the dynamic of the leader is unknown to any of them, i.e., the global asymptotic consensus can be achieved. At last, a simulation example is given to illustrate the feasibility and efficiency of the proposed protocols.

T–S fuzzy model-based adaptive repetitive consensus control for second-order multi-agent systems with imprecise communication topology structure

This paper investigates the consensus problem of the second-order nonlinear multi-agent systems (MAS) with unknown periodic time-varying parameters (UPTVP) and imprecise communication topology structure (ICTS). T–S fuzzy models is used to express the ICTS, and the concept of fuzzy union connected (FUC) is defined. Under the condition that the ICTS is FUC, an adaptive repetitive learning control protocol is presented such that all the followers can track the leader asymptotically. With the information of leader agent is known to a small portion of following agents, an auxiliary control term was presented for each follower agent to handle leaders dynamics. The distributed MAS consensus is analyzed based on the Lyapunov stability theory. Furthermore, the proposed protocol is further promoted to solve the formation control problem. Finally, simulation results are shown to demonstrate the validity of the proposed design methods in this paper.

Resonance Response of Reverse Flow Reactors: A Numerical Simulation

The effect of periodic time-varying inlet parameters on reverse flow reactor behavior is simulated using a one-dimensional heterogeneous model with methane as the model reactant. When the flow-reversal cycle is an odd multiple of the inlet concentration variation cycle, a resonance response occurs. Such reactor behavior will occur with various values of superficial inlet velocity, mean inlet methane concentration, flow-reversal time and inert-to-catalyst ratios during this simulation work. A synchronization of the two cycles will cause a sharp increase in the variation of maximum temperature, which may impair reactor stability. Simulation results reveal that the resonance response is attributed to the breakdown of temporal and spatial symmetry in the temperature field of reactor. When a resonance response occurs, adjusting the flow-reversal time is a feasible method to maintain autothermal operation of the reactor. Different from commonly used control strategies both increasing and decreasing flow-reversal time can be used to avoid reactor extinction, and so does avoiding thermal runaway. Simulation work of introducing periodic variation of inlet gas velocity is performed, and a similar resonance response behavior is observed.