Time-varying Lags Research Articles

Some new uniqueness and Ulam–Hyers type stability results for nonlinear fractional neutral hybrid differential equations with time-varying lags

Abstract This paper deals with some qualitative properties of solutions to nonlinear neutral hybrid differential equations connected to ψ-Caputo fractional derivative with time-varying lags. First, we demonstrate the problem possesses a mild solution uniquely where the source function may have temporal singularities. Second, in some cases, we indicate that the problem possesses a unique mild solution under some weaker conditions than the previous one. Third, we also obtain a result on a global mild solution for the problem. Finally, the results are further enriched by studying a new type of Ulam–Hyers stability for the main equation. The main results are obtained by applying the nice inequality, first proposed and proven in this paper. Some befit examples are given to justify the applicability of the main results.

Extremal problems for parabolic systemswith time-varying lags

Extremal problems for parabolic systemswith time-varying lags

Extremal Problems for Second Order Hyperbolic Systems with Boundary Conditions Involving Multiple Time-Varying Delays

Extremal problems for second order hyperbolic systems with multiple time-varying lags are presented. An optimal boundary control problem for distributed hyperbolic systems with boundary conditions involving multiple time-varying lags is solved. The time horizon is fixed. Making use of Dubovitski-Milyutin scheme, necessary and sufficient conditions of optimality for the Neumann problem with the quadratic performance functionals and constrained control are derived.

Accounting for snowpack and time-varying lags in statistical models of stream temperature

Water temperature plays a primary role in driving ecological processes in streams due to its direct impact on biogeochemical cycles and the physiological processes of stream fauna, such as growth, development, and the timing of life history events. Streams influenced by snowpack melt are generally cooler in the summer and demonstrate less sensitivity to climate variability in what is commonly referred to as “climate buffering”. Despite the substantial influence of snowpack on stream temperature and expected changes in snowpack accumulation and melt timing with climate change, methods for representing snowpack in statistical models for stream temperature have not been well explored. In this investigation, we quantified the extent of stream temperature buffering in free-flowing streams across a geographically diverse region in the Pacific Northwest USA. We demonstrated that statistical models of daily mean stream temperature can be improved by explicitly accounting for temporal variability in a small number of climate covariates believed to be mechanistically related to stream temperature. Our novel statistical approach included as predictors combinations and interactions between the following variables: (1) air temperature, (2) lagged air temperature (where the lag duration varied according to its relationship with flow on a given day at that site), (3) flow, (4) snowpack in the upstream catchment, and (5) day of year. We found that sites with substantial snow influence were associated with increased air temperature buffering during the warm season and longer air temperature lags (>30 days during spring high flows and ∼ 10 days during late summer low flows) compared to sites where precipitation predominantly fell as rain (<6 days year-round). By accounting for snowpack and temporal variation in lagged heat transfer processes, our models were able to accurately predict seasonal patterns and interannual variability in stream temperature in validation data from years not used in model fits using publicly available data sources (average RMPSE ∼ 0.80).

$ S $-asymptotically $ \omega $-periodic dynamics in a fractional-order dual inertial neural networks with time-varying lags

&lt;abstract&gt;&lt;p&gt;This paper investigates global dynamics in fractional-order dual inertial neural networks with time lags. Firstly, according to some crucial features of Mittag-Leffler functions and Banach contracting mapping principle, the existence and uniqueness of $ S $-asymptotically $ \omega $-periodic oscillation of the model are gained. Secondly, by using the comparison principle and the stability criteria of delayed Caputo fractional-order differential equations, global asymptotical stability of the model is studied. In the end, the feasibility and effectiveness of the obtained conclusions are supported by two numerical examples. There are few papers focus on $ S $-asymptotically $ \omega $-periodic dynamics in fractional-order dual inertial neural networks with time-varying lags, apparently, the works in this paper fill some of the gaps.&lt;/p&gt;&lt;/abstract&gt;

Cooperative Adaptive Cruise Control and exhaust emission evaluation under heterogeneous connected vehicle network environment in urban city

With the development of information communication and artificial intelligence, the ICV (intelligent connected vehicle) will inevitably play an important part in future urban transport system. In this paper, we study the car following behaviour under the heterogeneous ICV environment. The time to receive information varies from vehicle to vehicle, since the manual vehicles and autonomous vehicles co-exist on the road. By introducing time-varying lags function, a new car following model is proposed, and the cooperative control strategy of this model is studied. Based on Lyapunov function theory and linear matrix inequality (LMI) approach, the sufficient condition that the existence of the feedback controller is given, which makes the closed-loop system asymptotically stable under mixed traffic flow environment. That is to say, traffic congestion phenomenon under heterogeneous traffic flow can be effectively suppressed, and the feedback controller gain matrix can be obtained via solving linear matrix inequality. Finally, by simulation the method is verified effective in alleviating traffic congestions and reducing fuel consumption and exhaust emissions. It could be a useful reference to Cooperative Vehicle Infrastructure System and Smart City.

New Results on the Exponential Stability of Class Neural Networks with Time-Varying Lags

In this article, some novel approaches to the analysis of globally exponential stability (GES) for a class of neural networks with time-varying lags are presented. These approaches to functional differential equations are based on Lyapunov stability theory. Then, the necessary and sufficient conditions for GES of the equation taking into account have been discussed. An example was given to illustrate the qualitative behavior of the solution of the proposed equation and MATLAB-Simulink Program was used to demonstrate the validity of the results obtained in these samples. Consequently, the obtained results include and improve the results found in the related literature.

Backstepping adaptive control for real-time hybrid simulation including servo-hydraulic dynamics

Abstract A backstepping adaptive control method is proposed for on-line estimation of unknown servo-hydraulic dynamics and the compensation of time-varying lags in real-time hybrid simulation tests. The response tracking problem becomes a critical challenge when realistic experimental conditions are taken into consideration, such as control-structure interaction effects and sensor measurement noise. Unlike a conventional time-lag compensator, the proposed adaptive controller generates a command trajectory for the actuated system according to adaptive laws. Besides bringing response tracking error to zeros, the estimation of a first-principle actuator dynamic model is also facilitated in the proposed approach. Lyapunov stability analysis is systematically presented for designing the adaptive control law. Illustratively, a three-story seismically excited structure with different control strategies is utilized to demonstrate the efficiency and robustness of the proposed controller. A benchmark problem is then utilized for the verification of controller’s advancement. Four simulation cases with different damping/mass conditions and four ground excitation scenarios are selected for the application. As stated, favorable tracking performance has been observed with a remarkable improvement in performance evaluation.

Improving the prediction of arbovirus outbreaks: A comparison of climate-driven models for West Nile virus in an endemic region of the United States

Models that forecast the timing and location of human arboviral disease have the potential to make mosquito control and disease prevention more effective. A common approach is to use statistical time-series models that predict disease cases as lagged functions of environmental variables. However, the simplifying assumptions required for standard modeling approaches may not capture important aspects of complex, non-linear transmission cycles. Here, we compared a set of alternative models of human West Nile virus (WNV) in 2004–2017 in South Dakota, USA. We used county-level logistic regressions to model historical human case data as functions of distributed lag summaries of air temperature and several moisture indices. We tested two variations of the standard model in which 1) the distributed lag functions were allowed to change over the transmission season, so that dependence on past meteorological conditions was time varying rather than static, and 2) an additional predictor was included that quantified the mosquito infection growth rate estimated from mosquito surveillance data. The best-fitting model included temperature and vapor pressure deficit as meteorological predictors, and also incorporated time-varying lags and the mosquito infection growth rate. The time-varying lags helped to predict the seasonal pattern of WNV cases, whereas the mosquito infection growth rate improved the prediction of year-to-year variability in WNV risk. These relatively simple and practical enhancements may be particularly helpful for developing data-driven time series models for use in arbovirus forecasting applications.

Time-Optimal Control of Infinite Order Distributed Parabolic Systems Involving Multiple Time-Varying Lags

ABSTRACTIn this article, a time-optimal control problem for linear infinite order distributed parabolic systems involving multiple time-varying lags appearing both in the state equation and in the boundary condition is presented. Some particular properties of the optimal control are discussed.

An optimization problem for infinite order distributed parabolic systems with multiple time-varying lags

In this paper, the optimal boundary control problem for (n×n) infinite order distributed parabolic systems, with boundary conditions involving multiple time-varying lags is considered. Constraints on controls are imposed. Necessary and sufficient optimality conditions for the Neumann problem with the quadratic performance functional are derived.

Linear feedback controller design method for time-delay chaotic systems

Based on the stability theory of time-delay systems, this paper discusses chaos control and synchronization problem of time-delay chaotic systems. Through the combining of a new theorem and the characters of the chaotic system, we have designed a linear controller to realize chaos control and synchronization for Lorenz system with time-varying lags. Finally, numerical simulations are provided to verify the effectiveness and feasibility of the developed method.

Moment exponential stability and integrability of stochastic functional differential equations

The main objective of the paper is to present sufficient conditions ensuring the pth mean and almost sure exponential stability, as well as the pth mean integrability of solutions to non-linear stochastic functional differential equations and, especially, to stochastic differential equations with time-varying lags. Some examples are given to illustrate the theoretical considerations.

On the chaotic synchronization of Lorenz systems with time-varying lags

Based on the stability theory of time-delay systems, the synchronization problem of chaotic systems with time-varying lags is discussed. Through the analysis of the error dynamical systems, the time-delay correlative synchronization controller is designed to achieve chaos synchronization. Finally, numerical simulations are provided to verify the effectiveness and feasibility of the developed method.

Optimal boundary control problem for n × n infinite-order parabolic lag system

In this paper, we study the linear quadratic optimal boundary control problem for n × n coupled system of infinite-order parabolic partial differential equation, in which time-varying lags appear in the state equation and in the Neumann boundary condition simultaneously. By Lions scheme, necessary and sufficient condition of optimality for the Neumann problem with quadratic functional and constraint control is derived. Finally, several mathematical examples for derived optimality conditions are presented.

Optimal control problem for infinite order parabolic lag system

In this paper, we study the linear quadratic optimal control problem for n×n coupled system of infinite order parabolic partial differential equation, in which time-varying lags appear in the state equation and in the Neumann boundary condition simultaneously. By Lions scheme, necessary and sufficient condition of optimality for the Neumann problem with quadratic functional and constraint control is derived. Finally, special cases for derived optimality conditions are presented.

Optimal control of distributed parabolic systems with multiple time-varying lags

Various optimal control problems for linear parabolic systems with multiple timevarying lags are considered. Necessary and sufficient conditions of optimality are derived for the Neumann problem. Optimal control is obtained in the feedback form. Making use of the results of Schwartz, a representation of optimal feedback control is given.

Optimal control of a distributed hyperbolic system with multiple time-varying lags

In this paper an optimal distributed control problem for a hyperbolic system in which different multiple time-varying lags appear both in the state equation and in the boundary condition is considered. Making use of Lion's scheme, necessary and sufficient conditions of optimality for the Neumann problem with the quadratic performance functional and constrained control are derived. A simple example of application is also presented

Optimal control of a hyperbolic system with time-varying lags

In this paper, an optimal distributed control problem for a hyperbolic system in which time-varying lags appear in the state equation and in the boundary condition simultaneously is considered. Making use of Lions' scheme, necessary and sufficient conditions of optimality for the Neumann problem are derived.

Minimum time problem for a parabolic system with time-varying lags

Minimum time problem for a parabolic system with time-varying lags