Duality theorems for convex problems with time delay

In this paper, we examine a class of convex problems of Bolza type, involving a time delay in the state. It encompasses a variety of time-delay problems arising in the calculus of variations and optimal control. A duality analysis is carried out which, among other things, leads to a characterization of minimizers in terms of the Euler-Lagrange inclusion. The results obtained improve in significant respects on what is achievable by techniques previously employed, based on elimination of the time delay by introduction of an infinite-dimensional state space or on the method of steps.     

Stability analysis of structurally unstable man–machine system involving time delays

In this paper, a structurally unstable man–machine system is considered and a rigorous mathematical analysis is performed to study the influence of time delays in the control force on stability of the equilibrium solution of this system. Results on stability, instability and conditions for the preservation of stability (instability), besides the existence of bifurcation are presented.     

Representing workloads in GI/G/1 queues through the preemptive-resume LIFO queue discipline

We give in this paper a detailed sample-average analysis of GI/G/1 queues with the preemptive-resume LIFO (last-in-first-out) queue discipline: we study the long-run state behavior of the system by averaging over arrival epochs, departure epochs, as well as time, and obtain relations that express the resulting averages in terms of basic characteristics within busy cycles. These relations, together with the fact that the preemptive-resume LIFO queue discipline is work-conserving, imply new representations for both actual and virtual delays in standard GI/G/1 queues with the FIFO (first-in-first-out) queue discipline. The arguments by which our results are obtained unveil the underlying structural explanations for many classical and somewhat mysterious results relating to queue lengths and/or delays in standard GI/G/1 queues, including the well-known Bene's formula for the delay distribution in M/G/l. We also discuss how to extend our results to settings more general than GI/G/1.     

Sampling Consensus of 2nd-Order Multi-Agent Systems Based on Time-Varying Topology北大核心CSCD

基于速度一致位移差保持不变的一致性概念,研究了二阶多智能体系统在时变拓扑下的采样一致性问题。首先,引入虚拟领导者,将具有时变拓扑结构的多智能体系统的采样一致性问题转换为误差系统的采样控制稳定性问题。其次,通过预估采样误差,研究采样误差对系统达到一致性的影响。最后,应用Lyapunov稳定性理论,分析所构造的误差系统的稳定性,并给出该误差系统最终稳定的充分条件。数值仿真结果验证了理论分析的有效性和正确性。     

Exponential stability of discrete-time systems with slowly time-varying delays

Slowly time-varying delays are seldom, but do need to be, considered in the context of discrete-time systems. This paper addresses the exponential stability issue of discrete-time systems with slowly time-varying delays. The basic idea is to transform, by utilizing the switching transformation approach, the original system with slowly time-varying delays into an equivalent switched system with special switching signal. Different types of delays correspond to different types of switching signals, and the stability issue of the original system is converted into that of a switched system. It is the first time that the method of switched homogeneous polynomial Lyapunov function is applied to general delayed systems. Some sufficient exponential stability conditions for the original system are proposed in several situations. It is numerically shown that the conservativeness of the proposed conditions reduces as the degree of the switched homogeneous polynomial Lyapunov function increases.     

Precise bounds for the petersen time-varying real parameter uncertainty system stabilized via linear static controllers

Using a class of linear static controllers, we stabilize the Petersen open-loop two-dimensional linear system (Ref. 1), which consists of one time-varying uncertainty in the state matrixA and one timevarying uncertainty in the input matrixB. We show that the worst-case uncertainty strategy for the closed-loop system is a piecewise constant strategy of the angular state with three switches on the half-turn, –/2/2; it is unique with respect to a set of measure zero. Formulas are derived for the worst-case half-turn radius gainr _HT as a function of the parameters of the class of stabilizing linear static controllers. Using the class of scalar-quadratic Lyapunov functions, we show that a necessary and sufficient condition for the closed-loop system to be robustly stable against all time-varying admissible uncertainties is thatr _HT be less than unity. The bound on the time-varying real parameter uncertainties for the closed-loop system to be robustly stable is derived for the class of linear static feedback controllers. We obtain stabilizing linear static controllers such that the bound is as close to infinity as desired. The derived results are compared with numerical results obtained using commerical robust-control software.     

ACTIVE CONTROL OF A FLEXIBLE CANTILEVER PLATE WITH MULTIPLE TIME DELAYS

Active control of a flexible cantilever plate with multiple time delays is investigated using the discrete optimal control method. A controller with multiple time delays is presented. In this controller, time delay effect is incorporated in the mathematical model of the dynamic system throughout the control design and no approximations and assumptions are made in the controller derivation, so the system stability is easily guaranteed. Furthermore, this controller is available for both small time delays and large time delays. The feasibility and efficiency of the proposed controller are verified through numerical simulations in the end of this paper.     

Stability analysis of fractional order fuzzy cellular neural networks with leakage delay and time varying delays

In this paper we investigated the stability of fractional order fuzzy cellular neural networks with leakage delay and time varying delays. Based on Lyapunov theory and applying bounded techniques of fractional calculation, sufficient criterion are established to guarantee the stability. Hybrid feedback control is applied to derive the proposed results. Finally, numerical examples with simulation results are given to illustrate the effectiveness of the proposed method.     

Time-delay effects on dynamics of a two-actor conflict model

We present a study of time-delay effects on a two-actor conflict model based on nonlinear differential equations. The state of each actor depends on its own state in isolation, its previous state, its inertia to change, the positive or negative feedback and a time delay in the state of the other actor. We use both theoretical and numerical approaches to characterize the evolution of the system for several values of time delays. We find that, under particular conditions, a time delay leads to the appearance of oscillations in the states of the actors. Besides, phase portraits for the trajectories are presented to illustrate the evolution of the system for different time delays. Finally, we discuss our results in the context of social conflict models.     

The role of delay times in subcycle-resolved probe retardation measurements

The delay in the nonlinear response of matter to intense laser pulses has been studied since a long time regarding its nuclear contribution. In contrast, the electronic part of the nonlinear response in wide-band-gap dielectrics, which is usually dominant, is not well explored regarding its delay, and previous studies have revealed that the timescale is below 1 fs. Here, the influence of delay times on the recently introduced method of subcycle-resolved probe retardation measurements is investigated using a simulation. In the model assumed, the electronic nonlinearity is divided into the third order Kerr effect and the plasma contribution due to conduction band population in the strong laser field. In the regime of close-to-collinear pump-probe geometries, the probe retardation shows both π- and 2π-oscillations in the pump-probe delay. Sub-femtosecond delay times influence the phase of the oscillations significantly, but it remains difficult to distinguish the influence of the Kerr response from the plasma contribution.