Multiple Unknown Time-varying Delays Research Articles

Exponential synchronization of discontinuous chaotic systems via delayed impulsive control and its application to secure communication

This paper investigates drive-response synchronization of chaotic systems with discontinuous right-hand side. Firstly, a general model is proposed to describe most of known discontinuous chaotic system with or without time-varying delay. An uniform impulsive controller with multiple unknown time-varying delays is designed such that the response system can be globally exponentially synchronized with the drive system. By utilizing a new lemma on impulsive differential inequality and the Lyapunov functional method, several synchronization criteria are obtained through rigorous mathematical proofs. Results of this paper are universal and can be applied to continuous chaotic systems. Moreover, numerical examples including discontinuous chaotic Chen system, memristor-based Chua’s circuit, and neural networks with discontinuous activations are given to verify the effectiveness of the theoretical results. Application of the obtained results to secure communication is also demonstrated in this paper.

Design of control strategies for robust dynamic routing in traffic networks

In this study, improved centralised and decentralised routing control strategies are developed based on minimisation of the worst-case queuing length. The centralised routing problem is formulated as an ℋ∞ optimal control problem to achieve a robust routing performance in the presence of unknown fast time-varying network delays. Then a decentralised routing problem is reformulated by treating every node as a single subsystem thereby yielding an algorithm that obtains the fastest route. In both cases, unconstrained solution is derived to design a delay-dependent ℋ∞ controller and expressed in terms of the feasibility of linear matrix inequality (LMI). Subsequently, physical constraints are imposed and added as LMIs. Salient features of the developed routing methodology including the increase of robustness against multiple unknown time-varying delays, and the enhancement of the scalability of the algorithm to large-scale traffic networks are delineated. Simulation results are presented to demonstrate the effectiveness and capabilities of the developed dynamic routing strategies.

Approximation-Based Adaptive Tracking Control of Pure-Feedback Nonlinear Systems With Multiple Unknown Time-Varying Delays

This paper presents adaptive neural tracking control for a class of non-affine pure-feedback systems with multiple unknown state time-varying delays. To overcome the design difficulty from non-affine structure of pure-feedback system, mean value theorem is exploited to deduce affine appearance of state variables x(i) as virtual controls α(i), and of the actual control u. The separation technique is introduced to decompose unknown functions of all time-varying delayed states into a series of continuous functions of each delayed state. The novel Lyapunov-Krasovskii functionals are employed to compensate for the unknown functions of current delayed state, which is effectively free from any restriction on unknown time-delay functions and overcomes the circular construction of controller caused by the neural approximation of a function of u and [Formula: see text] . Novel continuous functions are introduced to overcome the design difficulty deduced from the use of one adaptive parameter. To achieve uniformly ultimate boundedness of all the signals in the closed-loop system and tracking performance, control gains are effectively modified as a dynamic form with a class of even function, which makes stability analysis be carried out at the present of multiple time-varying delays. Simulation studies are provided to demonstrate the effectiveness of the proposed scheme.

A novel Hα control strategy for design of a robust dynamic routing algorithm in traffic networks

In this paper novel centralized and decentralized routing control strategies based on minimization of the worst-case queuing length are proposed. The centralized routing problem is formulated as an H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">infin</sub> optimal control problem to achieve a robust routing performance in presence of multiple and unknown fast time-varying network delays. Unlike similar previous work in the literature the delays in the queuing model are assumed to be unknown and time-varying. A Linear Matrix Inequality (LMI) constraint is obtained to design a delay-dependent H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">infin</sub> controller. The physical constraints that are present in the network are then expressed as LMI feasibility conditions. Our proposed centralized routing scheme is then reformulated in a decentralized frame work. This modification yields an algorithm that obtains the "fastest route", increases the robustness against multiple unknown time-varying delays, and enhances the scalability of the algorithm to large scale traffic networks. Simulation results are presented to illustrate and demonstrate the effectiveness and capabilities of our proposed novel dynamic routing strategies.

LMI-based stability criteria for neural networks with multiple time-varying delays

In this paper, the stability of neural networks with multiple time-varying delays is studied. A new class of Lyapunov–Krasovskii functionals is constructed and the S-procedure and free-weighting matrix method are employed to derive a delay-dependent stability criterion, from which a delay-independent criterion is obtained as a special case. Moreover, the result is also extended to delay-dependent and rate-independent stability criteria for multiple unknown time-varying delays. Finally, numerical examples are given to illustrate the effectiveness of our methods and improvement over the existing ones.

Sufficient Conditions for the Stability of Interval Systems with Multiple Time-Varying Delays

In this paper, the global asymptotic stability of interval systems with multiple unknown time-varying delays is considered. Some criteria are derived to guarantee the global asymptotic stability of such systems. A numerical example is provided to illustrate the use of our main results.