Nonuniform Time-varying Delays Research Articles

Consensus of second-order multi-agent systems with nonuniform time-varying delays

This paper is concerned with the consensus problem in directed networks with double-integrator dynamics and non-uniform time-varying communication delays. With the help of Lyapunov–Razumikhin function a necessary and sufficient condition is presented in the case when the delays are non-uniform and time-varying. Simulation results are provided to illustrate the theoretical results.

Delay Depending Decentralized Adaptive Attitude Synchronization Tracking Control of Spacecraft Formation

This paper deals with the problem of cooperative attitude tracking with time-varying communication delays as well as the delays between inter-synchronization control parts and self-tracking control parts in the spacecraft formation flying. First, we present the attitude synchronization tracking control algorithms and analyze the sufficient delay-dependent stability condition with the choice of a Lyapunov function when the angular velocity can be measured. More specifically, a class of linear filters is developed to derive an output feedback control law without having direct information of the angular velocity, which is significant for practical applications with low-cost configurations of spacecraft. Using a well-chosen Lyapunov-Krasovskii function, it is proven that the presented control law can make the spacecraft formation attitude tracking system synchronous and achieve exponential stability, in the face of model uncertainties, as well as non-uniform time-varying delays in communication links and different control parts. Finally, simulation results are presented to demonstrate the effectiveness of the proposed control schemes.

Leader-following consensus of second-order agents with multiple time-varying delays

In this paper, a leader-following consensus problem of second-order multi-agent systems with fixed and switching topologies as well as non-uniform time-varying delays is considered. For the case of fixed topology, a necessary and sufficient condition is obtained. For the case of switching topology, a sufficient condition is obtained under the assumption that the total period over which the leader is globally reachable is sufficiently large. We not only prove that a consensus is reachable asymptotically but also give an estimation of the convergence rate. An example with simulation is presented to illustrate the theoretical results.

Consensus problems in networks of agents with double-integrator dynamics and time-varying delays

In this article, we consider consensus problems in networks of agents with double-integrator dynamics and non-uniform time-varying delays. The agent dynamics is adopted as a typical point mass model based on Newton's law. Without assuming that the weighting factors in the information update schemes are non-negative, we propose two protocols such that both the state and the velocity of agents achieve consensus. An equivalent reduced-order system is introduced to analyse the convergence of the protocols. Some necessary and (or) sufficient conditions for consensus are established in terms of linear matrix inequalities. Simulation results are provided that demonstrate the effectiveness of our theoretical results.

Consensus of Multi-Agent Systems in Directed Networks With Nonuniform Time-Varying Delays

In this note, we study consensus problems for continuous-time multi-agent systems in directed networks with dynamically changing topologies and nonuniform time-varying delays. We have analyzed consensus problems in the following three cases: 1) directed networks with dynamically changing topologies and nonuniform time-varying delays; 2) directed networks with intermittent communication and data packet dropout; and 3) finite-time consensus in directed networks with dynamically changing topologies and nonuniform time-varying delays. We propose a new approach based on a tree-type transformation to investigate consensus problems in all three cases. Some necessary and/ or sufficient conditions are established. Simulation results are also given to demonstrate the theoretical results.

Robust attitude synchronisation controllers design for spacecraft formation

The attitude synchronisation control problem for spacecraft formation with switching communication topologies and information transmission delays is addressed. Common Lyapunov functions are employed to tackle such a problem. To compensate the adverse effect on an individual spacecraft arising from model uncertainties and external disturbances, parameter estimation variables and nonlinear integral terms are incorporated into the Lyapunov functions. The main result of this research is that one of the presented controllers can render a spacecraft formation consistent to a given trajectory globally with dynamic information exchange graph and non-uniform time-varying delays while coping with the parameter uncertainties and unexpected disturbances. In addition, several corollaries of the main results are provided. By virtue of a corollary of Barbalat's lemma, attractiveness of the proposed controllers for the corresponding closed-loop systems is proven. Numerical simulations are also included to demonstrate the theoretical results.