Maximum Allowable Communication Research Articles

Time-Varying Trajectory Tracking Formation H∞ Control for Multiagent Systems With Communication Delays and External Disturbances

Time-varying formation (TVF) and trajectory tracking <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$H_{\infty }$ </tex-math></inline-formula> control problem of multiagent systems (MASs) subject to communication delays and external disturbances under the directed communication topology is studied. This article’s objective is for all agents to attain the desired TVF and track the pregiven formation center trajectory simultaneously. First, a distributed TVF and trajectory tracking control protocol employing neighborhood interaction information is developed in the presence of communication delays. Second, since the Laplacian matrix of a graph can be decomposed into the product of two specific matrices, the TVF and trajectory tracking <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$H_{\infty }$ </tex-math></inline-formula> control problem is converted into the lower dimension asymptotic stability problem of a closed-loop system by applying an appropriate variable conversion. Third, a Lyapunov–Krasovskii functional is constructed to analyze the stability of MASs. Sufficient conditions are obtained in the form of linear matrix inequalities (LMIs) to ensure the completion of the TVF and formation center trajectory tracking of MASs. In the meantime, the maximum allowable communication delay can be calculated by the LMIs. Finally, the results of numerical simulations are presented to verify the validity of the approach this article proposes.

Fully distributed hierarchical control strategy for multi‐inverter‐based AC microgrids

A fully distributed hierarchical control strategy for multiple inverters-based AC microgrid is proposed. The developed controller provides real-time economic dispatch along with the network frequency and average voltage restoration. The controllers cooperate with neighbours using sparse communication network and perform local computations to achieve the assigned objectives. The economic dispatch control unit is embedded with the frequency restoration at the secondary level controller to change the active power supply from the inverter. The voltage controller along with reactive power controller ensures the proportional reactive power sharing as well as network average voltage regulation. The average voltage regulation aids the individual inverter to provide required reactive power demand, with a small, comprise at the terminal output voltages from the nominal values. The convergence of the proposed controller is proved using the Lyapunov stability criteria. The maximum allowable communication delay that obligate stable microgrid operation is derived. The simulation results verify the efficacy of the proposed controller. Experimental validation is also presented, and the controller ability to ride through communication failure and load perturbation condition is demonstrated.

A class of cooperative relay analysis of multi-agent systems with tracking number switching and time delays

This paper investigates a complicated class of cooperative tracking problems with time-varying number of tracking agents and communication time delays. During the entire tracking process, tracking agents are dynamically changing and the number is not fixed. This results in jumping of tracking errors and dynamic dimensions of the corresponding Laplacian matrices. Consequently, the stability analysis turns to be difficult especially when the effect of communication time delays is taken into consideration. In order to solve this issue, a new type of average Lyapunov function is constructed to compensate the unmatched dimensions of communication topologies over different time intervals. Generalized reciprocally convex Lemma and a more relaxed switched technique are employed to achieve a less conservative switched stability condition for the multi-agent system with variable tracking number and time delays. Finally, through a series of numerical simulations, the effectiveness and feasibility of derived results are verified. The relationship between maximum allowable communication time delays and various control parameters is obtained in a quantitative way.

Event‐triggered output tracking control for wireless networked control systems with communication delays and data dropouts

This study addresses the event-triggered output tracking control under wireless network environments. First, an improved event-triggered communication scheme and a sampled-state-error dependent tracking model for wireless networked control systems is presented. In this scheme and model, (a) the sensor takes samples in a periodic manner; (b) an improved event-triggering condition is applied in the communications to determine whether the sampled data is transmitted to the controller or not; and (c) the closed-loop tracking system with a networked state-dependent controller is modelled as an augmented time-delay system. Second, by constructing a novel Lyapunov–Krasovskii functional, two theorems are derived with guaranteed H∞ tracking performance subject to imperfect wireless communications. The tracking performance is based on two permissible limits on the signal transmission. That is, the maximum allowable communication delay bound and maximum allowable number of successive data dropouts. Finally, a satellite tracking example is given to show the effectiveness of the proposed method.

Noise tolerance leader-following of high-order nonlinear dynamical multi-agent systems with switching topology and communication delay

This paper investigates the leader-following tracking consensus problem for high-order nonlinear dynamical multi-agent systems with switching topology and communication delay under noisy environments. In order to reflect a more realistic situation, we introduce a general multi-agent systems model and also further investigate its robust consensus under noisy environments, the topology of the network is assumed to be in a finite set of arbitrarily stochastic switching, the communication delay is also considered in the tracking control protocols. The mean square consensus sufficient conditions of multi-agent systems are explored via the common stochastic Lyapunov functional stability theory, in other words, can be solved by linear matrix inequality schemes. The mean square consensus condition is derived to provide a rigorous condition for leader-following of high-order nonlinear dynamical multi-agent systems with considerable scale. In particular, we prove that the proposed algorithm is robust against the bounded communication delay in noisy environments. On the other hand, when it involves many multi-agent systems, a more conservative but effective consensus protocol is also raised. The consensus protocols only require low-dimensional matrices, which are independent of the network size. In addition, the consensus criteria of two cases without communication delay or noisy environment are also proposed. A simple optimization program is also developed to determine the maximum allowable communication delay. Finally, in order to demonstrate the effectiveness and feasibility of the consensus protocol obtained in this paper, the numerical examples are given.

Swarm Motion as Particles of a Continuum With Communication Delays

In this paper, we give an upper bound for the communication delay in a multi-agent system (MAS) that evolves under a recently developed continuum paradigm for formation control. The MAS is treated as particles of a continuum that transforms under special homeomorphic mapping, called a homogeneous map. Evolution of an MAS in ℝn is achieved under a special communication topology proposed by Rastgoftar and Jayasuriya (2014, “Evolution of Multi Agent Systems as Continua,” ASME J. Dyn. Syst. Meas. Control, 136(4), p. 041014) and (2014, “An Alignment Strategy for Evolution of Multi Agent Systems,” ASME J. Dyn. Syst. Meas. Control, 137(2), p. 021009), employing a homogeneous map specified by the trajectories of n+1 leader agents at the vertices of a polytope in ℝn, called the leading polytope. The followers that are positioned in the convex hull of the leading polytope learn the prescribed homogeneous mapping through local communication with neighboring agents using a set of communication weights prescribed by the initial positions of the agents. However, due to inevitable time-delay in getting positions and velocities of the adjacent agents through local communication, the position of each follower may not converge to the desired state given by the homogeneous map leaving the possibility that MAS evolution may get destabilized. Therefore, ascertaining the stability under time-delay is important. Stability analysis of an MAS consisting of a large number of agents, leading to higher-order dynamics, using conventional methods such as cluster treatment of characteristic roots (CTCR) or Lyapunov–Krasovskii are difficult. Instead we estimate the maximum allowable communication delay for the followers using one of the eigenvalues of the communication matrix that places MAS evolution at the margin of instability. The proposed method is advantageous because the transcendental delay terms are directly used and the characteristic equation of MAS evolution is not approximated by a finite-order polynomial. Finally, the developed framework is used to validate the effect of time-delays in our previous work.

Event-triggered communication and [formula omitted] control co-design for networked control systems

This paper studies an event-triggered communication scheme and an H∞ control co-design method for networked control systems (NCSs) with communication delay and packet loss. First, an event-triggered communication scheme and a sampled-state-error dependent model for NCSs are presented. In this scheme and model, (a) the sensor takes samples in a periodic manner; (b) a triggering condition is applied to the sampled signal to determine whether a signal is transmitted to the controller or not; and (c) the closed-loop system with a networked state feedback controller is modeled as a time-delay system. Secondly, by constructing a novel Lyapunov–Krasovskii functional, three theorems for the system asymptotical stability subject to imperfect communications are derived. Thirdly, a new algorithm is developed for the triggering condition and the controller feedback gain to meet the specified performance. This design algorithm is based on the two permissible limits on the signal transfer. These limits are: the maximum allowable communication delay bound and the maximum allowable number of successive packet losses, respectively. Finally, the proposed co-design method is demonstrated by two numerical examples.