Finite-time coordination in multiagent systems using sliding mode control approach

Abstract

Finite-time stability in dynamical systems theory involves systems whose trajectories converge to an equilibrium state in finite time. In this paper, we use the notion of finitetime stability to apply it to the problem of coordinated motion in multiagent systems. Specifically, we consider a group of fully actuated agents described by Euler-Lagrange dynamics along with a leader agent with an objective to reach and maintain a desired formation characterized by steady-state distances between the neighboring agents in finite time. We use graph theoretic notions to characterize communication topology in the network determined by the information flow directions and captured by the graph Laplacian matrix. Furthermore, using sliding mode control approach, we design decentralized control inputs for individual agents that use only data from the neighboring agents which directly communicate their state information to the current agent in order to drive the current agent to the desired steady state. Sliding mode control is known to drive the system states to the sliding surface in finite time.The key feature of our approach is in the design of non-smooth sliding surfaces such that, while on the sliding surface, the error states converge to the origin in finite time, thus ensuring finite-time coordination among the agents in the network.

Adaptive practical preassigned finite‐time stability for a class of pure‐feedback systems with full state constraints

“…One of FTC methods is to use the sign function (see other works [17][18][19] ). The terminal sliding mode control is another FTC technique (see other works [20][21][22] ). However, both of them belong to the discontinuous control, which can cause jittering.…”

Multi‐manipulators coordination for bilateral teleoperation system using fixed‐time control approach

“…On one hand, through the analysis of the control scheme, it can be found that the prior TSM suffers from a singularity problem, that is, in some areas of the state space, the TSM control torque may require to be infinity large to maintain the ideal TSM motion . To avoid the singularity problem, a lot of effective methods were proposed, which can be broadly split into two classes, ie, direct method and switching method . For the direct method, the zero velocity states will decelerate and complicate the reaching phase even though they are not attractors.…”

“…7 To avoid the singularity problem, a lot of effective methods were proposed, which can be broadly split into two classes, ie, direct method 21,22 and switching method. [23][24][25][26][27] For the direct method, the zero velocity states will decelerate and complicate the reaching phase even though they are not attractors. Additionally, for the switching method, the system settling time will be extended with the switching motion between the LSM and the TSM.…”

Heterogeneous consensus of higher‐order multi‐agent systems with mismatched uncertainties using sliding mode control

“…Because the dynamics of many mechanical systems can be modeled as double integrators, the MAS with double‐integrator dynamics have gained great attention in recent years . Recently, MAS with general high‐dimensional linear dynamics have attracted much attention of researchers in the control field .…”

“…Traditional sliding mode design methods fail to maintain stabilizations when facing mismatched uncertainties [16][17][18]. 2304 S. MONDAL, R. SU AND L. XIE Because the dynamics of many mechanical systems can be modeled as double integrators, the MAS with double-integrator dynamics have gained great attention in recent years [1,2,9]. Recently, MAS with general high-dimensional linear dynamics have attracted much attention of researchers in the control field [19][20][21][22].…”