Abstract
This paper proposes robust formation control laws for uncertain multiagent systems subjected to an unknown control direction and disturbances under the assumption that information about the reference trajectory is only available to some of the agents. Different from the existing results, the proposed control algorithms can enable the agents to converge to the specified points utilizing only local relative measurements, in which no control direction information and upper bounds of external uncertainties are required. To simplify and facilitate the analysis, external disturbances are roughly divided into structured and unstructured uncertainties. To attenuate the errors caused by the structured uncertainties, an adaptive control technique is applied to obtain the estimates of the unknown constant coefficients, and compensating functions with learning ability are developed to eliminate the errors caused by the unstructured uncertainties. A Nussbaum-type function is employed to settle the formation control problem in the presence of unknown signs of the control direction. Formation stability analysis for uncertain nonlinear multiagent systems is performed according to the Lyapunov stability theory. It is proved that the formation errors are bounded within a small desired accuracy by implementing the proposed robust control laws, and the desired formation is then achieved. Finally, two illustrative examples are presented to support the obtained theoretical results.
Highlights
In recent years, formation control for multiagent systems has received considerable research attention due to its advantageous potential in many practical application areas, such as military and civilian areas [1]–[8]
The desired formation can be achieved by the agents, it can be broken when a multiagent system encounters different kinds of disturbances, such as saturated inputs constrained by actuators, dead-zones, and other nonlinearities
Motivated by the above facts and discussions, in this paper, the robust adaptive formation control laws are proposed for uncertain nonlinear multiagent systems in the presence of unknown control directions and structured and unstructured disturbances
Summary
Formation control for multiagent systems has received considerable research attention due to its advantageous potential in many practical application areas, such as military and civilian areas [1]–[8]. In [43], the time-varying formation robust tracking problems for multiagent systems in the presence of parameter uncertainties and disturbances are studied, by using the adaptive updating scheme, no global knowledge about the information interaction topology and upper bounds of the parameter uncertainties, disturbances, and unknown input of the leader are not required in the proposed control protocol. Motivated by the above facts and discussions, in this paper, the robust adaptive formation control laws are proposed for uncertain nonlinear multiagent systems in the presence of unknown control directions and structured and unstructured disturbances. In denotes the n×n matrix, 1n is a vector in which each entry is 1; and X ⊗Y represents the Kronecker product of any given matrices X and Y
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