Observer-based adaptive fuzzy output constrained control for uncertain nonlinear multi-agent systems☆
Introduction
Consensus is one of the basic problems in the cooperative control of multi-agent systems (MASs), which contains multiple followers and one leader. There exists an active leader or a virtual leader, who only provides command to a small portion of the followers. Its aim is to make all followers track the trajectory of the leader successfully. During the past few years, several consensus control schemes have been proposed [3,6,8,10,14,33,35] for MASs. Among them, the consensus control methods require the system functions either known or parameterized, that is, the unknown parameters appear linearly with respect to the unknown nonlinear functions.
However, the presented results in [3,6,8,10,14,33,35] are invalid when the controlled systems contain uncertain nonlinear functions. To eliminate this restriction, neural networks (NNs) and FLS because of good approximation capability have been combined with distributed adaptive backstepping controller for nonlinear strict-feedback MASs with uncertainties. Adaptive fuzzy/NNs control schemes were proposed [25,27,28] for nonlinear systems, whose unknown dynamics are nonlinear functions. A distributed adaptive NNs control scheme was proposed [8] for uncertain nonlinear MASs. The literature [7] presented a fuzzy adaptive consensus control method for uncertain controlled systems, in which the considered nonlinear functions have unknown dynamics. Peng and Wang [16] were concerned with distributed maneuvering of multiple autonomous surface vehicles. Peng et al. [17] developed an output feedback path-following control scheme such that under-actuated autonomous underwater vehicles moving in a vertical plane without employing surge, heave, and pitch velocities. The author in [32] proposed a distributed adaptive NNs consensus control approach for unknown nonlinear MASs in strict-feedback form. [22], [26], [34] presented adaptive fuzzy/NNs control methods, which not only can make tracking errors converge to be a neighborhood of the origin, but also can determine the exact size of tracking errors. Adaptive fuzzy consensus control approaches were presented for uncertain nonlinear systems having initial-state learning [11] and input saturation [31]. Adaptive NNs schemes were proposed [5,18] for uncertain nonlinear MASs. The adaptive NNs control strategies were presented for uncertain nonlinear MASs having state time-delay [2] and unknown dynamic [1]. Shen et al. [20] studied the problem of output constraint for uncertain nonlinear MASs, in which an adaptive fuzzy control scheme was presented to address the problem of actuator faults. Wang et al. [30] developed a fuzzy adaptive output feedback control method for uncertain nonlinear systems.
Apparently, all proposed schemes in above literatures [1–[3], [5]–8,10,11,14,18,20,21,24–28,30,31–35] did not consider the problem of output constraint, which is commonly exists in the real world, such as electrostatic micro actuators, robotic systems, thruster assisted position mooring systems, the temperature of chemical reactor, physical stoppages, flexible marine riser and crane systems. It is well known, the design of BLF can effectively solve output constraint problem. Hence, [4,9,12,13,15,19,22,23,29] proposed several adaptive fuzzy and NNs control schemes for uncertain nonlinear systems with output constraint. However, the proposed control schemes in [4,9,12,13,15,19,22,23,29] were not for uncertain nonlinear MASs. To the best of our knowledge, until now, no results on adaptive NNs or fuzzy consensus control are developed for uncertain nonlinear MASs with output constraint and unmeasured states. Therefore, adaptive fuzzy control problem of uncertain nonlinear MASs needs to be further studied.
Motivated by the aforementioned observations, the output constraint problems are investigated in this paper for uncertain nonlinear MASs. In control design, FLSs are applied to approximate the unknown nonlinear functions and the fuzzy state observer is constructed. BLF is utilized to handle with the problem of output constraint. Combining adaptive backstepping design with DSC, a distributed observer-based fuzzy adaptive control strategy is presented, which can avoid “explosion of complexity”. The major contributions can be described in two aspects: (1) In [13,29], BLF is used to solve the problem of output constraint for general nonlinear systems. However, in this paper, the design of BLF is firstly used to deal with output constraint problem for uncertain nonlinear MASs with unmeasured states. 2) By designing a fuzzy state observer, the observer-based fuzzy adaptive control scheme can remove the limitation of the measurable states required by previous literatures [11,21,32].
The rest of this paper is organized as follows. The problem formulation and preliminaries are shown in Section 2. Section 3 gives the fuzzy state observer design. In Section 4, the distributed consensus controller design and stability analysis are given. The simulation example is demonstrated to show the effectiveness of the approach in Section 5. Finally, the conclusion is drawn in Section 6.
Section snippets
Problem formulations
Consider the following a class of uncertain nonlinear MASs, which are made up of one leader and N follower agents. The dynamics of the ith follower can be expressed as where is the state vector and is unknown nonlinear function. ui and yi ∈ R denote control input and control output of system (1), respectively. It is assumed that the only measurable variable is .
Control objective: This
Fuzzy state observer design
Since the states in system (1) can not be measured directly, fuzzy state observer needs to be constructed for estimating the unmeasurable states. Rewritten (1) as follows where
The vector Ki is chosen such that Ai is a strict Hurwitz matrix. Thus, for any matrix , and satisfies where Pi > 0 denotes the definite
Distributed consensus controller design and stability analysis
The distributed fuzzy adaptive control method will be developed in this part by backstepping DSC technique. Firstly, define coordinates transformation as follows:where si, 1 means the tracking error, si, l is the error surface, ωi, l represents error between αi, l and . αi, l is intermediate control function and is a newly introduced state variable, which can be obtained by first-order filter.
Step 1: According
Simulation example
In this part, the simulation example is provided to depict the effectiveness of the presented fuzzy adaptive control approach. Considering the following nonlinear multi-agent systems, which contain a leader and four followers (see Fig. 2). where ,,,,,,
Conclusion
In this paper, a consensus adaptive fuzzy control scheme has been proposed for uncertain nonlinear MASs with output constraint. FLSs and BLF are utilized to approximate unknown nonlinear functions and address the problem of output constraint, respectively. Moreover, the presented control method does not require the states of the uncertain nonlinear controlled systems to be measured directly. It has demonstrated that the presented control strategy not only can achieves semi-globally uniformly
References (35)
- et al.
Observer-based adaptive fuzzy output constrained control for MIMO nonlinear systems with unknown control directions
Fuzzy Sets Syst.
(2016) - et al.
Consensus of nonlinear multi-agent systems with observer-based protocols
Syst. Control Lett.
(2014) - et al.
Tracking control for multi-agent consensus with an active leader and variable topology
Automatica
(2006) - et al.
Adaptive fuzzy iterative learning control with initial-state learning for coordination control of leader-following multi-agent systems
Fuzzy Sets Syst.
(2014) - et al.
Adaptive control-based Barrier Lyapunov Functions for a class of stochastic nonlinear systems with full state constraints
Automatica
(2018) - et al.
Consensus for multi-agent systems with inherent nonlinear dynamics under directed topologies
Syst. Control Lett.
(2013) - et al.
Distributed command filtered backstepping consensus tracking control of nonlinear multiple-agent systems in strict-feedback form
Automatica
(2015) - et al.
Control of nonlinear systems with time-varying output constraints
Automatica
(2011) - et al.
Global adaptive neural control for strict-feedback time-delay systems with predefined output accuracy
Inf. Sci.
(2015) - et al.
Practical adaptive fuzzy tracking control for a class of perturbed nonlinear systems with backlash nonlinearity
Inf. Sci.
(2017)
Adaptive fuzzy control for full states constrained systems with nonstrict-feedback form and unknown nonlinear dead zone
Inf. Sci.
Decentralized adaptive neural approximated inverse control for a class of large-scale nonlinear hysteretic systems with time delays
IEEE Trans. Syst. Man Cybern. Syst.
Neural-network-based adaptive leader-following control for multi-agent systems with uncertainties
IEEE Trans. Neural Netw.
Adaptive consensus control for a class of nonlinear multi-agent time-delay systems using neural networks
IEEE Trans. Neural Netw. Learn. Syst.
Information flow and cooperative control of vehicle formations
IEEE Trans. Autom. Control
Decentralized robust adaptive control for the multi-agent system consensus problem using neural networks
IEEE Trans. Syst. Man Cybern. Part B (Cybernetics)
Distributed backstepping-based adaptive fuzzy control of multiple high-order nonlinear dynamics
Nonlinear Dyn.
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