Event-triggered formation control of AUVs with fixed-time RBF disturbance observer

Abstract

Aiming at the problem of model parameter uncertainty, unknown current disturbance and actuator input saturation of multi-AUVs formation control, an event-triggered formation strategy based on fixed-time Radial Basis Function(RBF) neural network adaptive disturbance observer is proposed, which can ensure formation control converge in fixed time. First of all, fixed time RBF disturbance observer (FRBFDO) is put forward to estimate lumped disturbance accurately. Based on the FRBFDO, with the combination of command filter and the back-stepping method, which is used to eliminate repeated derivation calculation explosion problem; Secondly, in order to save the energy consumption of network transmission resources, the event trigger mechanism is introduced into the multi-AUVs formation control. The fixed-time distributed formation controller is designed to realize the fixed-time stability of formation system, and the system convergence time is independent of the initial state. Finally, the effectiveness and rationality of the proposed algorithm are proved by the multi-AUVs formation simulation experiment.

Introduction

The development and utilization of marine resources are important means for each country to complete strategic resources. Autonomous Underwater Vehicle (AUV) is an auxiliary intelligent tool for marine exploration. It plays an important role in civil and military fields such as resource exploration, marine environment monitoring, military reconnaissance, marine defense and so on (Wang et al., 2019; Braginsky et al., 2020; Yang et al., 2019). Due to the complex operating environment and the continuous expansion of operating range, the changes of meteorological conditions, the different operation sea areas and the increasing complexity of operating tasks requirements, it is necessary to cooperate with multiple AUVs to improve the work efficiency and achieve the performance and indicators required by the work. To achieve the performance and index required by the operation, the multi-AUVs system coordinates and cooperates, involving many factors such as architecture, components, communication and so on. By establishing formation cooperative detection mechanism among multi-AUVs that meet the requirements, the function defects of single AUVs can be overcome and the underwater operation can be improved in high quality and efficiency. Therefore, higher requirements are put forward for the consistency and formation control of multi-AUVs (J. Li et al., 2019). The virtual leader-follower formation method has become one of the most widely used strategies in formation control due to its advantages of simple control and low difficulty in realizing formation structure (Gao and Guo, 2019).

In traditional engineering applications, multi-agents usually adopt fixed sampling time, however, periodic state information collection, update of control input, communication between neighbors and other operations, which results in unnecessary resource consumption. Event-triggered strategy is effective and well-researched tool that focus on reduce the communication burden while ensuring satisfactory system performance (Xing et al., 2019). Event triggered control, triggering only depends on the designed event triggering condition, which is often related to the system state. Such a process can guarantee the control performance as well as it can reduce the computational load and communication pressure, which is popular in some practical problem (C. Wang et al., 2020). The main communication mode of AUVs system is underwater acoustic communication. Communication network is limited by limited bandwidth and communication resources. Previous research on formation control is based on cycle triggering time sampling. Continuous communication will not only lead to network congestion, but also bring to a large amount of energy consumption. In order to effectively utilize communication resources and reduce system energy consumption, it is an effective control method to reduce resource consumption in the underwater vehicle formation transmission network by suppressing the number of updates of controllers and reducing the frequency of information transmission between individuals and neighbors. Therefore, the control strategy based on event triggering mechanism is highly valuable. Xing et al. (Xing et al., 2017) proposed a distributed event triggering consistency protocol for linear multi-agent system with external interference. Hua et al. (Hua et al., 2018) studied the dynamic output feedback adaptive fuzzy decentralized control of a class of interrelated stochastic non-linear systems based on event triggering. Viel et al. (Viel et al., 2019) discussed the formation control and tracking of an Eulerian-Lagrange multi-agent system, and used event triggering mechanism to reduce the number of communication among agents, which reduced energy consumption to some extent.

AUV system model has strong non-linearity, coupling, complexity and other non-linear dynamics problems, as well as model parameter perturbation and external complex working environment, which bring challenges to multi-AUVs formation control. In particular, interference suppression and control input saturation are the key issues to be considered in the design of AUV control system. In order to deal with the uncertainty of model parameters and external ocean current interference and enhance the anti-interference performance of the system, the advanced control theory technologies such as adaptive control technology, neural network algorithm, fuzzy adaptive algorithm, and observer technology have attracted the attention of scholars. In literature (Peng et al., 2011; J.Q. Wang et al., 2020), adaptive neural network technology has been proposed to deal with the external disturbances of autonomous surface ship formation control system. To ensure that the system signals were uniformly and eventually bounded, Wu et al. (Wu et al., 2015) proposed a fuzzy adaptive technology to deal with external disturbances. Moreover, disturbance observer is a key technology for reconstructing external uncertain information. Cui et al. (Cui et al., 2017) designed an extended state observer to obtain system state information and external disturbances. Observers designed in Literature (Hu et al., 2015) can only ensure that the observed errors converge to the defined region, and obtain a uniformly bounded observation effect. In order to obtain a faster convergence rate and anti-interference ability, Huang et al. (Huang et al., 2019) designed a time-limited convergence observer to achieve accurate estimation of parameter uncertainties and ocean disturbances, thus obtaining global finite-time stable tracking performance. Although disturbances can be accurately estimated by a finite-time observer, however, its convergence time depends heavily on the initial observation error, which limits the feasibility of application. In addition, actuator saturation is one of the most important problems in formation control systems. The saturation of the controller will affect the system performance and cause degradation, and even threaten the stability of the control system. The problem of actuator saturation in AUV control system has been verified in literatures (Fu et al., 2017; Zhou et al., 2020). Fu et al. (Fu et al., 2017) addressed the saturation constraint problem of autonomous surface ship formation control with model uncertainty and external disturbance. An adaptive robust method based on sliding mode control with a nonlinear disturbance observer has been presented, and input constraints of the system have been damped through a dynamic auxiliary compensator in literature (Zhou et al., 2020). It is of great practical significance to solve the problem of saturation input and external disturbance at the same time to realize the AUV formation control performance better.

On the other hand, fast convergence of multi-AUVs formation is an important performance index of control system. In the past, most AUVs formation control systems were asymmetrically stable (J. Li et al., 2019), or limited-time stable (Li et al., 2018; Wang et al., 2017). This means that the convergence time of the system increases infinitely with the increase of initial value, which greatly weakens the system's convergence performance. It is difficult to know the initial value of state information in practical engineering. Fixed-time control theory (Polyakov, 2012) is developed on the basis of finite-time algorithm. It not only improves the convergence speed of the system, but also depends on the design parameters of the controller. It overcomes the slack to the initial state of the system. For systems with strict convergence time, the controller design based on fixed-time theory is more suitable for practical application. In recent years, fixed-time theory has achieved some research results in the fields of multi-agent consistency (Zuo, 2015), power system (Ni et al., 2016), and remote operated robot arm (Li et al., 2017). In this paper, a control algorithm which combines fixed-time theory with event triggering mechanism is proposed and studied under the background of underwater vehicle. Finally, fixed time convergence for formation control of multi-AUVs system is achieved.

This paper proposes a control algorithm based on the integration of fixed-time RBF neural network disturbance observer (FRBFDO) and event triggering strategy for multi-AUVs formation control with model parameter perturbation, external current disturbance, and actuator saturation. The formation controller is designed based on event triggering strategy, which not only achieves fixed-time bounded convergence of the system, but also makes the convergence time is not rely on the initial state. Meanwhile, the presented method which not only accelerates the convergence speed of the system, but also improves the utilization ratio of limited communication network resources, and saves the communication energy of the system, by reducing the trigger frequency and communication times of the controller. At the same time, it proves theoretically that the event triggering mechanism has no Zeno behavior, so as to ensure the rationality of the controller design. Finally, the feasibility of the algorithm is verified by simulation of multiple AUVs. The main innovations of this paper are as follows:

• Taking the uncertainty parameters of system model, external disturbance, and actuator saturation nonlinear item as lumped disturbance, based on fixed-time theory and Radial Basis Function (RBF) neural network adaptive algorithm, novel adaptive RBF disturbance observer with fixed-time convergence is constructed to accurately estimate the lumped disturbances. The designed observer is practical stable in a fixed time, and the maximum convergence time only depends on the system design parameters and is independent of the initial value of system state.

• Combining with back-stepping algorithm, command filtering technology, and undirected topology with leader-follower strategy, distributed event triggering fixed-time controller with anti-saturation ability are applied for multi-AUVs formation control research, and the closed-loop system is ensured fixed time stability. The overall control system performance and robustness of the formation tracking are effectively increased.

The content structure of this paper is arranged as follows: Section 2 gives the description of the problem; Section 3 lists the main results of this paper; Section 4 shows the description and results of simulation experiments; Section 5 summarizes the whole paper.