Neural network-based adaptive fault tolerant consensus control for a class of high order multiagent systems with input quantization and time-varying parameters

Abstract

This paper studies the adaptive leader-following consensus control for a class of strict-feedback multi-agent systems. All the agents possess the quantized inputs, the time-varying unknown parameters and the actuator failures. By estimating the upper bounds of the induced uncertainties, the obstacles caused by discontinuous input quantization can be circumvented. Meanwhile, several distributed adaptive laws are established such that the coupled uncertainties caused by the actuator faults and the time-varying unknown parameters can be handled. Since the desired trajectory is only partly known, an adaptive compensating term is introduced in the control structure. Moreover, to deal with the completely unknown nonlinear functions, radial basis function neural networks (RBFNNs) are introduced for approximation and compensation. It is shown that the output consensus can be achieved and the boundedness of all the signals can be guaranteed. Finally, we show the efficacy of our theoretical results using a numerical example.

Introduction

In practice, the quantized signals are inevitable and useful in many engineering systems such as digital control systems, hybrid systems and networked control systems [1], [2], [3]. The signal quantization, which are commonly regarded as a map from continuous signals to discrete finite sets, has received much attention in the past decades [4], [5]. Recently, to deal with the uncertainties and disturbances in the quantized control systems, several robust control schemes have been investigated [6], [7], [8]. Most recently, by introducing the backstepping technique, an adaptive quantized control scheme has been developed for a class of high order strict-feedback nonlinear systems [9]. Furthermore, to relax the restrictive constraints for the nonlinear functions and the quantization parameters in [9], an adaptive asymptotic tracking controller have been proposed [10].

On the other hand, there has been a surge of interest among researchers in the consensus and synchronization of multiagent systems recently [11], [12], [13], [14], [15], [16], [17], [18]. In the past decades, many excellent consensus control approaches have been investigated. Aiming at the multiagent systems with fixed or switching network topologies, the consensus and synchronization problems have been investigated in [19], [20]. To deal with the nonlinear protocols in the multiagent systems, two consensus control schemes have been proposed in [21], [22]. Meanwhile, the synchronization methods have also been proposed for heterogeneous multi-agent systems [23], [24], [25] and network systems with dynamic edges [26]. As further development, the higher-order multiagent systems have been investigated in [16], [27]. Unfortunately, the match conditions are necessary in [16], [27]. To overcome the limitations, an anti-disturbance output consensus algorithm is developed for higher-order multi-agent systems with mismatched disturbances [28]. Additionally, based on the well-known backstepping control technique, two distributed adaptive control protocols were established for the strict-feedback multiagent systems with linearly parameterized uncertainties [29], [30].

In spite of the progress, the quantized inputs have never been investigated in the aforementioned consensus controllers for the multiagent systems. When the input signals are quantized, the concerned multi-agent system becomes a hybrid system and most of the existing consensus schemes are hard to be applied. Because of the discontinuous characteristics of the quantized input signals, the consensus controller design becomes challenging and interesting. Moreover, in the existing consensus control works, the unknown parameters are required to be constants. Obviously, for the multiagent systems with time-varying unknown parameters, which are encountered more often in practice, these consensus schemes cannot achieve desired performances anymore. Since it is difficult to estimate the unknown parameters which vary with time, a novel adaptive consensus controller have to be developed. Furthermore, the actuator failures are inevitable in many practical control systems. They are one of the factors that largely degrade the control performances [31], [32], [33], [34], [35], [36] and have to be taken into consideration. In a word, it is of theoretical and practical significance to consider the quantized inputs, the time-varying parameters and the actuator failures simultaneously in the consensus control design for the multiagent systems.

Motivated by the aforementioned observations, this paper focuses on the distributed adaptive control design for a class of strict-feedback multiagent systems with quantized input signals, time-varying unknown parameters and actuator faults. The main difficulty arises from the intrinsic discontinuous characteristics of the quantized inputs, the time-varying features of the unknown parameters and the changing actuator failures. Compared with the existing literature, the following contributions are worth to be emphasized:

• To the best of the author’s knowledge, it is the first solution for the leader-following consensus control of a class of strict-feedback multi-agent systems with input quantization, time-varying unknown parameters, mismatched disturbances and actuator faults [29], [30].

• Compared with [10], the results have been extended to the multi-agent systems and the time-varying systems. Moreover, the agents are allowed to have nonidentical dynamics and the desired trajectory y_r is only known by part of the agents.

• In contrast with the existing results [6], [7], [8], [9], the global Lipschitz continuity condition and the bounds, which are commonly required in the quantized control systems, are not required anymore.

The remainder of the paper is organized as follows. Section 2 begins with the problem formulation, some useful definitions and lemmas. In Section 3, the distributed adaptive consensus control scheme and the stability analysis are presented. Numerical simulations are then performed in Section 4, for verifying the effectiveness of the proposed control approach. Throughout this paper, the notations are defined as follows: ${\mathbb{R}}^n$ denotes the real n-dimensional space, while ${\mathbb{R}}^{m\times n}$ denotes the space of m × n matrices with real entries. For a given matrix A , A^T denotes its transpose. The Euclidean norm is denoted by ‖·‖.