Neural-Network-Based Collaborative Control for Continuous Unknown Nonlinear Systems

S.-N. Gao ,Xin Wang

doi:10.1155/2021/5535971

Abstract

This paper proposes an NN-based cooperative control scheme for a type of continuous nonlinear system. The model studied in this paper is designed as an interconnection topology, and the main consideration is the connection mode of the undirected graph. In order to ensure the online sharing of learning knowledge, this paper proposes a novel weight update scheme. In the proposed update scheme, the weights of the neural network are discrete, and these discrete weights can gradually approach the optimal value through cooperative learning, thereby realizing the control of the unknown nonlinear system. Through the trained neural network, it is proved if the interconnection topology is undirected and connected, the state of the unknown nonlinear system can converge to the target trajectory after a finite time, and the error of the system can converge to a small neighbourhood around the origin. It is also guaranteed that all closed-loop signals in the system are bounded. A simulation example is provided to more intuitively prove the effectiveness of the proposed distributed cooperative learning control scheme at the end of the article.

Highlights

A cooperative learning scheme is often mentioned in neural network-based control systems. is is because cooperative learning can divide the task into several parts, which can be distributed to multiple agents, and the learning efficiency can be improved through the communication between the agents [26]
Benefiting from previous research, this paper proposes an adaptive cooperative control scheme for continuous unknown nonlinear systems based on the radial basis function neural network
Inspired by consensus theory and deterministic learning theory, this paper proposes a distributed adaptive learning control scheme for a kind of unknown nonlinear systems

Summary

Preliminaries

In system (2), if there is a uniform and local exponentially stable equilibrium point when x 0, there are two positive definite constantsc, c2, and the following condition is meet when r > 0:. By proving the cooperative PE condition, we can use the following lemma to analyse the stability. We use Lemma 1 to prove that a conventional system is uniformly exponentially stable under the condition of PE. Where Wτ represents the subvector of the weight matrix in the neural network, Sτ denotes the activation function vector in RBF NNs, and ετ means the estimation error of the neural network. In order to analyse the stability of this neural network, we need to prove that Sτ meets the PE condition; the following lemma can be used to prove this requirement. If a trajectoryQ(t) is periodic or periodic-like, Q(t) is a continuous graph and its derivative is bounded in Ω. en, for the localized RBF NN S(Q)TW whose centre is in a space that can contain Ω, the regression vectors Sτ(Q(t)) defined in (9) of this neural network almost all meet the PE condition

Cooperative Adaptive Control of a Nonlinear System

Nε2 2b

Simulation

Conclusions