Consensus tracking of multi-agent systems using constrained neural-optimiser-based sliding mode control

Abstract

In this paper, an optimal Sliding-Mode Control (SMC) technique based on Projection Recurrent Neural Network (PRNN) is proposed to solve the tracking consensus for the robotic multi-agent system. Based on a connection topology between the leader and agents and relative degree of the system, the sliding surfaces are defined in terms of the error signals. Then, a performance index is defined to realise the exponential reaching law and minimum control effort. By considering the actuator limits, a constrained Quadratic Programming (QP) problem is derived. The solution of the QP is calculated using PRNN, which is developed based on Variational Inequality (VI) problem. The structure of PRNN is composed of a dynamic and an algebraic equation, in which a projection operator acts as an activation function. The convergence analysis of PRNN as a numerical optimiser has been performed using Lyapunov theorem. Moreover, the sufficient conditions are derived for ensuring the robust stability of the closed-loop system. The performance of the proposed algorithm has been investigated by applying it to a robotic multi-agent system and has been compared with an adaptive backstepping SMC.