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.

中文翻译：

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使用基于约束神经优化器的滑模控制的多智能体系统的共识跟踪

在本文中，提出了一种基于投影循环神经网络（PRNN）的最优滑模控制（SMC）技术来解决机器人多智能体系统的跟踪一致性问题。基于领导者和代理之间的连接拓扑以及系统的相对程度，滑动面是根据误差信号定义的。然后，定义性能指标以实现指数到达律和最小控制工作量。通过考虑致动器的限制，可以推导出受约束的二次规划 (QP) 问题。QP 的解是使用 PRNN 计算的，它是基于变分不等式 (VI) 问题开发的。PRNN 的结构由动态方程和代数方程组成，其中投影算子充当激活函数。PRNN 作为数值优化器的收敛分析已使用李雅普诺夫定理进行。此外，推导出了保证闭环系统鲁棒稳定性的充分条件。已通过将其应用于机器人多智能体系统来研究所提出算法的性能，并与自适应反步 SMC 进行了比较。