Estimator-Based Reinforcement Learning Consensus Control for Multiagent Systems With Discontinuous Constraints

This article focuses on the optimal consensus control problem for multiagent systems (MASs) with discontinuous constraints. The case of discontinuous constraints is a particular instance of state constraints, which has been studied less but occurs in many practical situations. Due to the discontinuous constraint boundaries, the traditional barrier function-based backstepping methods cannot be used directly. In response to this thorny problem, a novel constraint boundary reconstruction technique is proposed by designing a class of switch-like functions. The technique can convert discontinuous constraint boundaries into continuous ones, and it strictly proves that when the states satisfy the transformed constraint boundaries, the original constraints are also absolutely fulfilled. Meanwhile, with the aid of the barrier function and distributed event-triggered estimator, an improved coordinate transformation is constructed, which can remove the "feasibility condition" and simplify the controller design. In addition, by introducing prediction error and revised term into the learning process of neural networks (NNs), the optimal consensus problem is resolved by constructing a modified reinforcement learning strategy. Finally, the stability of the MASs is testified through the Lyapunov stability theory, and a simulation example verifies the effectiveness of the proposed method.