Adaptive fixed-time inverse optimal consensus of multi-agent systems with limited-time interval state constraints

Abstract

This article presents a study on fixed-time adaptive fuzzy inverse optimal consensus for multi-agent systems (MASs) subject to limited-time interval state constraints. To handle the constraints that occur within a limited-time interval during the system's operating cycle, we introduce a shifting function to shift the boundary and a state-dependent transformation function to transform the constrained MASs into non-constrained ones. We then propose an adaptive fixed-time inverse optimal consensus controller that achieves the convergence of consensus error within a fixed-time and inverse optimality without directly learning the solution of the Hamilton-Jacobi-Bellman (HJB) equations. To establish the criteria for fixed-time stabilization, we design an auxiliary controller instead of the auxiliary system and introduce two Lyapunov functions to prove the inverse optimality and fixed-time stabilization. The developed consensus scheme ensures that the synchronization error asymptotically converges to a user-predefined region within a fixed settling time. We validate the effectiveness of the developed scheme through a simulation example.