Fixed-Time-Synchronized Bipartite Time-Varying Formation Tracking Control of Networked Euler-Lagrange Systems

This article solves the fixed-time-synchronized (FTS) bipartite time-varying formation (BTVF) tracking control problem of networked Euler-Lagrange systems (NELSs) with disturbances, where all state elements of the NELSs can achieve BTVF at the same time. An improved hierarchical control strategy is proposed, comprising a distributed estimator layer and a local control layer. The former is responsible for estimating the desired position and velocity, while the latter employs a novel interval observer-based algebraic reconstruction mechanism to compensate for the unknown disturbance. Subsequently, a singularity-free FTS BTVF control protocol is established, leveraging a norm-normalized sign function-based switching sliding mode control technique. This protocol guarantees that, in the presence of a signed antagonistic interaction graph, all system states converge synchronously to equilibrium within a fixed time. Finally, comparisons and simulations are conducted to validate the feasibility, significance, and merits of the developed control scheme. Note to Practitioners—In practical applications, the performance of networked systems depends not only on when the system state converges, but also significantly on when and how each subsystem state element converges. Despite the superior convergence property of fixed-time control, its standalone application proves inadequate in scenarios where all state elements of the network systems are required to reach the desired values synchronously, as observed in coordinated transportation and formation, particularly in the domain of space attack and defense. In this article, the BTVF tracking control issue with FTS convergence of networked systems is studied for the first time. The design of non-singular and FTS coordination schemes is challenging in NELSs. In addition, the developed distributed strategy based on the hierarchical control technique is suitable for NELSs with unknown disturbances and antagonistic interaction graphs, and the use of the norm-normalized sign function-based switching sliding mode control method excludes the singular problem.