Event-triggered fault-tolerant optimal coordination for multiple Euler-Lagrange systems with semi-Markov jumping networks

This article explores a distributed optimal coordination control problem for multiple Euler-Lagrange systems with actuator faults. To address this problem, an event-triggered fault-tolerant optimisation algorithm is first proposed to eliminate unexpected faults and reduce the consumption of control resources. In order to further enhance the system's reliability, another algorithm based on the Nussbaum function is proposed to handle faulted systems with uncertain control directions. Note that an auxiliary system with adaptive gains is introduced to eliminate the need for agents to interact with their actual state information, and thus has the effect of protecting privacy. Moreover, the stochastic semi-Markov jumping networks are considered in the algorithms to describe the switching process of uncertain communication graphs. Additionally, the algorithms are fully distributed since it does not require global information of topologies. Finally, numerical simulations are conducted in the article to verify the effectiveness of the proposed algorithms.