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SummaryThis article investigates the active fault‐tolerant consensus problem for Lipschitz nonlinear multiagent systems under detailed balanced directed graph and actuator faults. First, a fault detection filter for each agent is designed, and all agents can be divided into two categories: healthy agents and possibly faulty agents. Second, fully distributed adaptive fault‐tolerant consensus protocols for healthy and possibly faulty agents are proposed to achieve state consensus. Third, based on the fault detection method and fault‐tolerant consensus protocols, active fault‐tolerant consensus algorithms are given. Simulation examples are presented to verify the effectiveness of the proposed active fault‐tolerant algorithms.

Deoxyribonucleic acid (DNA) is an attractive medium for long-term digital data storage due to its extremely high storage density, low maintenance cost and longevity. However, during the process of synthesis, amplification and sequencing of DNA sequences with homopolymers of large run-length, three different types of errors, namely, insertion, deletion and substitution errors frequently occur. Meanwhile, DNA sequences with large imbalances between GC and AT content exhibit high dropout rates and are prone to errors. These limitations severely hinder the widespread use of DNA-based data storage. In order to reduce and correct these errors in DNA storage, this paper proposes a novel coding schema called DNA-LC, which converts binary sequences into DNA base sequences that satisfy both the GC balance and run-length constraints. Furthermore, our coding mode is able to detect and correct multiple errors with a higher error correction capability than the other methods targeting single error correction within a single strand. The decoding algorithm has been implemented in practice. Simulation results indicate that our proposed coding scheme can offer outstanding error protection to DNA sequences. The source code is freely accessible at https://github.com/XiayangLi2301/DNA.