Fixed-Time Distributed Consensus Optimization Control of High-Order Nonlinear Multi-Agent Systems via a Penalty-Function-Based Method

This paper studies the distributed optimization problem of high-order multi-agent systems with unknown nonlinear terms and input saturation. Unlike existing results, nonlinear functions in the considered system are not required to satisfy the Lipschitz linear growth condition. Moreover, a more general convexity condition is provided for certain local functions, relaxing the traditional strong convexity condition. In addition, the contradiction issue between input saturation and the requirement of a large initial input in existing fixed-time control schemes is handled by constructing an appropriate auxiliary system. In the paper, to begin with, the original optimization problem is transformed into an unconstrained optimization one by constructing a quadratic penalty function. Furthermore, by resorting to fuzzy logic systems with adaptive technique, nonlinear functions in systems are dealt with. And, by the back-stepping method, a distributed fixed-time optimization control strategy based on a penalty function is developed. The proposed controllers can ensure the achievement of the output consensus and the expected optimization objective within a fixed time. Finally, stability analysis and simulation examples are provided to illustrate the effectiveness of the proposed control scheme.