Distributed Continuous-Time Algorithms for Time-Varying Constrained Convex Optimization
Distributed Continuous-Time Algorithms for Time-Varying Constrained Convex Optimization
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DOI：
10.1109/tac.2022.3198113
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发表时间：
2023-07
影响因子：
6.8
通讯作者：
Shan Sun;J. Xu;W. Ren
中科院分区：
文献类型：
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作者：
Shan Sun;J. Xu;W. Ren
本文研究具有时变目标函数和时变约束的分布式连续时间优化问题。与大多数研究的具有时不变目标函数和约束的分布式优化问题不同，本文的最优解是时变的，并且形成一个轨迹。首先，对于只存在时变的非线性不等式约束的情况，我们提出了一种分布式控制算法，该算法由滑模一致性部分和基于海森优化部分的对数障碍罚函数耦合而成。该算法能够保证最优解的渐近跟踪，且跟踪误差为零。其次，我们将以前的结果推广到既有时变的非线性不等式约束又有线性等式约束的情况。提出了一种扩展算法，引入二次罚函数来考虑等式约束，并设计了自适应控制增益来消除对已知某些信息的上界的限制。在适当的假设条件下，研究了扩展算法在最优解附近的渐近收敛性质。仿真结果表明了所提算法的有效性。此外，将提出的算法应用于多机器人多目标导航问题，并在多机器人平台上进行了实验演示，验证了理论结果。
This article is devoted to the distributed continuous-time optimization problems with time-varying objective functions and time-varying constraints. Different from most studied distributed optimization problems with time-invariant objective functions and constraints, the optimal solutions in this article are time varying and form a trajectory. First, for the case where there exist only time-varying nonlinear inequality constraints, we present a distributed control algorithm that consists of a sliding-mode consensus part and a Hessian-based optimization part coupled with the log-barrier penalty functions. The algorithm can guarantee the asymptotical tracking of the optimal solution with a zero tracking error. Second, we extend the previous result to the case where there exist not only time-varying nonlinear inequality constraints but also linear equality constraints. An extended algorithm is presented, where quadratic penalty functions are introduced to account for the equality constraints and an adaptive control gain is designed to remove the restriction on knowing the upper bounds on certain information. The asymptotical convergence of the extended algorithm to the vicinity of the optimal solution is studied under suitable assumptions. The effectiveness of the proposed algorithms is illustrated in simulation. In addition, one proposed algorithm is applied to a multirobot multitarget navigation problem with experimental demonstration on a multicrazyflie platform to validate the theoretical results.