Distributed Continuous-Time Optimization With Uncertain Time-Varying Quadratic Cost Functions
研究了参数不确定的时变二次成本函数的分布式连续时间优化问题，提出了集中式和分布式自适应算法，并证明了全局收敛性。
This article studies distributed continuous-time optimization for time-varying quadratic cost functions with uncertain parameters. We first propose a centralized adaptive optimization algorithm using partial information of the cost function. It can be seen that even if there are uncertain parameters in the cost function, exact optimization can still be achieved. To solve this problem in a distributed manner when different local cost functions have identical Hessians, we propose a novel distributed algorithm that cascades the fixed-time average estimator and the distributed optimizer. We remove the requirement for the upper bounds of certain complex functions by integrating state-based gains in the proposed design. We further extend this result to address the distributed optimization where the time-varying cost functions have nonidentical Hessians. We prove the convergence of all the proposed algorithms in the global sense. Numerical examples verify the proposed algorithms.