  This paper 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.
