  In this paper, we propose a model-free feedback solution method to solve
generic constrained optimization problems, without knowing the specific
formulations of the objective and constraint functions. This solution method is
termed projected primal-dual zeroth-order dynamics (P-PDZD) and is developed
based on projected primal-dual gradient dynamics and extremum seeking control.
In particular, the P-PDZD method can be interpreted as a model-free controller
that autonomously drives an unknown system to the solution of the optimization
problem using only output feedback. The P-PDZD can properly handle both the
hard and asymptotic constraints, and we develop the decentralized version of
P-PDZD when applied to multi-agent systems. Moreover, we prove that the P-PDZD
achieves semi-global practical asymptotic stability and structural robustness.
We then apply the decentralized P-PDZD to the optimal voltage control problem
in power distribution systems with square probing signals, and the simulation
results verified the optimality, robustness, and adaptivity of the P-PDZD
method.
