  For various typical cases and situations where the formulation results in an
optimal control problem, the Linear Quadratic Regulator (LQR) approach and its
variants continue to be highly attractive. In certain scenarios, it can happen
that some prescribed structural constraints on the gain matrix would arise.
Consequently then, the Algebraic Riccati Equation (ARE) is no longer applicable
in a straightforward way to obtain the optimal solution. This work presents a
rather effective alternative optimization approach based on gradient
projection. The utilized gradient is obtained through a data-driven
methodology, and then projected onto applicable constrained hyperplanes.
Essentially, this projection gradient determines a direction of progression and
computation for the gain matrix update with a decreasing functional cost; and
then the gain matrix is further refined in an iterative framework. With this
formulation, a data-driven optimization algorithm is summarized for controller
synthesis with structural constraints. This data-driven approach has the key
advantage that it avoids the necessity of precise modeling which is always
required in the classical model-based counterpart; and thus the approach can
additionally accommodate various model uncertainties. Illustrative examples are
also provided in the work to validate the theoretical results.
