Abstract
Unimodality of a performance function with respect to adjustable parameters is essential for convergence of algorithm to the global optimal solution in learning optimization problems. We study this problem for the linear time-invariant (stationary) dynamical system with the quadratic cost in signals. The unimodality does not necessarily hold with respect to adjustable gains in feedback part. We establish this unimodality under the case that the adjustable gains construct the state feedback or dynamical output feedback such that the optimized system is equivalent to the optimal LQ (linear-quadratic) or LQG (linear-quadratic-Gaussian) regulator.
