Unimodality of Performance Functions Related to the LQ and the LQG Learning Optimization Problem

1993 Transactions of the Society of Instrument and Control Engineers  
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
more » ... namical output feedback such that the optimized system is equivalent to the optimal LQ (linear-quadratic) or LQG (linear-quadratic-Gaussian) regulator.
doi:10.9746/sicetr1965.29.555 fatcat:emjxnvcavrhmhit2x5ko4u62la