Optimal Feedback Synthesis based on an Energy Eigenvalue Calculation using Random-Walk Quantum Monte-Carlo Methods

Abstract

Value functions for stationary optimal feedback control have been approximated using eigenfunctions with lowest real part of energy eigenvalues of linear Hamiltonian operators for nonlinear optimal feedback control systems. Random-walk quantum Monte-Carlo method to calculate lowest energy eigenvalues in quantum physics is extened to deal with state dependent diffusion and convection terms that appear in the Hamiltonian operators. After calculation of eigenvalues with the lowest real part, eigenfunctions ϕ0 that correspond to the eigenvalues are represented as vectorial expressions. This is done by working with matrix representations of the Hamiltonian operators. We achieve decreases in calculation time in two respects: avoidance of calculating whole spectrum of eigenvalues and lower dimensionality of the Hamiltonian matrix utilized to find ϕ0. Nonlinear optimal feedback is synthesized using that vectorial form of ϕ0.