A structure-preserving Lanczos-type algorithm with application to control problems

A Hamiltonian structure-preserving Lanczos-type method, named the J-Lanczos algorithm, is introduced for solving large sparse Hamiltonian eigenvalues problem which arises in both continuous-time and discrete-time optimal control applications. Shift and invert techniques are incorporated to approximate all stable eigenvalues and the associated invariant subspace. Numerical results for solving high order continuous-time Riccati equation arising from position and velocity control for a string of high speed vehicles are presented.