Gradient Flow Formulation Research Articles

Robust partial pole-placement via gradient flow

This paper provides a computational procedure for the robust partial pole-placement problem. The algorithm is based on a gradient flow formulation on a differentiable potential function which provides a minimizing solution for the Frobenius condition number of the closed-loop state matrix. The algorithm faces no singularity problem with the resulting eigenvector matrix. Convergence properties of the algorithm are discussed. A numerical example is employed to illustrate the technique and comparison to other existing methods is made. © 1977 John Wiley & Sons, Ltd.

Regional pole assignment with eigenstructure robustness

The paper provides a computational procedure for a type of robust regional pole assignment problem. It allows closed-loop poles to be settled at certain perturbation insensitive locations within some prespecified regions in the complex plane. The novelty of our approach lies in the versatility of the proposed algorithm which provides a rick set of constrained subregions applicable for the assignment of individual or subsets of closed-loop poles, in contrast to other conventional regional pole assignment methods. The algorithm is based on a gradient flow formulation on a differentiable potential function which provides a minimizing solution for the Frobenius condition number of the closed-loop eigenvector matrix. A numerical example is employed to illustrate the technique. The improvement on the eigenstructure robustness is compared with different kinds of constrained region.