This paper reviews and provides perspectives on the design of nonlinear model predictive
control systems for polynomial systems. General nonlinear systems can often be rewritten …

Numerical algebraic geometry provides tools for approximating solutions of polynomial
systems. One such tool is the parameter homotopy, which can be an extremely efficient …

A MATLAB interface to the numerical homotopy continuation package Bertini is described.
Bertini solves systems of polynomial equations. BertiniLab can be used to create input files …

This study introduces an approach to obtain a neighboring extremal optimal control (NEOC)
solution for a closed-loop optimal control problem, applicable to a wide array of nonlinear …

In this paper we investigate how the equilibrium characteristics of conventional power
systems may change with an increase in wind penetration. We first derive a …

Phylogenetic models admit polynomial parametrization maps in terms of the root distribution
and transition probabilities along the edges of the phylogenetic tree. For symmetric …

In this technical note, a method of solving finite-horizon optimal control problems involving
discrete-time rational systems is proposed. Sequences of algebraic equations for the control …

Homotopy methods are attractive due to their capability of solving difficult optimisation and
optimal control problems. The underlying idea is to construct a homotopy, which may be …

This paper presents a new approach to trajectory optimization for nonlinear systems. The
method exploits homotopy between a linear system and a nonlinear system and …

Homotopy methods are attractive due to their capability of solving difficult optimisation and
optimal control problems. The underlying idea is to construct a homotopy, which may be …