Efficient construction of dynamic precompensators for dynamic feedback linearization

Develop a computationally efficient constructive procedure to compute the dynamic precompensator that renders a given nonlinear control system dynamically feedback linearizable, going beyond existence conditions to provide a practical method for finding the required precompensator whenever one exists.

Background

Dynamic feedback linearization extends static feedback linearization by allowing dynamic precompensation to render nonlinear control systems feedback linearizable. While necessary and sufficient conditions for dynamic feedback linearizability are known, notably following Guay, McLellan, and Bacon (1997), the practical, efficient computation of the needed dynamic precompensator remains a challenge.

This paper frames the search for minimal dynamic extensions as a category-theoretic optimization problem and proposes dynamic programming and heuristic-guided search as a means to navigate the space of extensions. The open problem underscores the need for an efficient, constructive algorithm to actually compute the precompensator in general settings.