6 papers · 1 filter
Nonlinear Feedback Control in High Dimensions using the Polynomial-Polynomial Regulator
Nicholas A. Corbin, Boris Kramer
We consider the problem of computing Taylor approximations to the optimal feedback law and value function for infinite-horizon finite-dimensional nonlinear optimal control problem-…
Nonlinear balanced truncation model reduction through scalable Taylor series
Nicholas A. Corbin, Boris Kramer
The theory of nonlinear balanced truncation provides a system-theoretic framework for model reduction that preserves important properties such as stability, controllability, and ob…
Scalable computation of input-normal/output-diagonal balanced realization for control-affine polynomial systems
Nicholas A. Corbin, Arijit Sarkar, Jacquelien M. A. Scherpen +1
We present a scalable tensor-based approach to computing input-normal/output-diagonal nonlinear balancing transformations for control-affine systems with polynomial nonlinearities.…
Computing Solutions to the Polynomial-Polynomial Regulator Problem
Nicholas A. Corbin, Boris Kramer
We consider the optimal regulation problem for nonlinear control-affine dynamical systems. Whereas the linear-quadratic regulator (LQR) considers optimal control of a linear system…
Scalable Computation of Energy Functions for Polynomial Control-Affine Systems
Nicholas A. Corbin, Boris Kramer
We present a scalable approach to computing nonlinear balancing energy functions for control-affine systems with polynomial nonlinearities. Al'brekht's power-series method is used…
Scalable Computation of Energy Functions for Polynomial Drift Nonlinear Systems
Nicholas A. Corbin, Boris Kramer
This paper presents a scalable tensor-based approach to computing controllability and observability-type energy functions for nonlinear dynamical systems with polynomial drift and…