8 papers
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…
Reachability Analysis for Design Optimization
Steven Nguyen, Jorge Cortés, Boris Kramer
We present an approach to approximate reachable sets for linear systems with bounded L-infinity controls in finite time. Our first approach investigates the boundaries of these set…
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…
An approximate control variates approach to multifidelity distribution estimation
Ruijian Han, Boris Kramer, Dongjin Lee +2
Forward simulation-based uncertainty quantification that studies the distribution of quantities of interest (QoI) is a crucial component for computationally robust engineering desi…