A Collocation-Based Approach to Solve the Finite Horizon Hamilton-Jacobi-Bellman Equation Conference Paper

abstract

• This paper presents an approach to derive the optimal feedback control laws by solving the finite time Hamilton Jacobi Ballman equation. Conventional methods to solve the HJB equation suffer from curse of dimensionality as the number of spatial variables is equal to the state dimension, which is twice the number of degrees of freedom of a mechanical system. The presented approach exploits the recently developed non-product quadrature method known as Conjugate Unscented Transformation (CUT) in conjunction with sparse approximation tools to devise a collocation method to solve the HJB equation in a computationally efficient manner. Numerical simulation results are presented to assess the efficacy of the proposed ideas.

name of conference

• 2016 American Control Conference (ACC)

authors

• Majji, Manoranjan

published proceedings

• 2016 AMERICAN CONTROL CONFERENCE (ACC)

author list (cited authors)

• Mercurio, M., Adurthi, N., Singla, P., & Majji, M.

citation count

• 2

complete list of authors

• Mercurio, Michael||Adurthi, Nagavenkat||Singla, Puneet||Majji, Manoranjan

publication date

• July 2016

publisher

• Institute of Electrical and Electronics Engineers (IEEE)  Publisher

published in

• Proceedings of the ... American Control Conference. American Control Conference  Journal

keywords

• Aerospace Engineering
• Approximation Theory
• Collocation-based Approach
• Conjugate Unscented Transformation
• Cut
• Degrees Of Freedom
• Electronic Mail
• Feedback
• Feedback Control
• Finite Horizon Hamilton-jacobi-bellman Equation
• Hjb Equation
• Integration
• Mathematical Model
• Mechanical System
• Method Of Moments
• Nonproduct Quadrature Method
• Optimal Control
• Optimal Feedback Control Laws
• Partial Differential Equations
• Sparse Approximation Tools
• Spatial Variables
• State Dimension
• Transforms

Digital Object Identifier (DOI)

• 10.1109/acc.2016.7525430

start page

• 3322

end page

• 3327

URL

• http://dx.doi.org/10.1109/acc.2016.7525430