A trajectory‐based method for constructing null controllable regions Journal Articles

abstract

• SummaryThe problem of determining a system's set of stabilizable states, the null controllable region (NCR), is intricately related to the problem of determining control Lyapunov functions. In this paper, we address the problem of construction of the NCR for control‐affine nonlinear systems with input constraints. To this end, we explain how the boundary of the NCR is covered by time‐optimal trajectories. To construct the NCR, we employ an algorithm based on Pontryagin's minimum principle, which integrates optimal trajectories of a special smooth system in reverse time from the boundary of an initial NCR estimate. We illustrate this algorithm with linear and nonlinear system examples.

authors

• Homer, Tyler
• Mahmood, Maaz
• Mhaskar, Prashant

status

• published 

publication date

• January 25, 2020

has subject area

• 0102 Applied Mathematics (FoR)
• 0906 Electrical and Electronic Engineering (FoR)
• 0913 Mechanical Engineering (FoR)
• Industrial Engineering & Automation (Science Metrix)

published in

• International Journal of Robust and Nonlinear Control  Journal

keywords

• Automation & Control Systems
• Engineering
• Engineering, Electrical & Electronic
• Mathematics
• Mathematics, Applied
• Physical Sciences
• SUFFICIENT CONDITIONS
• SYSTEMS
• Science & Technology
• Technology
• control Lyapunov function
• nonlinear systems
• null controllable region
• optimal control
• reachable sets

Digital Object Identifier (DOI)

• 10.1002/rnc.4805

start page

• 776

end page

• 786

volume

• 30

issue

• 2