A trajectory‐based method for constructing null controllable regions. (12th November 2019)

• Record Type: Journal Article
• Authors: Homer, Tyler; Mahmood, Maaz; Mhaskar, Prashant
• Is Part Of: International journal of robust and nonlinear control. Volume 30:Number 2(2020)
• Page Start: 776
• Page End: 786
• Publication Date: 2019-11-12
• Subjects: control Lyapunov function -- nonlinear systems -- null controllable region -- optimal control -- reachable sets; Automatic control -- Periodicals; Control theory -- Periodicals; Nonlinear systems -- Periodicals; 629.836
• DOI: 10.1002/rnc.4805
• Languages: English
• ISSNs: 1049-8923

Abstract

Summary: The 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.