A fundamental solution concept for a family of state constrained regulator problems. Issue 30 (2022)

• Record Type: Journal Article
• Authors: Dower, Peter M.; McEneaney, William M.
• Is Part Of: IFAC-PapersOnLine. Volume 55:Issue 30(2022)
• Page Start: 278
• Page End: 283
• Publication Date: 2022
• Subjects: Optimal control -- Hamilton-Jacobi-Bellman equations -- fundamental solution -- state constraints; Automatic control -- Periodicals; 629.805
• DOI: 10.1016/j.ifacol.2022.11.065
• Languages: English
• ISSNs: 2405-8963

Abstract

Abstract: A family of continuous-time regulator problems, subject to linear time-varying dynamics and convex state constraints, is parameterized with respect to a space of semiconcave terminal costs. By embedding the state constraints into an extended real-valued running cost, a family of relaxations is employed to develop a min-plus convolution-based fundamental solution concept for the family of regulator problems. A representation of the fundamental solution concept is provided in terms of solutions of associated differential Riccati and related equations, and possible avenues for efficient numerical computation are explored.