Work

Approximate Reachability for Feedback Linearizable Systems

Year: 2026

Type: article

Abstract: ABSTRACT In Hamilton–Jacobi reachability analysis, reachable sets are characterized by sublevel sets of the value function of an optimal control problem. Although grid‐based approaches provide a general‐purpose means of numerically computing this value function, the curse‐of‐dimensionality often limits their use in all but simple applications. In this article, inner approximations of the backward reachable set are characterized through the design of a feedback control law for feedback linearizable systems subject to input constraints. This structure is exploited to propose a selection of control gains via an optimization problem. For a fixed sampling/discretization choice, the computational cost and memory requirement of the proposed scheme are tied to the number of system states and inputs in a polynomial manner. Thus, the proposed approximation scheme is computationally tractable for feedback linearizable systems of relatively high dimension.

Source: Optimal Control Applications and Methods

DOI: 10.1002/oca.70112

Authors: Vincent Liu, Chris Manzie, Peter M. Dower

Institution: The University of Melbourne

Language: English

Topic: Advanced Control Systems Optimization

Subfield: Control and Systems Engineering

Field: Engineering

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $4,020

Funders: Australian Government, Air Force Office of Scientific Research