Approximate Reachability for Feedback Linearizable Systems

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.