ZonoReach: A Reachability-Guided Controller Using Zonotopes and Local Hamilton–Jacobi Analysis

Abstract

This paper presents a reachability-guided controller for nonlinear systems that synthesizes pseudo-optimal control using only local linear models. At each step, a forward reachable tube (FRT) is computed via zonotope-based set propagation; the closest point in the FRT to the target is chosen as an intermediate waypoint, around which a backward reachable tube (BRT) is solved using Hamilton–Jacobi (HJ) reachability. The resulting value function yields a locally optimal control action. This process is repeated iteratively to steer the system toward the target without requiring global nonlinear dynamics. We evaluate the method on the double integrator, inverted pendulum, and Dubins car, benchmarking against model predictive control baselines. For the double integrator, we additionally benchmark against its ground-truth time-optimal bang-bang solution. Our proposed ZonoReach controller achieves successful setpoint tracking and near time-optimal performance. Results highlight the influence of planning and control horizons, while limitations include reliance on local linear approximations and grid-based solvers for BRT computation. We conclude with directions for improving scalability toward real-world systems.