A RHC scheme for constrained nonlinear systems based on Data-Driven Robust Backward Reachable Sets

In this paper the problem of computing backward reachable sets directly from noisy data without requiring a known system model is considered. Starting from a Lipschitz continuous nonlinear system, a procedure deriving inner-approximations of time-backward reachable sets using matrix zonotopes is considered. Theoretical results ensuring that the computed reachable sets properly inner-approximates the true reachable set are proposed and a computable scheme obtained. A Receding Horizon Control based numerical example to prove the effectiveness of the proposed approach is illustrated.