A data-driven guaranteed zonotopic estimation for unknown time-varying system

Time-varying system is a widespread class of systems in reality. Model of such system is difficult to obtain because the parameters vary with time. Hence, a data-driven state estimation for unknown discrete time-varying system is investigated with zonotopic reachability analysis. Since the system model is unknown, a time-varying matrix zonotope which contains all possible models is computed by the available prior input-state trajectories. On this basis, an over-approximated reachable zonotope of system state is obtained through iteration. Then, the boundedness of over-approximated reachable zonotope is proved by introducing $P$-radius definition. This method guarantees that the actual system state falls within the estimation range and maintains the compactness of the estimation result. Finally, a numerical example and a circuit system simulation show the validity and applicability of the proposed method.