Observer-Assisted Gain-Scheduling for Minecart Suspension Systems via Biharmonic Polynomial Framework: Expanded Solvability in Complex Transitions

This research focuses on gain-scheduling control for minecart active suspension systems (ASSs). Addressing practical scenarios in complex mining environments where transition probability information may be imprecisely accessible or completely unavailable, we establish a stochastic nonlinear suspension model featuring incomplete transition probability matrix (TPM) information. To ensure reliable controller design under such demanding conditions, a novel biharmonic polynomial framework is proposed. At the structural level, this framework reconstructs partially unknown TPMs into weighted convex combinations of precisely known TPMs using polytopic techniques. Simultaneously considering the challenges of suspension state acquisition and potential packet losses, an observer-assisted polynomial gain-scheduling controller is developed. By further integrating homogeneous polynomial techniques into both controller and observer synthesis, this framework achieves significantly expanded feasible solution domains. Hardware-in-the-loop (HIL) validation demonstrates 64.2% conservatism reduction in control design constraints and 18.2% root mean square (rms) reduction in body acceleration, confirming superior design generality and enhanced ride comfort performance.