Finite-time fuzzy control based on Markov jump nonlinear system for tether towed vehicle under sudden disturbance

In this paper, the issue of rapid stabilization control of the tethered towed vehicle, a distinct type of vehicle, is studied under the combined influence of main aircraft bumps and sudden wind disturbances in extreme weather conditions. Initially, the tether tension, vehicle aerodynamic force, and aerodynamic moment are designated as the principal mutating quantities. Subsequently, the vehicle position and attitude dynamics are modeled as a nonlinear Markovian jump system (MJS), which is then linearized through the utilization of type-2 fuzzy polynomials. Subsequently, the conventional interval type-2 fuzzy logic controller is enhanced by establishing the dynamic variation law for the footprint of uncertainty using the hyperbolic tangent function. The proposed scheme is capable of significantly enhancing the convergence speed while ensuring the steady-state performance. Concurrently, an MJS backstepping control framework is devised to address the problem of deriving the high-order multi-input and multi-output MJS finite time control law, and the stochastically finite-time boundedness of the closed-loop system is proved. The simulation results demonstrate that the proposed control scheme can achieve rapid and stable control of the tethered towed vehicle when the tension and aerodynamic force frequently jump among 50%, 100%, and 300%.