Efficient adaptive constrained control with time-varying predefined performance for a hypersonic flight vehicle

A novel low-complexity adaptive control method, capable of guaranteeing the transient and steady-state tracking performance in the presence of unknown nonlinearities and actuator saturation, is investigated for the longitudinal dynamics of a generic hypersonic flight vehicle. In order to attenuate the negative effects of classical predefined performance function for unknown initial tracking errors, a modified predefined performance function with time-varying design parameters is presented. Under the newly developed predefined performance function, two novel adaptive controllers with low-complexity computation are proposed for velocity and altitude subsystems of the hypersonic flight vehicle, respectively. Wherein, different from neural network-based approximation, a least square support vector machine with only two design parameters is utilized to approximate the unknown hypersonic dynamics. And the relevant ideal weights are obtained by solving a linear system without resorting to specialized optimization algorithms. Based on the approximation by least square support vector machine, only two adaptive scalars are required to be updated online in the parameter projection method. Besides, a new finite-time-convergent differentiator, with a quite simple structure, is proposed to estimate the unknown generated state variables in the newly established normal output-feedback formulation of altitude subsystem. Moreover, it is also employed to obtain accurate estimations for the derivatives of virtual controllers in a recursive design. This avoids the inherent drawback of backstepping - "explosion of terms" and makes the proposed control method achievable for the hypersonic flight vehicle. Further, the compensation design is employed when the saturations of the actuator occur. Finally, the numerical simulations validate the efficiency of the proposed finite-time-convergent differentiator and control method.