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

Caisheng Wei,Honghua Dai,Jianping Yuan,Jianfeng Xie,Jianjun Luo

doi:10.1177/1729881416687504

Abstract

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.

Highlights

Hypersonic flight vehicles (HFVs) have drawn growing attention since they are promising to provide a reliable and cost-efficient way to explore space for critical military and commercial applications.[1]
The backstepping technique has been evolved as an efficient control method for hypersonic flight vehicles (HFVs), tedious and complex analysis is required for virtual controllers and their repeated derivatives
In order to further eliminate the complexity of the immediate controllers in the recursive design, a hyperbolicsine-function-based tracking differentiator was constructed to obtain good estimations for the derivatives of virtual controllers involved in the control system design of an air-breathing hypersonic vehicle (AHV) in the work by Bu et al.[15]

Summary

Introduction

Hypersonic flight vehicles (HFVs) have drawn growing attention since they are promising to provide a reliable and cost-efficient way to explore space for critical military and commercial applications.[1]. The objective pursued in this work is to shrink the tracking errors V~ 1⁄4 V À Vr and h~ stably with a time-varying bounded transient and steady-state performance in spite of the coexistence of unknown nonlinearities and input saturation. Note that the newly defined weight in equation (19) is obtained by solving a linear function in equation (16) based on the first-order optimality conditions in equation (15) In this procedure, no optimization methods such as the quadratic programming method or the dynamic programming method, which are often applied to NN-based approximation, are needed. When smallscale training samples (N is small) are chosen, high confidence levels of the approximation can be obtained as well according to Vapnik and Suykens and Vandewalle.[17,18] it is advantageous to adopt the LS-SVM to approximate the unknown nonlinearities in equations (3) and (5) so the HFV benefits from its attractive computational property. In order to attenuate the negative effect induced by the sharp corner, the applied control 1⁄2de; È can be approximated by the HTSF in a general form like

15 Actual control input Approximation by HTSF

Z t 2 kV 2 0

Findings

Conclusions