Reliability-constrained optimal attitude-vibration control for rigid-flexible coupling satellite using interval dimension-wise analysis

Abstract

This study proposes an uncertain optimal attitude–vibration control method for rigid–flexible coupling satellites with reliability constraints based on the interval dimension-wise analysis. To model the complex uncertain control system, multi–source uncertainties in rigid–flexible coupling satellites are quantified to interval parameters. Based on the nominal rigid–flexible coupling satellite dynamic model, the interval attitude–vibration model is derived and the corresponding coupled state equation is established. Considering polynomial chaos expansions in the surrogate model, an interval dimension-wise analysis (IDWA) method is proposed to predict the uncertain state response of the uncertain attitude–vibration control system, which can help solve the overestimation problem of the conventional perturbation method. An interval linear quadratic regulator (LQR) is proposed by combining the IDWA method and deterministic LQR, to accurately optimize the uncertain control input and cost function. With regard to harsh deterministic state response constraints, this study proposes a non-probabilistic time-dependent reliability method, which allows for an effective evaluation by flexibly characterizing the relationship between the uncertain state response and threshold. The reliability-constrained multi–objective optimal attitude–vibration control problem can be solved by considering the nominal cost function and uncertain state response as two optimization objectives. The effectiveness of the proposed method is verified using a rigid–flexible coupling satellite.