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To realize the optimal attitude control for periodic satellites with bounded uncertainties, this study investigates an interval-based periodic linear quadratic regulator (I-PLQR) method subjected to reliability constraint. As one of the typical periodic satellites, the periodic dynamics of attitude control in space solar power station (SSPS) and its nominal state-space equation are constituted with the known period. To alleviate the cost of the control system for quantifying the probabilistic uncertainty, the uncertainty factors within the system are regarded as interval numbers based on set theory. An adaptive polynomial-based interval decoupling analysis (AP-IDA) method is introduced to accurately estimate the uncertainty boundaries of the state response and other control parameters. Considering the periodicity of the system, an interval-based periodic optimization control method based on discrete-time periodic algebraic Riccati matrix equations (DPARE) is proposed. The interval theory-based recursive formula of uncertain iterative optimal control and the convergence criterion are deduced and defined respectively. The security state is evaluated by an interval theory-based time-varying reliability (I-TVR) method, which will be considered as a constraint to constitute the uncertain optimization for attitude control. A numerical of the SSPS is applied to verify the proposed method.
Yang et al. (2024) studied this question.