Convex set reliability-based optimal attitude control for space solar power station with bounded and correlated uncertainties

Considering the bounded and correlated uncertainties in the inherently nonlinear attitude dynamics, this paper proposes an uncertain optimal attitude control for space solar power stations (SSPS), subjected to the convex set-based reliability constraint. To accurately and cost-effectively quantify the uncertainty in the SSPS attitude control system, the uncertain attitude dynamics are proposed based on nominal SSPS with convex set-based uncertainties. Given the known bounds and correlations of the random variables, the convex set-based attitude dynamics of SSPS can be conveniently constructed and transformed into corresponding uncertain state-space equations. Uncertain state and output can be solved using the extended-order matrix and uncertainty propagation method. A convex set-based Riccati equation is: developed using the convex set theory, traditional algebraic Riccati equation (ARE), and Lyapunov equation, which can obtain all the uncertain components of feedback gain, input torque, and cost function, respectively. Convex set-based time-dependent reliability (CSTR) is applied to assess the safety of the attitude control system by setting critical values and considering the time-dependent effect, which is regarded as an important constraint in the optimal attitude control issue with uncertainty. A numerical example of SSPS is provided to verify the proposed uncertain controller within the reliability-constrained optimization framework, demonstrating its effectiveness in managing nonlinear system dynamics under uncertainty.