Multi-dimensional robust tracking control integrating input-constrained extended model predictive static programming with receding horizon control strategy

Abstract

To address the multi-dimensional tracking control problem with control saturation and uncertainties, a receding horizon control (RHC) based scheme is explored. The RHC guarantees the instructions change softly and smoothly with controllable transition time by utilizing the rolling window optimization mode, whereas its practical application still suffers from the computational efficiency limitation and stability problem in presence of disturbances. To reduce the computational complexity of RHC, a rolling optimization approach is proposed for tackling the input-constrained nominal RHC problem by incorporating a regularization approach, spectral-form discretization and quadrature collocation to extend the model predictive static programming technique. To further guarantee the anti-interference ability, an input-constrained state feedback control based on the linear-matrix-inequality (LMI) theory is proposed as the ancillary correction control of RHC for restricting the disturbed states motion caused by exogenous disturbances in an admissible invariant set. Finally, the robust stability of the whole closed-loop system is theoretically illustrated. Applying the proposed method into the multi-constrained tracking control scenario, the comparative simulations demonstrate its marked superiorities in computational performance and robustness.