“…Due to the benefit of symplectic-conserved property and local pseudospectral discretization, SPMs are of high efficiency and precision. More recently, taking the SPM as the internal solver, a fast MPC algorithm is developed (Wang et al, 2019) and successfully applied to trajectory tracking for various mechanical systems (Liu et al, 2019a; Liu et al, 2019b; Liu et al, 2020; Wang et al, 2020a; Wang et al, 2020c), further demonstrating its good robustness and online computational efficiency. Hence, it seems appealing to develop fast MHE algorithms by incorporating the SPM.…”