Nonlinear optimal control with disturbance rejection for asteroid landing

This paper presents an optimal solution to asteroid soft landing problem, on the base of $\theta ?D$ control technique and disturbance rejection mechanism. The control objective is to drive a probe to reach the surface of an asteroid with a desirable line-of-sight angle and zero velocity, eliminating the influence of external disturbance. Firstly, elementary $\theta ?D$ technique is applied in the absence of disturbance to tackle the nonlinear optimal control problem. Secondly, the disturbance is estimated in the fast-estimation framework with explicitly bounded estimation error. Afterwards, an integrated control protocol is presented in a feed-forward structure by the aid of an additional variable-structure term to ensure stability under time-varying disturbance. Simulation results of the proposed approach compared with the results of elementary $\theta ?D$ method and robust $\theta ?D$ method are presented at the end of this paper, demonstrating the effectiveness of the proposed control protocol.     

A relaxed gradient based algorithm for solving generalized coupled Sylvester matrix equations

The present work proposes a relaxed gradient based iterative (RGI) algorithm to find the solutions of coupled Sylvester matrix equations $AX+YB=C,DX+YE=F$. It is proved that the proposed iterative method can obtain the solutions of the coupled Sylvester matrix equations for any initial matrices X₀ and Y₀. Next the RGI algorithm is extended to the generalized coupled Sylvester matrix equations of the form $A_{i1}{X}_1{B}_{i1}+A_{i2}{X}_2{B}_{i2}+?+A_{ip}{X}_p{B}_{ip}=C_i,(i=1,2,\dots ,p)$. Then, we compare their convergence rate and find RGI is faster than GI, which has maximum convergence rate, under an appropriative positive number ω and the same convergence factor µ₁ and µ₂. Finally, a numerical example is included to demonstrate that the introduced iterative algorithm is more efficient than the gradient based iterative (GI) algorithm of (Ding and Chen 2006) in speed, elapsed time and iterative steps.