摘要
Lyapunov-based model predictive control(LMPC)is an effective approach for trajectory tracking because of its wellguaranteed and easy-to-implement stability.However,traditional LMPC utilizes pre-designed auxiliary controllers to estimate the domain of attraction(DOA)and construct stability constraints,which inevitably reduces its stable domain and degrades tracking performance.For this problem,this paper proposes a relaxed LMPC(RLMPC)which is designed independently of auxiliary controllers.The control Lyapunov function(CLF)is firstly introduced to decouple the DOA and auxiliary control,alleviating the conservatism in traditional LMPC.Subsequently,a multi-resolution sampling-based search algorithm is developed to estimate the DOA,where the state space is partitioned into hyper-rectangles.A verification condition is derived to extend the verification validity of sampling points to all states within hyper-rectangles,thereby reducing DOA estimation error.Based on the auxiliary-controller-independent DOA(ACI-DOA)and CLF,stability constraints are formulated to ensure stability for RLMPC,while relaxing the stable domain of RLMPC to the entire ACI-DOA.Furthermore,a convergence rate adaptive adjustment technology is developed to enhance the convergence rate while balancing it with control effort.Through numerical simulations involving asteroid orbiting missions,the proposed method is found to significantly expand the stable domain and improve tracking performance.
基金
supported by the National Natural Science Foundation of China(12472354)
the National Key Research and Development Program of China(2020YFC2200902)
the Key Technology Research Project of TW-3(TW3005).
