Tham khảo tài liệu 'sliding mode control part 16', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | 514 Sliding Mode Control T 8Vp k Ì Jplant sign . I du k J 23 as in Yasser et al. 2006 b . Stability For the stability analysis of our method we start by defining its Lyapunov function and its derivation as follows VSMCNN t - VNN t VSMC t VSMCNN t - VNN t VSMC t 24 where VNN t is the Lyapunov function of the NN of our method and VSMC t is the Lyapunov function of SMC of our method. For Vnn t we assume that it can be approximated as V m AVNN k VNN t AT 25 where AVNN k is the derivation of a discrete-time Lyapunov function and AT is a sampling time. According to Yasser et al. 2006 b AVNN k can be guaranteed to be negative definite if the learning parameter c satisfies the following conditions 2 0 c 26 nq for the weights between the hidden layer and the output layer mqj k and 0 c n maxk mqj k maxk K k 27 for the weights between the input layer and the hidden layer mq k . Furthermore if the conditions in 26 and 27 are satisfied the negativity of Vnn t can also be increased by reducing AT in 25 . For VSMC t it is defined as S t VSMC t --y VsMC t - Syp t Syp t . 28 Then we the following assumption. Assumption 1 The sliding surface in 13 can approximate the sliding surface in 3 Yasser et al. 2006 c S t S t . yp xp 29 t z 1 . 1 VSMC t in 28 can be assured to be negative definite if Sliding Mode Control Using Neural Networks 515 _ Syp t Á t 30 -k ypSyp t where k is a positive constant. Following the stability analysis method in Phuah et al. __ yp _ _ __ 2005 a we apply 1 3 7 14 15 29 and 30 to 28 and assume that 15 can . n-11 t z 1 1 11 approximate 4 . Thus VSMC t can be described as V SMC t t Sxr t Sy t cTp eXp t Syp t cT xp t - xp t J Syp t Xp t - cxpf xp t - cTPBpUp t J . 31 Syp t cTxp t - CT f xp t - cTpBp u t Uc t Syp t -kypSyp t t which is negative definite where ky CT Bpky . The reaching condition Phuah et al. 2005 a can be achieved if -kyPSyP t nsign Syp t . 32 where n is a small positive constant.