By Jing Zhou, Changyun Wen

From the reviews:

"‘The ebook is useful to benefit and comprehend the elemental backstepping schemes’. it may be used as an extra textbook on adaptive regulate for complex scholars. keep an eye on researchers, specifically these operating in adaptive nonlinear keep watch over, also will commonly reap the benefits of this book." (Jacek Kabzinski, Mathematical experiences, factor 2009 b)

**Read or Download Adaptive backstepping control of uncertain systems: Nonsmooth nonlinearities, interactions or time-variations PDF**

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**Additional info for Adaptive backstepping control of uncertain systems: Nonsmooth nonlinearities, interactions or time-variations**

**Sample text**

116) where ˆ is an estimate of = 1/bm and αi−1 is the virtual control at each step and will be determined in later discussions. 120) ˆ is the estimate of Θ. 121) ˜ = Θ − Θ. 124) where Γ is a positive deﬁnite design matrix, γ is a positive design parameter, and P is a deﬁnite positive matrix such that P A0 + AT0 P = −I, P = P T > 0. 127) Deﬁne and τ1 is called the ﬁrst tuning function. 129) which implies that z1 converges to zero asymptotically. Since z2 = 0, we do not ˆ˙ = Γ τ1 as an update law for Θ at this step to avoid over-parametrization use Θ problem, because Θ will also appear in the following steps.

5), we choose the following matrix K = [k1 Ir , . . 16) where ki > 0, i = 1, . . 17) is stable. This is suﬃcient if sv +k1 sv−1 +. +kv−1 s+kv is a Hurwitz polynomial. 18) Preliminary Results 55 where ⊗ is the Kronecker product, and ei is the ith coordinate vector in Rv . We also denote vectors ξv (t), ξ(t), vj (t), as the outputs of the ﬁlters ξ˙v = A0 ξv + Ky ξ˙i = A0 ξi + Ev−i y i = 0, 1, . . 20) v˙ j = A0 vj + Ev−j u j = 0, 1, . . 21) T T T where ξv = [ξv,1 , . . , ξv,v ] . 23) j=0 ¯ i = diag[Bi , .

100) 48 Adaptive Control of Time-Varying Nonlinear Systems where f = min{ P1 2 , 2c1 , 2c2 , . . , 2cρ , } > 0. Due to the utilization of projection operations for θˆ and qˆ, the boundedness of θ˜ and q˜ can be guaranteed. Together t the boundedness d(t), q and θ˙ ,the boundedness of Mρ and 0 f2 (θ˜T Γ −1 θ˜ + t q˜2 )e−f (t−τ ) dτ + 0 Mρ e−f (t−τ )dτ can be guaranteed. 4), f0 is selected as the upper bound of Vρ (0)+ 0 f2 (θ˜T Γ −1 θ+ t Mρ e−f (t−τ ) dτ, g(t) = bm (t). 1, we can conclude that Vρ (t) 0 and χ(t), hence zi , (i = 1, .