By Jing Zhou, Changyun Wen
From the reviews:
"‘The publication is beneficial to benefit and comprehend the elemental backstepping schemes’. it may be used as an extra textbook on adaptive regulate for complicated scholars. keep watch over researchers, specially these operating in adaptive nonlinear regulate, also will broadly make the most of this book." (Jacek Kabzinski, Mathematical experiences, factor 2009 b)
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Additional info for Adaptive backstepping control of uncertain systems: Nonsmooth nonlinearities, interactions or time-variations
44) T ω = [vm,2 , vm−1,2 , . . , v0,2 , Ξ2 + Ψa1 ] ω ¯ = [0, vm−1,2 , . . 1) is restricted to the ﬁrst ρ equations. 37), the design system is ¯T θ + y˙ = bm vm,2 + β + ω 2 + d(t)Φa1 (y) v˙ m,i = vm,i+1 − ki vm,1 , i = 2, 3, . . 50) ˙ = A0 + Φa (y)d(t)T − Ω T θ˙ Remark 1. 50), their eﬀects should be considered in controller design. However for the state-feedback control in , no ﬁlter is required for state estimation. Their eﬀects may not be necessarily considered in controller design and this makes problem much simpler.
As projection operation is used, the design of tuning functions are diﬀerent from existing schemes. With our proposed controller, system stability can be ensured. 1 Problem Formulation Consider the following class of single-input-single-output (SISO) nonlinear timevarying systems in the feedback form x˙ 1 = x2 + θa1 (t)ψa1 (y) + d1 (t)φa1 (y) + ψ01 (y) .. x˙ ρ−1 = xρ + θaρ−1 (t)ψaρ−1 (y) + dρ−1 (t)φaρ−1 (y) + ψ0ρ−1 (y) x˙ ρ = xρ+1 + θaρ (t)ψaρ (y) + dρ (t)φaρ (y) + ψ0ρ (y) + bm (t)u .. 1) y = eT1 x where x = [x1 ,· · · , xn ]T ∈ Rn , u ∈ R and y ∈ R are system states, input and output, respectively, bj (t), j = 0, .
Gr }. Proof. 43), it can be shown that ⎡ ⎤ ⎡ ⎤ F1 e1 G1 2,1 ⎢ ⎥ ⎢ ⎥ ⎢ . ⎥ ⎢ . ⎥ e˙ = ⎢ .. ⎥ − ⎢ .. ⎥ ⎣ ⎦ ⎣ ⎦ Fr er Gr 2,r With the auxiliary error e, we can express q2 as ⎡ ⎤ ψ1T η1 ⎥ ⎢ ⎢ . ⎥ q2 = ⎢ ..
Adaptive backstepping control of uncertain systems: Nonsmooth nonlinearities, interactions or time-variations by Jing Zhou, Changyun Wen