By Jing Zhou, Changyun Wen

ISBN-10: 3540778063

ISBN-13: 9783540778066

From the reviews:

"‘The booklet is beneficial to profit and comprehend the elemental backstepping schemes’. it may be used as an extra textbook on adaptive keep watch over for complex scholars. keep watch over researchers, in particular these operating in adaptive nonlinear regulate, also will greatly take advantage of this book." (Jacek Kabzinski, Mathematical stories, factor 2009 b)

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**Sample text**

V − 1, and Bj ∈ Rr×r , j = 0, . . , m, m ≤ v − 1 are matrices. 5) Bp y = Cg x where x ∈ Rn is the system state, A ∈ Rn×n is the matrix Ag with the ﬁrst r columns equal to zero, Ap ∈ Rn×r are the ﬁrst r columns of Ag and BP Problem Formulation 53 ¯ ∈ R(m+1)r×r , d(t) = [0 Bp ]T d(t) = [dT1 , . . , dTv ]T ∈ Rn and di ∈ Rr , (i = 1, . . , v). 6) where S is an unknown n × n matrix having distinct eigenvalues with zero real parts. The disturbance rejection problem in this chapter is based on the internal model principle in Appendix D.

E. ˙a = A0 with a (0) = (0), and b = a = a + b, where a satisﬁes + Φa (y)d(t)T t A0 (t−τ ) ˙ . 54) where h(t) is generated by h˙ = −λθ h + kθ ( Ω 2 1 + ). 1) BIBO stable. 1 Design Procedure In this section, we present the adaptive control design using the backstepping technique with tuning functions in ρ steps. 58) zi = vm,i − αi−1 , i = 2, 3, . . 59) 42 Adaptive Control of Time-Varying Nonlinear Systems where αi−1 is the virtual control at each step and will be determined in later discussions.

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, . . , m are bounded uncertain time-varying System Model and Problem Formulation 35 T piecewise continuous high-frequency gains, θai (t) ∈ Rpi are uncertain timevarying parameters, di (t) denote unknown time-varying bounded disturbances, ψai ∈ Rpi , ψ0i ∈ R and φai ∈ R are known smooth nonlinear functions, for i = 1, . . , n. Similar class of systems was analyzed in [84].

### Adaptive backstepping control of uncertain systems: Nonsmooth nonlinearities, interactions or time-variations by Jing Zhou, Changyun Wen

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