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By Jing Zhou, Changyun Wen

ISBN-10: 3540778063

ISBN-13: 9783540778066

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"‘The ebook is useful to profit and comprehend the elemental backstepping schemes’. it may be used as an extra textbook on adaptive keep an eye on for complex scholars. keep watch over researchers, in particular these operating in adaptive nonlinear keep an eye on, also will largely reap the benefits 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

Example text

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.

The existence of a non-singular M is ensured by the facts that S and F have exclusively different eigenvalues and that {S, L} is observable. 39) where ψ T = LM −1 . S is similar to F + Gψ. Note that, since {F, G} is controllable, and G has just one column, the row vector ψ is precisely the unique solution to the problem of assigning to F + Gψ the poles of S. 40) where η = M d and ψ T = LM −1 . 4, for any known controllable pair {Fi , Gi }, i = 1, . . , r with Fi ∈ Rv×v being Hurwitz and Gi ∈ Rv , there exists a ψi ∈ Rv such that η˙ i = (Fi + Gi ψiT )ηi q2,i = ψiT ηi , i = 1, 2, .

1⎥ ⎦ 0 .. 1 ... . . 0 0 0 ... 0 ⎤ ⎡⎡ ⎤ 0 (ρ−1)×(m+1) ⎦ u, Ψa (y) ⎦ F (y, u)T = ⎣ ⎣ Im+1 ⎤ ⎡ ⎤ ⎡ T 0 ... 0 ψa1 Ψa1 (y) ⎥ ⎥ ⎢ ⎢ . ⎥ ⎢ . ⎥ ⎢ Ψa (y) = ⎢ 0 .. . .. ⎥ = ⎢ .. ⎥ ⎦ ⎣ ⎦ ⎣ T 0 0 . . 20) State Estimation Filters ⎤ ⎡ φa1 0 ⎢ . ⎢ Φa (y) = ⎢ 0 .. ⎣ 0 0 ⎡ ⎤ ΦTa1 (y) ⎢ ⎥ ⎥ ⎢ . ⎥ ⎥ ⎥ == ⎢ .. ⎥ ⎣ ⎦ ⎦ . . φan ΦTan (y) ... . 39 0 .. θ = [bm (t), . . , b0 (t), θa1 (t), . . , θan (t)]T d(t) = [d1 (t), . . , dn (t)] ψ0 (y) = [ψ01 (y), . . 26) k = [k1 , k2 , . . 27) is chosen such that the matrix A0 is strictly stable.

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


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