Get Adaptive backstepping control of uncertain systems: PDF

By Jing Zhou, Changyun Wen

ISBN-10: 3540778063

ISBN-13: 9783540778066

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

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

Example text

Assumption 1. The uncertain parameter vector θ is inside a compact set Ωθ , where θ = [bm (t), . . , b0 (t), θa1 (t), . . , θan (t)]T . In addition, there exists an unknown bounded positive constant q so that θ˙ ≤ q. Also q is inside a compact intervals Ωq = [I − , I + ] and bm (t) = 0, ∀t. Assumption 2. The relative degree ρ is fixed and known. Assumption 3. The reference signal yr and its (ρ − 1)th order derivatives are assumed to be known and bounded. Assumption 4. The system is minimum phase.

A1 p + A0 m N (p) = Bm p + . . + B1 p + B0 ⎡ ⎤ ⎤ ⎤ ⎡ ⎡ −Av−1 Ir 0 . . 0 ⎢ ⎥ 0 Bm ⎢ ⎥ ⎥ ⎥ ⎢ ⎢ ⎢ −Av−2 0 Ir . . 0 ⎥ ⎢ .. ⎥ ⎢ .. ⎥ ⎢ ⎥ ⎥ ⎢ ⎢ . ⎥ . ⎥ .. .. . ⎥ ⎢ ⎥ Ag = ⎢ , Bp = ⎢ . ⎥ , Bg = ⎢ . . ⎥ ⎥ ⎢ ⎢ ⎢ ⎥ ⎢ 0 ⎥ ⎢ B1 ⎥ ⎢ ⎥ ⎦ ⎦ ⎣ ⎣ ⎢ −A1 0 0 . . Ir ⎥ ⎣ ⎦ B0 Bp −A0 0 0 . . 0 Cg = [Ir 0 . . 4) where v is the observability index of G(p), rv = n, Ir is the r × r identity matrix, and Ai ∈ Rr×r , i = 0, . . , 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 , .

To handle the disturbances, well defined functions are introduced to eliminate their effects in the Lyapunov functions employed in the recursive design steps. To deal with the time variation problem, an estimator is used to estimate the bound of the variation rates. Furthermore, the overparamterization problem is also solved by using the concept of tuning functions. As projection operation is used, the design of tuning functions are different from existing schemes. With our proposed controller, system stability can be ensured.

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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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