By Jing Zhou, Changyun Wen

ISBN-10: 3540778063

ISBN-13: 9783540778066

From the reviews:

"‘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)

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

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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.

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

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