By Jing Zhou, Changyun Wen

From the reviews:

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

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

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

**Sample text**

Similarly, the boundedness of xi (i = 3, . . 82) and the fact that xi = zi + αi−1 + xr . 87) we conclude that the control u(t) is also bounded. Therefore boundedness of all signals and asymptotic tracking are ensured as formally stated in the following Theorem. 1. 90) guarantee global boundedness of x(t) ˆ pˆ and the asymptotic tracking limt→∞ (x1 − xr ) = 0. and θ, The controller designed in this section achieves the goals of stabilization and tracking. The proof of these properties is a direct consequence of the recursive procedure, because a Lyapunov function is constructed for the entire system including the parameter estimates.

Note that the backstepping design starts with its output y, which is the only available system state allowed to appear in the control law. 108) Θ = [bm , . . , b0 , θT ]T ω = [vm,2 , vm−1,2 , . . 110) ω ¯ = [0, vm−1,2 , . . 111) where Output Feedback Control 25 In above equations, 2 , vi,2 , ξ2 and Ξ2 denote the second entries of , vi , ξ and Ξ, respectively, and y, vi , ξ, Ξ are all available signals. 94) is represented as y˙ = bm vm,2 + ξ2 + ψ1 (y) + ω ¯T Θ + 2 i = 2, 3, . . 114) will be our design system, whose states y, vm,2 , .

Note that the design of tuning functions does not follow the standard tuning function design in [1] as the projection operations are used in the parameter estimators. 98) . 100) 48 Adaptive Control of Time-Varying Nonlinear Systems where f = min{ P1 2 , 2c1 , 2c2 , . . , 2cρ , } > 0. Due to the utilization of projection operations for θˆ and qˆ, the boundedness of θ˜ and q˜ can be guaranteed. Together t the boundedness d(t), q and θ˙ ,the boundedness of Mρ and 0 f2 (θ˜T Γ −1 θ˜ + t q˜2 )e−f (t−τ ) dτ + 0 Mρ e−f (t−τ )dτ can be guaranteed.