System Theory

Get Adaptive backstepping control of uncertain systems: PDF

Posted On April 18, 2018 at 9:30 am by / Comments Off on Get Adaptive backstepping control of uncertain systems: PDF

By Jing Zhou, Changyun Wen

ISBN-10: 3540778063

ISBN-13: 9783540778066

From the reviews:

"‘The publication 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. regulate researchers, specifically these operating in adaptive nonlinear keep watch over, also will largely take advantage of this book." (Jacek Kabzinski, Mathematical experiences, factor 2009 b)

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

Example text

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. The over-parametrization problem is overcomed by using tuning functions. The number of parameter estimates are equal to the number of unknown parameters.

94), the resulting closed-loop system is stable. An Illustrative Example 49 Since ρ = 2 = n, we have vρ = vn = λ. 112) In the simulation, the design parameters were set as c1 = c2 = 2, l1 = l2 = 1, k1 = 5, k2 = 4, Γ = I3 and γ = 1. 2 show the system output y(t) with reference signal yr (t) and the control input u(t). Clearly, simulation results verify the effectiveness of proposed scheme. 5 −2 0 5 10 15 20 t(sec) Fig. 1. 5 0 5 10 15 20 t(sec) Fig. 2. 6 Summary In this chapter, a scheme is proposed to design an adaptive output-feedback controller for uncertain time-varying nonlinear systems with unknown sign of high-frequency gains in the presence of disturbances.

Accordingly, w has no upper bound. 16) Thus, there must exist a monotone increasing variable {wi = w(ti )} with w0 = |w(t0 )| > 0, limi→∞ ti = tf , and limi→∞ wi = ∞. Following the procedure as in Case 1), we can also construct a subsequence that leads to a contradiction. Accordingly, we can claim that w has upper bound on [0, tf ). Since χ = −w, we know that χ has lower bound on [0, tf ). The above argument is true for all tf > 0. Therefore, χ must be bounded. t And also V (t) and 0 [g(τ )N (χ) + 1]χdτ ˙ are bounded on [0, tf ).

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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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