Adaptive backstepping control of uncertain systems: - download pdf or read online

By Jing Zhou, Changyun Wen

ISBN-10: 3540778063

ISBN-13: 9783540778066

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

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

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Is a smooth projection operation to ensure the estimates belong to compact sets for all time. Such an operation can be found in Appendix C. Remark 4. 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.

V0,2 ] . 36) 2 are the second entries of ξv , q and . 37) T T where E1 = [Tr , 0r×(v−1)r ]T , Θ = [Θa , Θb ], ω ¯ = [ξ(2) + (E1 y)T ,[01,r , vm−1,2 , . , T T v0,2 ]] . 3. The difficulty now is that the term q(d) is not available, because the disturbance d(t) and the matrix Q are unknown. For the adaptive backstepping approach proposed in [1], the state ζ2 serves as the link between the output and the filter used for the output backstepping. The contribution of σ(d) to ζ2 is reflected by q2 in .

1 Problem Formulation Consider the following class of single-input-single-output (SISO) nonlinear timevarying systems in the feedback form x˙ 1 = x2 + θa1 (t)ψa1 (y) + d1 (t)φa1 (y) + ψ01 (y) .. x˙ ρ−1 = xρ + θaρ−1 (t)ψaρ−1 (y) + dρ−1 (t)φaρ−1 (y) + ψ0ρ−1 (y) x˙ ρ = xρ+1 + θaρ (t)ψaρ (y) + dρ (t)φaρ (y) + ψ0ρ (y) + bm (t)u .. 1) y = eT1 x where x = [x1 ,· · · , xn ]T ∈ Rn , u ∈ R and y ∈ R are system states, input and output, respectively, bj (t), j = 0, . . , m are bounded uncertain time-varying System Model and Problem Formulation 35 T piecewise continuous high-frequency gains, θai (t) ∈ Rpi are uncertain timevarying parameters, di (t) denote unknown time-varying bounded disturbances, ψai ∈ Rpi , ψ0i ∈ R and φai ∈ R are known smooth nonlinear functions, for i = 1, .

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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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