System Theory

Download Adaptive backstepping control of uncertain systems: by Jing Zhou, Changyun Wen PDF

By Jing Zhou, Changyun Wen

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"‘The e-book is beneficial to profit and comprehend the basic backstepping schemes’. it may be used as an extra textbook on adaptive regulate for complex scholars. keep an eye on researchers, specially these operating in adaptive nonlinear regulate, also will broadly make the most of this book." (Jacek Kabzinski, Mathematical reports, factor 2009 b)

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

Example text

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. 4), f0 is selected as the upper bound of Vρ (0)+ 0 f2 (θ˜T Γ −1 θ+ t Mρ e−f (t−τ ) dτ, g(t) = bm (t). 1, we can conclude that Vρ (t) 0 and χ(t), hence zi , (i = 1, .

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. Definition: System is said to be minimum phase if its zero dynamics, subject to appropriate initial conditions and a suitable control producing output identically zero, is stable. 1) satisfying Assumptions 1-4 such that the closed-loop system is stable and the system output can track a given reference signal yr (t) as close as possible.

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, . . , n. Similar class of systems was analyzed in [84].

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