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

By Jing Zhou, Changyun Wen

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"‘The ebook is useful to profit 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, specially these operating in adaptive nonlinear regulate, also will greatly reap the benefits of this book." (Jacek Kabzinski, Mathematical studies, factor 2009 b)

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

Sample text

In [83] state-feedback control was considered for a class of uncertain time-varying nonlinear systems in the presence of disturbances. Due to state feedback, no filter is required for state estimation. Thus the derivatives of the time varying parameters and the disturbance term do not need to be considered in controller design. This also makes the stability analysis greatly simplified. Again, parameters are required to be estimated at every step, which results in the overparametrization problem. In the case of output feedback control of nonlinear time-varying systems in the presence of disturbances, filters are required to estimate system states and the equations of the state estimation error will be used in the design and analysis.

T And also V (t) and 0 [g(τ )N (χ) + 1]χdτ ˙ are bounded on [0, tf ). 17) where ⎤ ⎡ 0 1 0 ... 0 ⎢ ⎢ ⎢0 ⎢ ⎢. A = ⎢ .. ⎢ ⎢ ⎢0 ⎣ ⎥ ⎥ 0⎥ ⎥ .. ⎥ ⎥ ⎥ 0 0 ... 1⎥ ⎦ 0 .. 1 ... . . 0 0 0 ... 0 ⎤ ⎡⎡ ⎤ 0 (ρ−1)×(m+1) ⎦ u, Ψa (y) ⎦ F (y, u)T = ⎣ ⎣ Im+1 ⎤ ⎡ ⎤ ⎡ T 0 ... 0 ψa1 Ψa1 (y) ⎥ ⎥ ⎢ ⎢ . ⎥ ⎢ . ⎥ ⎢ Ψa (y) = ⎢ 0 .. . .. ⎥ = ⎢ .. ⎥ ⎦ ⎣ ⎦ ⎣ T 0 0 . . 20) State Estimation Filters ⎤ ⎡ φa1 0 ⎢ . ⎢ Φa (y) = ⎢ 0 .. ⎣ 0 0 ⎡ ⎤ ΦTa1 (y) ⎢ ⎥ ⎥ ⎢ . ⎥ ⎥ ⎥ == ⎢ .. ⎥ ⎣ ⎦ ⎦ . . φan ΦTan (y) ... . 39 0 .. θ = [bm (t), .

Therefore, χ must be bounded. t And also V (t) and 0 [g(τ )N (χ) + 1]χdτ ˙ are bounded on [0, tf ). 17) where ⎤ ⎡ 0 1 0 ... 0 ⎢ ⎢ ⎢0 ⎢ ⎢. A = ⎢ .. ⎢ ⎢ ⎢0 ⎣ ⎥ ⎥ 0⎥ ⎥ .. ⎥ ⎥ ⎥ 0 0 ... 1⎥ ⎦ 0 .. 1 ... . . 0 0 0 ... 0 ⎤ ⎡⎡ ⎤ 0 (ρ−1)×(m+1) ⎦ u, Ψa (y) ⎦ F (y, u)T = ⎣ ⎣ Im+1 ⎤ ⎡ ⎤ ⎡ T 0 ... 0 ψa1 Ψa1 (y) ⎥ ⎥ ⎢ ⎢ . ⎥ ⎢ . ⎥ ⎢ Ψa (y) = ⎢ 0 .. . .. ⎥ = ⎢ .. ⎥ ⎦ ⎣ ⎦ ⎣ T 0 0 . . 20) State Estimation Filters ⎤ ⎡ φa1 0 ⎢ . ⎢ Φa (y) = ⎢ 0 .. ⎣ 0 0 ⎡ ⎤ ΦTa1 (y) ⎢ ⎥ ⎥ ⎢ . ⎥ ⎥ ⎥ == ⎢ .. ⎥ ⎣ ⎦ ⎦ . . φan ΦTan (y) ...

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